A THEORETICAL AND EMPIRlCAL INVESTIGATLON 0F DEBT MATURITY TlMiNG AND YIELD CURVE SLOPE ANALYSIS Thesis for the Degree of Ph. D. MECHEGAN STATE UNEVERSITY WELLERM CHARLES HANBORF 197 3 LIB “a Michigan State University This is to certify that the thesis entitled AN EMPIRICAL INVESTIGATION OF DEBT MATURITY TIMING AND YIELD CURVE SLOPE ANALYSIS presented by William C. Handorf has been accepted towards fulfillment of the requirements for Ph.D degree in Finance — Business 1' r‘ I F\ 'I... r __I‘.I'"J k -‘ .I' ‘.',<- 7 E7~ (\{iLL-Lrvl (\ I t W (gig Major professor Date 1/10/73 0-7639 BINDING BY , HOA6&SONS' I . aaoxamom mc. LIBRARY BINDERS mills-An. no.1".- ABSTRACT A THEORETICAL AND EMPIRICAL INVESTIGATION OF DEBT MATURITY TIMING AND YIELD CURVE SLOPE ANALYSIS BY William Charles Handorf Economists have been attempting to eXplain the term structure of interest rates for more than a generation. In spite of considerable effort, the diversity of explanations remains large. Nevertheless, enough is now known to justify an effort to deve10p normative rules for debt management. Specifically, this study scrutinizes the information content of the term structure for elements that might aid in finan- cial management. The research hypothesis tested in this Study is that the slope of a yield curve contains informa- tion useful for debt management, both governmental and corporate. If the hypothesis cannot be rejected. debt interest cost benefits may be obtained by judicious timing 0f long-term issues. In order to do so. however. the tradi— tional normative financial rule that debt maturity should I. ‘ I '9 u..‘ I.) . ~Q'I l h t I n... .- u ‘ .l- ..‘ William Charles Handorf parallel asset life must be waived. Selection of debt maturities and the timing of financing may be brought within a dynamic programming model. The framework minimizes present valued interest costs and requires that the issuer specify debt needs, maturity con- straints and forecasted interest rates. The model concen- trates on the relationship between a yield curve slope and forecasted interest rates. It does not explicitly consider flotation costs and financial risk of debt maturity deci- sions. Given that long-term rates are presumed to be equal to the serial sequence of future short-term rates and that the current yield curve is known, forward interest vectors Hwy be forecast. If a yield curve lepe contains statis- tically significant information, a rational basis for adjusting the forward interest vector facing the issuer exists. The empirical test is designed to indicate whether the sIOpe of a yield curve may predict deviations from Projected forward interest rates. Funds needed for a given length of time may be supplied either by single-stage or by double-stage financings. Larger number of stages are Possible but were not examined in this study. The slope Of a Yield curve is defined as the difference in yields between William Charles Handorf the yield on a single-stage issue and the yield on the first stage of a double-stage issue. By equating the known present interest cost of a single-stage issue to the unknown present interest cost of a double-stage issue, a breakeven yield for the second stage of the double stage may be computed. The real yield that later prevailed for the second—stage matu- rity is compared to the breakeven yield. If the later real yield is greater than the breakeven yield, the single issue would have been advantageous: if the later real yield is less than the breakeven yield, the double issue would have been advantageous. An ordinary least squares regression tests the rela— tiOnship between the realized yield minus the breakeven Yield (dependent variable) and the yield curve slope as defined (independent variable). Desirability of stage financing is indicated by the combination of both the regression constant B0 and the lepe B1. Regression esti- mattors significantly different from zero based on the F test justify the hypothesis that information is contained by a yield curve sloPe. The two-stage least squares tech- nique is used to reduce the effect of positive autoregres- 8ion of residuals to acceptable limits. Various plans ranging in maturity from two to twenty years are tested on '7 A William Charles Handorf quarterly yields over the 1952-71 period. Interest cost minimization is often a stated goal of Treasury debt management. The purpose of this study is not advocacy of a procyclical approach; but, rather, illus- tration of the potential for interest cost reduction. The test of this hypothesis with the U.S. Treasury debt yield curve showed that the regression slope B1 is not signifi- cantly different from zero at the ten per cent level. Knowledge of a yield curveSIOpe is of no consequence for Treasury debt management with regard to present valued interest cost minimization. The expectations theory gains Support because a yield curve of period t does reflect future interest rates in period t+l,...,t+n, regardless of the associated yield curve lepe. For the plans tested the regression constant B0 is not significantly different from Zero at the ten per cent level. The existence of a liquidity premium is substantiated on the basis of an increasing BO as the maturity of the plans tested lengthens. Negative B0 ' s in the 1950's and positive Bo's in the 1960's are nQted and weakly support a change from the money-substitute to the "normal" hypothesis of the liquidity preference theory and also reflect the cyclical increase in interest rates over the time period. Results do not support or William Charles Handorf reject the institutional theory since relative supply and demand is not measured. A comprehensive yield curve for corporate debt does not exist. The substitute test was of a commercial paper alternative and a bank prime alternative where both plans are funded in year one by a nineteen year AA long-term Utility. The regression results of these tests are signifi- cant at the two per cent level and indicate that double- stage financing becomes more advantageous as the yield curve slopes more steeply upward. The information contained by a yield curve slope is ascribed to be a result of market Participant overreaction. The bank prime plans is statis— ti<2ally more significant than the commercial paper plan. Market inefficiencies and administered rates increase the chadice that information may be contained within the interest rate term structure. The astute corporate financial manager may lower the overall cost of creditor funds by recognition of the slope of a yield curve. A THEORETICAL AND EMPIRICAL INVESTIGATION OF DEBT MATURITY TIMING AND YIELD CURVE SLOPE ANALYSIS BY William Charles Handorf A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Accounting and Financial Administration 1973 TO LINDA ii "b... au‘ . u " P_ ._." U . s ‘ I ~.. .‘ s...‘ “.--.“ ‘ .dx "'4... ‘ 1 1 "v a F L. ‘- \ :C'AHI ‘rtt E I l N. . ACKNOWLEDGMENTS A dissertation does not stand by itself; but, reather, reflects the combined efforts of many involved and dedicated people. I wish to express my gratitude to these pueOple and acknowledge the financial support provided by tflae Department of Accounting and Financial Administration, hmichigan State University. Professor Roland I. Robinson, Chairman, continu- Ous ly provided very responsive and necessary guidance and Eftzructure. Professor Robinson's incredibly quick and in- sisghtful response to written work and Open door for verbal Connmunication greatly aided a successful completion. Pro— fessor Alden C. Olson skillfully edited the thesis and pro— "ilfled beneficial research structure. Professor Olson is also the only person, to my knowledge, that has volunteered 'tCD serve on a time consuming dissertation committee. Dr. RC>1nald M. Marshall enhanced the theoretical and statistical a"S'opects while improving readability, especially for the '. I O tion—finance major." Mr. Jerry St. Amand was extremely helpful in iii .ev ’ n .a. _. an‘ ’5 .ly - IT. “-- n u... n o.‘ w... untangling the administrative red tape of the computer facilities in addition to offering consistent and construc— tive computer prOgramming advice. I appreciated the Oppor- tunity to repeatedly discuss dissertation related tepics with Dr. Richard Walter, Mr. Larry Lang and fellow Doctoral (candidates. Appreciation is also extended to Jo McKenzie viho typed the final draft and whom I had fullest confidence that the myriad administrative details for Michigan State Ilniversity would be met. Finally, I thank my wife, Linda, for being her wonderful self while remaining patient with our work and eruzouraging for our goals. It is her love that was and remains my greatest and most cherished asset. iv .unp \ .cuo .00:- \ “'1'. ,ud-. - . r—4 TABLE OF CONTENTS LIST OF TABLES. . . . . . . . . . . . . . . . . . . ILIST OF FIGURES . . . . . . . . . . . . . . . . . . Chapter I. II. PURPOSE OF STUDY AND LITERATURE REVIEW. . Introduction Debt Maturity Management Financial Return Financial Risk Term Structure of Interest Rate Theory Expectations Theory Error Learning Model Liquidity Preference Theory Institutional Theory Summary A THEORETICAL DEBT DECISION STRUCTURE AND RESEARCH DESIGN . . . . . . . . . . . Introduction A Theoretical Debt Decision Structure Multi—Stage Decision State Space Feasible Decision Space State Transformation Function Search Problem Single-Stage Decision Page viii 36 a'a ' .‘a g .‘D -" h.‘ g I Chapter Page Research Design A Regression Model The Regression Model and The Theoretical Debt Decision Structure A Rationale for the Model Statistical Assumptions of the Model Test Period and Financing Plans Interpretation of Regression Model III. TEST OF HYPOTHESIS WITH YIELDS ON GOVERNMENT SECURITIES . . . . . . . . . . . 69 Introduction Ordinary Least Squares Empirical Results 1952—71 1952—60 and 1961-71 Two-Stage Least Squares Empirical Results Rationale 1952-71 1952-60 and 1961-71 Summary ZEV. TEST OF HYPOTHESIS WITH YIELDS ON CORPORATE SECURITIES. . . . . . . . . . . . 95 Corporate Plans Tested Ordinary Least Squares Empirical Results 1952-71 1952—60 and 1961-71 Two-Stage Least Squares Empirical Results 1952-71 1952-60 and 1961-71 Utilization of Corporate Empirical Results Input for Multi-Stage Dynamic Programming Decision Model Adjustment of the Discount Rate for Two-Stage Financing Plans Summary vi Chapter Page V. SUMMARY AND IMPLICATIONS FOR FIIRTIER RESEARCH C C O O O O O O O O O O O O l l 0 Summary Theories of Interest Rate Term Structure and Yield Curve SlOpe Research Technique Empirical Results Governmental Corporate Application of Corporate Results Implications for Additional Research Normative Positive Government Implications for Yield Curve Analysis Conclusion SELECTED BIBLIOGRAPHY . . . . . . . . . . . . . . . . 130 vii LIST OF TABLES Financing Plans Tested . . . . . Results of Least Squares Regression for Financing Plans of Quarterly Yields for Government Securities: 1952-71. Results of Least Squares Regression for Financing Plans of Quarterly Yields for Government Securities: 1952-60 and 1961-71. Covariance Among Residuals from First-Stage Regression of Quarterly Government Yields. Results of Transformed Two—Stage Least Squares for Financing Plans of Quarterly Yields for Government Securities: 1952—71. . . . . . . . . . . . . Results of Transformed Two-Stage Least Squares for Financing Plans of Quarterly Yields for Government Securities: 1952-60 and 1961-71. . . . . . . Results of Least Squares Regression for Financing Plans of Quarterly Yields for Corporate Securities: 1952-71 . Results of Least Squares Regression for Financing Plans of Quarterly Yields for Corporate Securities: 1952-60 and 1961-71 Results of Transformed Two-Stage Least Squares for Financing Plans of Quarterly Yields for Corporate Securities: viii 1952-71. Page 63 75 80 86 87 9O 97 97 100 Table 10. Page Results of Transformed Two-Stage Least Squares for Financing Plans of Quarterly Yields for Corporate Securities: 1952-60 and 1961-71. . . . . . . . . . . . . . 103 ix Figure LIST OF FIGURES Multi-Stage Decision Structure . . . Overlay of Regression Variables. . . Graphical Regression Results and Financing Stage Superiority. . . . . Maturity Decision of Debt Stages . . Selected Government Yields: 1952—71 Selected Corporate Yields: 1952-71. Graphical Expression of Regression Models Results . . . . . . . . . . . Page 43 51 51 53 61 62 77 .u- (I) 16 ..‘_1 .l I ‘ ‘ ..‘ a... 'v CHAPTER I PURPOSE OF STUDY AND LITERATURE REVIEW Introduction The term structure of interest rates is the pattern of yields for a number of securities that differ only with reSpect to maturity. Usually this means the securities of a single issuer such as the United States government, but it ndght be corporate obligations of issuers of similar Cniality and character. Normally no issuer, or group of issuers emits an infinite number of securities so the pat- tern of yields to maturity is a series of point observa— timons. However, if the number of points is large enough a ccurtinuous curve can be reasonably fitted to the patterns of points. This is a "yield curve" which is the graphic representation of the term structure of interest rates. Irving Fisher was one of the first to note the dif- ference between long—term and short—term yields. Other _ 1Irving Fisher, The Theory of Interest (The Mac- Mlllan Company 1930) , p. 210. ... ,uv a i. u.- '0‘: '.\ \ I.‘ v.“ i r - N“ «.P 2 theorists, such as Hicks, Keynes, Kessel and Malkiel gave greater substance to the theory, but it was the work of an obscure Treasury Department economist, Henry Murphy, who first applied the idea to the practical prdblems of market financing.2 Soon thereafter, Durand applied a similar set of ideas to the corporate bond market.3 Except for Murphy's work, however, this set of ideas does not appear to have been used for decision making purposes in the capital mar- kets. Observation of the money and capital markets shows that not only do interest rates change, but the shape and slepe of the yield curves that can be fitted to market ob- servations also change. When such changes are material, there is a reasonable presumption that a shrewd manager of a Inarket financing might profit from a flexible approach to the market; of picking the maturity for current financing that will, in the long run, reduce financing costs. Economists have long attempted to explain the term Stlnacture of interest rates. In spite of repeated efforts, the subject is still far from settled, particularly in the , 2Henry C. Murphy, National Debt in War and Transi- m (McGraw-Hill, 1950), pp. 92-103. 1 3David Durand, Basic Yields of Corporate Bonds, 900—1942, NBER Technical paper #3 (1942). 3 area of application. This study attempts to develOp a deci- sion making model which will apply the term structure of interest rates to financial management. Specifically, the focus is on the term structure lepe, the differentials between rates for various periods to maturity. Results of the research have practical implications for the issuer of debt, both governmental and corporate. The hypothesis is that a combination of present and future maturities can reduce interest costs over that of a single maturity. The analysis departs from the strict assumption of traditional finance which has taught the financial manager to fit debt structure to approximate asset maturity. Interest cost reduction may be possible tlrrough more SOphisticated debt timing. The decade of the 1960's witnessed many manhours expended to define an Optimal debt/equity structure for corporations.4 Numerous debt/ equity studies have been made to support these prepositions eHHPirically. The results have not been conclusive. * 4See for example, David Durand, "Cost of Debt and EQUity Funds for Business: Trends and Problems of Measure- mentn; Franco Modigliani and Merton H. Miller, "The Cost of capital, Corporation Finance and the Theory of Investment," and numerous other replies and articles reprinted in The Theol'y of Business Finance (MacMillan Company, 1967) Stephen 3- Archer and Charles A. D'Ambrosio, eds., pp. 92—253. 5The debate continues. Michael Davenport, "Lever- :‘ge, Dividend Policy and the Cost of Capital: A Comment," he Journal of Finance, Vol. 25, No. 4 (September, 1970), pp. 893-70 4 Attention is this paper is on the management of short—term and long-term debt. Debt Maturity Management Financial Return Debt management, like any phase of financial manage- ment, does possess a greater potential for success with prior planning. Planning which requires the manager to time amount and maturity of debt should lead toward a more Opti- mal debt policy. A model that incorrectly interprets future interest rates will be in the same sorry position as a 100 per cent variable ratio bond portfolio in a bull market. A financial manager who committed a large prOportion of debt tc> a long-term maturity issue would indeed be upset to see ILJng-term interest rates suddenly decline. A debt structure plan may be analogous to a formula irrvestment plan. In a constant ratio plan an investor keeps a fixed percentage of funds between stocks and bonds. When stock prices are rising the investor sells part of his StOCR investment and buys bonds to maintain the fixed ratio of Stocks and bonds. By contrast, in a variable ratio plan the investor decreases the prOportion of stocks held in a Portfolio as stock prices rise and increases the preportion of equity funds as stock prices fall. The formula plans 5 have the advantage of requiring the investor to engage in prior planning and rule against emotional judgements such as might be possible in a bear market. Formula plans, especially variable ratio plans, do not always give superior results.6 A debt model might alter the proportion of debt maturity with regard to the lepe of the yield curve. The same general advantages and disadvantages of formula plans are applicable to a debt allocation model. The financial environment modifies a normative model. Corporate debt management mistakes are tempered by both income taxes and a smaller variability in long-term interest rates. Debt interest and flotation costs are legitimate business expenses. Additional expense is reduced b)? one minus the marginal corporate income tax rate. For example, if a firm did incur an extra interest cost of 15 per cent on debt, the effective after-tax cost amounts to ti per cent for a firm in the 50 per cent tax bracket. It 118 :important to note that the income taxes also limit the POtential gains from correct utilization of a normative Structure. Quarterly interest rates on twenty year to maturity IVA ITtility bonds have fluctuated between 2.95 per cent and \ .A 6Jerome B. Cohen and Edward 2. zinbarg, Investment Eé¥llY§is and Portfolio Management (Richard D. Irwin, 1967), . 553-4. M'V' . e .Ao I gain (I) ‘\a I A. v- .' 0‘.- “.Pl . l h . u i 5 ‘1 u‘.‘ “L 0..‘ 6 9.04 per cent from 1952 to 1971. The recent variability in interest rates of this maturity have not been as dramatic. The lack of severe fluctuations minimizes the potential for both gains and losses in debt structuring. However, the difference of even % per cent to the financial manager is A k per cent after-tax reduction on debt amounts to great. a $15,000,000 a year saving for a firm with the debt capacity of General Motors Acceptance Corporation. Gains of this Imignitude make the study both worthwhile and practical. Tflme impact is very clear for the corporate manager. In addition to considering possible returns from debt manage- ment, we will seek to ascertain the contribution to a firm's 1?iask. JEELJQancial Risk Financial risk increases as the preportion of funds -I>J?<3vided by debt and fixed charges increase. All other tllfidings equal, an increase in fixed obligations increases the probability that future fixed charges may not be met. 73711£e chance of potential bankruptcy increases likewise and ltr<319resents a very real risk to the creditors and share— holders of the firm. The maturity of debt within the ‘:=E‘£>ital structure represents a measure of risk as the f0 1 lowing examples demonstrate . .n' I ..q.u . no!‘ A. \ ”we .«Ia _‘ I). 1‘. . p. 5. ‘O ‘u u U ‘i A! ‘I «a 7 A utility that funds its total debt with short-term maturities would subject itself to the possible whims of the money market. The possibility of being unable to refund short-term debt continually represents risk for the firm. Most financial managers would shun a continual short-term debt policy, especially with long life assets. Shorter debt maturity may be translated into greater economic risk expo- sure. A firm may magnify financial risk by using a very high prOportion of debt funded by a very short—term Huiturity. On the other hand, a longer maturity allows the firm greater time to meet fixed obligations without the capriousness of a short-term market. The next example demonstrates the Opposite side of risk from debt usage. A sales finance company might fund its debt structure entirely with long-term debt. The assets of a finance company are short lived and demand is uncertain. The firm may find itself with unneeded long-term funds and uncancellable debt because of an economic downturn. Excess debt represents an unprofitable source of funds. This oIE>portunity loss is a risk for the shareholder, although the consequences are not as disasterous as cash insolvency. TTlese two examples represent the potential economic and opportunity losses that may result from imprOper debt ma turity decisions . '2... p-‘ .AO- .4..- v “".I .uu- . ..,, ‘ u ‘v‘. .._: I“ I l 1); ‘§ 8 Maturity Of debt does represent risk. Shorter debt maturity carries a greater potential for an economic loss. Longer debt maturity carries a greater potential for an Opportunity loss. The potential risk is easily recognized at the extremes; say average maturity Of debt equal to one year or equal to twenty years. Traditionalists have taught that debt should parallel asset maturity. With a given debt maturity that strictly reflects asset life, the manager may not make a decision with regard tO return. A debt cost reduction may be possible with combinations Of debt maturity equalling aSset life. In particular, gains may be possible by changing the prOportion Of long-term debt with relation to the lepe of the yield curve. These techniques enable a manager to fine tune debt management. First, management must decide the total debt/ eclnity relationship. Second, management must place bounds Over which the debt maturity and debt composition may change and maintain the amount Of financial risk the firm desires. of course, the above two decisiOns are most important to debt management. Financial leverage affects the potential earuings and the risk attached to those earnings. SOphis- ticated financial managers are needed who are capable Of determining prOper debt decisions. Numerous texts and .‘,.¢ .A.‘ .y.. .n- .uu 0..» one u ouy ‘0’ a II. . .H-I tu- D -. 9 financial literature exist to assist in determination Of proper financial leverage and these broad tOpics are not contained in the decision structure Of this paper. The plan Of this study is as follows. Chapter one continues with a presentation Of the theories Of the term structure Of interest rates. Effort is made to indicate the implications for debt management that arise from each theory. Chapter two presents the theoretical debt decision structure and the research design. Chapter three presents and interprets results Of the application Of the debt deci- sion model to governmental debt management. Chapter four Presents applications Of the model tO corporate debt. Chapter five presents the summary conclusions. Term Structure Of Interest Rate Theory Interest rates have differed among issues, dates Of issue and maturities. Issuer interest rate differentials may be explained by risk of default probabilities assigned 1) . 7 . . 3? investors and bond analysts. Date Of issue interest I1"<="l'te differentials may be explained by savings, rate of 7Lawrence Fisher, "Determinants Of Risk Premiums on '<3<>1:porate Bonds," The JOurnal Of Political Economy, NO. 67 (June, 1959), pp. 217-237. Also Avery B. Cohhan discussed 152i<=tors that affected yields in "Yields on Corporate Debt Directly Placed," NBER General Series #84 (1967) . 10 real investment, money stock rate Of growth, inflation expectations and returns desired by investors. Consider- able effort has been given to answering the question Of how maturity Of debt affects interest rate structure. Theories of the term structure Of interest rates are diverse and no one theory has yet gained full acceptance. The yield to maturity curve is the most widely used graphic device for showing the relationship between yield and remaining maturity for debt issues Of similar credit quality. Years to maturity is measured along the abscissa and annual yield to maturity is measured along the ordinate. During World War II Secretary of the Treasury Morganthau Ordered his Director Of Research tO make charts for members of the Federal Reserve comparing the pattern of interest rates between a base period Of 1942 and later dates. Each c1'1art contained the yield curve for a particular point in 1Z-‘-:i_rne. This posting allowed the Federal Reserve and the Treasury to be aware Of the interest position and provided a graphic history Of governmental yields. The Federal I{eserve felt short-term rates should be allowed to rise while the Treasury felt the rates should remain constant. \ 8Reuben A. Kessel, The Cyclical Behavior of the Term Structure Of Interest Rates, NBER Occasional Paper #91. (1965). 9Murphy, Op. cit. . 'aA v ,.v - .‘pn .‘,.... on u up. n... AA. ~v. .I01 “I b. on. (I! I a“ ‘v ‘1‘ 11 The yield curve provided the Treasury with graphical feed- back tO insure that short-term.rates were not increasing. Thus, the Federal Reserve felt the rates were "impaled" In any since the short—term rate could not float upward. event, the graphical presentation Of a yield curve has re— mained an integral part Of debt management. Many theories have been prOposed to explain the interest rate term structure but these fall into three expectations, liquidity preference and the broad groups : Indeed, the theories may prove institutional theory. C Omplementary . TO permit comparison Of these theories a standard Forward yields may be lirrterest rate notation will be used. A capital cIallculated from market yields at a point in time. te must sell at a discount so as to Offer new investors the current 6 per cent yield one year hence for a one year to maturity issue. The two year note sells at 99 per $100 :EDEiIT note and gives the original one year investor a return \ 11The mathematical approximations are as shown: ) is (1.05)2.(1.o4)(1.oe) or ( l+tR2)2 = (1+tR1) (1+ 1.102591.1024 t+lr1,t 0C .0- 14 of 4 per cent, the same as available from a one year alternative.12 The example may be mathematically repre- sented as: (1 + tR2)2 = (1 + tRl,t)(l + t+lrl,t) (1) More generally the relationship among interest rates and maturities posited is: (1+tR)=[(1+ R)(l+ r)...(1+ r)]l/n (2) n t 1 t+l l t+n-l 1 Long-term rates for period n are a function equal to the Inultiplication of n future short-term rates. Investor anticipations of future short-term rates Shape the yield curve. Assume the yield curve is currently iflat, long—term rates are equal to short-term rates, and liriflationary expectations do not exist. If inVestors now IDelieve that interest rates are low with regard to "normal" Jraites or because inflation is expected, the resulting yield c21:.Irve will slope upwards with increasing term to maturity. Given these expectations, the equilibrium level of short- izeerm is lower than long-term rates so as to avoid a poten- i::ia1 capital loss from a rising interest level. Investors ‘VV<3u1d buy short-term debt and sell long-term debt. These 61311y'and sell actions raise the price (lower yield) of short- 12The price of the bond is found as follows: Price = coupon + par , Price = 5 + 100 = 99 1 + yield 1 + .06 t , ‘ a 9A- ‘- o:.\ g A I I . 'll ( i i I I 0' l 15 term debt and decrease the price (increase yield) of long- term debt and give rise to the anticipated yield curve. Expectations may explain other yield curve shapes: flat, declining or humped.13 As previously noted, the empirical evidence does not explain completely nor accurately the term structure. In an effort to support an early and very simple form of the expectations theory, Macaulay found that time money rates anticipated a seasonal rise in call money rates.14 This constituted evidence of successful forecasting for Macaulay. More recently, Sargent applied spectral analysis in an application of Macaulay's test and supported the 15 earlier findings. Hickman continued with the test of accurate forecasting as evidence for the expectations L... l3Initial research of Professor Roland Rdbinson and this author indicates the humped yield curve may, in fact, be a myth. Long-term government maturities have been issued with an estate tax par redemption feature such that the yield curve points are not similar in all but remaining time to maturity. The impact of this possible "myth" is not incorporated into this research effort. 14Frederick D. Macaulay, The Movement of Interest Rates, Bonds and Stock Prices in the United States Since 1856, NBER (1938), p. 36. 15Thomas Sargent, "Expectations at the Short End of the Yield Curve: An Application of Macaulay's Test," NBER General Series # 93 (1971), pp. 391-412. .§ ‘7 I .1- IF- I‘U had. 16 theory, but failed to find the relationship.16 Hickman found mere inertia to be a better predictor, t's period yield curve will occur in t+1's period. Culbertson's empiri- cal research was similar to Hickman's and also found lack of 17 Culbertson found it difficult to accurate predictions. believe that speculators would Operate in the governments and predict as badly as his results indicated. Culbertson felt his findings supported the institutional theory which is discussed later. The underpinning of these original tests is one of accurate forecasting where realized rates are compared with calculated rates. Meiselman designed a test which did not require accurate forecasting and the sagging expectations theory was buoyed in the mid 1960's. Before turning to Meiselman's work, the implications for debt management from the pure expectations theory are examined. Relative supply of securities has no relevance for interest rates in the expectations theory. Interest rates are tied together by the mathematical model of equation (2). 16W. Braddock Hickman, "The Term Structure of Interest Rates: An Exploration Analysis," Unpublished manuscript, NBER (1942). 17John M. Culbertson, "The Term Structure of Interest Rates," ggarterlyJournal of Economics, Vol. 71, No. 4 (November, 1957), p. 502. 17 The supply of securities only affects interest rates if the supply changes expectations for the investor. Buy and sell actions of investors shape the yield curve to conform with their general anticipations of future interest rates. In- vestors receive the same return, regardless of maturity held. Given these assumptions a governmental unit such as the Treasury or the Federal Reserve could not effect interest level changes by altering the composition of debt maturities. Unless the change in supply of a maturity changes the expectations, the government could finance its debt as cheaply with any maturity desired. DeLeeuew indi- cates: Debt management operations influence interest rates for a brief period, the average composi- tion of the debt over longer pgriods does not have a perceptible influence. No interest cost advantages are possible through debt matu- rity decisions. The corporate debt manager is faced with the same framework as the government under the expectations theory. If equal risk premiums are added to the credit risk free rate of interest of the United States government maturities, the corporate manager has no potential for interest cost 18Frank DeLeeuew, "A Model of Financial Behavior." The Brookings Quarter1y_Economic Model of the United States, J. S. Duesenberry, G. Fromm, L. R. Klein and E. Kuh, eds. (1965), p. 503. g I Iv! "4 d- - I a. an... «A '4.— . A \ -...¢.. . .._. ,1 Mn. .1 ., a... \ con. -n x a .1 " v- I I‘v- D..‘ A. ~"‘A OI.U 5|: '1 ‘D . C ‘ 'Q ‘I -,‘ 18 reduction in temporal placement of debt. The cost of two one-year loans is equal to the cost of one two-year loan. The logic is definitional, not one of economic behavior. The different maturities of debt may affect the financial risk of the firm, but is not considered within the context of expectations theory application. The expectations theory allows a financial manager to concentrate on matters other than debt maturity and debt timing since a gain is impos- sible. However, if unequal risk premiums are added to various maturities of debt, a possible cost advantage exists. In general, the pure expectations theory indicates government and corporations may not effect interest cost benefits via debt timing and yield curve analysis. Error Learning Model Meiselman devised a simple test for support of the expectations theory.19 He assumes that market participants are able to derive forward rates from the existing term structure of interest rates equation (2). Long-term rates under the model are a function of future short—term rates and a change in these short—term estimates may affect the long-term rates. Next, Meiselman assumes that investors 19David Meiselman, The Term Structure of Interest Raises. (Prentice-Hall, 1962). J-r uh. 0-. p 19 react positively to differences between present rates and forward rates correSponding to the present rates implied in the past. Thus, if actual rates are higher than had been anticipated, the market may systemati- cally revise upward expectations of what short-term rates in the future are likely to be. Similarly, if actual rates are lower than had been anticipated, then the market may also systematically revise down- ward ex ectations of future short—term rates.2 Forward short—term rates change with regard to forecasting errors for the present short-term rate. This change may be shown notationally as: t+nr1,t - t+nr1,t-1 = fn(tRl ‘ tr1,t-1) (3) where fn is a function equal to the prediction error related to the difference in realized yield and forward yield for maturity n. The change may be represented as: At+nrl,t = gn(Et) (4) where gn is again a function equal to the prediction error and Et represents the difference of the realized yield and the forward yield. Assuming the relationship is linear, equation (4) may be solved by the regression: At+nr1.t = an + bnEt (5) This regression provides the basis for the test. 201bid., p. 20. 20 Meiselman found that changes in forward rates are highly correlated with the forecasting error. He used annual yield curve data on corporate bonds from 1901-54 .develOped by Durand. Forward rates behave as expected by the error-learning mechanism. Therefore, the eXpectations theory gains support. The existence of a near zero "a" term of the regression indicates no liquidity preference. The correlation coefficient of the regression varies in- versely with the maturity of the dependent variable, the period in which forward interest rates are being forecast.21 Investors are less likely to forecast effectively and seri- ously short-term rates far in the future. Although the error-learning model sparked new interest in the expecta- tions theory and term structure research, several criticisms have been made. Grant, using British data, found that the error- 1earning model does not provide good explanations of the yield changes.22 However, Grant interpolated linearly be— tween Observed yields resulting in larger fluctuations than when yields are taken from a "best fit" yield curve as had 21Ibid., p. 22. The correlation coefficient. R. drOpped from .952 to .590. 22J. A. G. Grant, "Meiselman on the Structure of Interest Rates: A British Test," Economica Vol. 31 (February, 1964), p. 61. 21 Meiselman. Buse suggested that the results obtained by Meiselman would be obtained by any set of smoothed yield curves and the test, therefore, had low discriminating power. Buse Obtained the same results as Meiselman gen- erated by both reversing the chronological order and random ordering of yield curves. The model does not discriminate between the behavior of investors acting on Meiselman postu- lates and alternative formulations. Thus, Buse reasoned: The Meiselman model is consistent with any set of smoothed yield curves in which the short rates show a greater variability.23 Malkiel and Kane provided support for the error—learning model for very near term (three month) forecasts based on questionnaires sent to financial institutions at different 24 This last test worked less well as the forward times. period increased. Modigliani and Sutch employed a technique similar to Meiselman's and were able to explain interest rate differentials between short and long rates for govern- ment securities.25 The eXplanatory model of Modigliani and 23A. Buse, "Interest Rates, The Meiselman Model and Random Numbers," JOurnal of Political Economy (February, 1967), p. 61. 24Edward J. Kane and Burton G. Malkiel, "The Term Structure of Interest Rates: An Analysis of a Survey of Interest-Rate Expectations," Review of Economics and Statistics (August, 1967), pp. 343-55. 25Franco Modigliani and Richard Sutch, "Debt Manage- ment and the Term Structure of Interest Rates: An Empirical Analysis," Journal of Political Economy (August, 1967 Supple— ment), pp. 569-89. -\ h ..h fits ‘1'... 22 Sutch assumed two parts with regard to investors. First, future interest levels tend toward a "normal" level of rates based on past experience. Secondly, future interest rates move with regard to the most recent past (like Meiselman). By combining these two hypotheses the yield curve could be predicted. The results were offered as support of the expectations hypothesis. Criticism of the basis for the expectations theory and its assumptions are well phrased from this question raised by Weaver. One need only ask: Why it is not possible for changes in expectations about future short-term rates to have an influence directly upon the present supply and demand conditions which determine the current short rate to negate his [Meiselman's] analysis?26 The debate is by no means settled and controversy continues. Empirical tests and the logical framework for the support of those tests have not completely explained the expecta- tions theory, nor the error—learning model variation. Liquidity Preference Theory Hicks argued that the expectations theory provides a good description of the term structure in a world of certainty but requires refinement for the real world 26Alex R. H. weaver, "The Uncertainty of the Expectations Theory of the Term Structure of Interest Rates," The Western Economic Journal. V01- 4 (Spring, 1966), p. 133. 23 environment.27 This followed the lead offered by the Keynesian theory of "normal backwardation" in the futures market. In particular, Hicks felt that a bond holder must be offered a risk premium for assuming the risk of greater price fluctuations for longer—term maturities. In a world of uncertainty shorter maturities are prefereable to longer maturities. Shorter maturities are more liquid and are able to be converted more quickly into cash, hence are more valuable. Longer maturities are subject to these risks over a longer period of time. Increased risk must be compensated by increased return: the essence of the liquidity prefer- ence theory. The liquidation preference theorists do not dis— agree with the expectations theorists, but argue there is a natural increase in yield as maturity increases. Simple bond yield calculations show that for a given rise in the general interest rate level, long-term bond prices fall more than short—term prices. For example, Observe the effect on bond prices for a 6 per cent coupon bond when the interest level changes from 6 per cent to 7 per cent. Mar- ket price drops to 99.05 for a one year to maturity note while the price drOps to 89.32 for a twenty year to maturity 27J. R. Hicks, Value and Capital (London, 1946), pp. 138-9. 24 bond. Clearly, the longer maturity leaves the investor Open to a greater possible change in price. If increased variability in market price for a bond is risk to the in- vestor, he should be compensated for this risk. A study of bonds from 1900-1957 indicates the mean return for bonds increases from 3.2 per cent for one year notes to 3.6 per cent for twenty year bonds; while the risk, as measured by the standard deviation, increases from 1.7 per cent to 3.6 per cent.28 Longer maturity does leave the investor sus- ceptible to a greater potential loss. These facts do lend support to the liquidity preference theory that risk in- creases as maturity increases. A liquidity premium may be thought of as an amount that is added to the expected rate. Thus, the forward rate calculated is equal to the expected rate plus the antici— pated liquidity premium. This may be defined notationally as: 2 _ (l + tR2) — (l + tR1)(l + t+lrl + L2) (6) > 4 at O at2 O The liquidity premium, Lt' is positive and increases with maturity but at a decreasing rate. Therefore, even if 28William L. Wilbur, "A Theoretical and Empirical Investigation of Holding Period Yields on High Grade Cor- porate Bonds” (Ph.D. dissertation, University of North Carolina, 1967). 25 expectations assume no change in future interest rates, the yield curve slopes upward due to the existence of a liquid— ity premium. Malkiel has demonstrated logic for this effect through the mathematics of bond prices and interest rate movement.29 First, for a given change in yield from the nominal yield, changes in bond prices are greater the longer the term to maturity. Second, the percentage price changes increase at a diminishing rate. The mathematics of bond prices also very neatly explain the "shoulder" Observed in most yield curves because of the diminishing rate of price movement for increasing maturity. Conard has indicated the effect of the liquidity premium is most often felt by a maturity of three to five years.30 The premium varies not only with maturity of an instrument but over the cyclical pattern Of interest rates. Two explanations exist for the cyclical movement of liquidity premiums. The first hypothesis indicates that the liquidity premium exists with reSpect to "normal" rates. One would expect liquidity premiums to be higher for long— term than short-term maturities when the interest level is 29Burton G. Malkiel, The_Term Structure of Interest Rates (Princeton University Press, 1966), pp. 50-9. 30Joseph W. Conard, The Behavior of Interest Rates (Columbia University Press, 1966), p. 80. 26 low. A low interest level subjects the long—term maturities to a greater potential of capital loss if yields increase. When the interest level is high the liquidity premium is low but always non-negative. The second hypothesis, the money-substitute hypothesis, Operates inversely to the "normal" hypothesis. During a business expansion interest rates rise which makes money more expensive to hold. Money is exchanged for short-term securities which holds down short—term rates relative to long—term rates. The liquidity premium increases when the interest level rises and the Op- posite occurs when the interest level declines. Note this does not imply the spread between long and short securities increases as interest levels rise. The expectations theory indicates that if the interest level is high relative to normal rates, the yield curve will lepe downwards. There— fore, the money-substitute hypothesis maintains that the downward lepe of the yield curve is not as great as might be expected with high interest levels because of the in- crease of the liquidity premium. Regardless of the hypothesis of the liquidity premium, investors are perceived to demand shorter maturi- ties over longer maturities without a risk premium included. Borrowers, on the other side, desire to sell long-term debt to assure themselves of a constant source of funds. The 27 desired supply of maturities does not equal the demand for maturities. Speculators are also considered to be risk— averters and must be paid a premium to accept longer matu- rities. The yield curve must possess a positive slope over time to equate the market investors and issuers. Before considering the empirical studies note Malkiel's comment: One must interpret the results of such studies [liquidity premium] very cautiously however. Since liquidity premiums can never be Observed and only estimated, it is impossible to reach a completely definitive verdict regarding their behavior over time. The liquidity premium might exist implicitly in the minds of financiers but not explicitly. One may ask but not find an answer to the question: What is the liquidity premium for maturity n? Kessel utilized a test similar to Meiselman and reasoned that forecasting errors did not invalidate the expectations theory.32 Kessel felt anticipated and realized yields would only tend to be equal in a world of certainty. In the test Kessel found that the forward rates were con- sistently greater than realized rates and this positive 31Burton G. Malkiel, "The Term Structure of Interest Rates: Theory Empirical Evidence, and Applica- tions," (The McCaleb-Seiler Company, 1971). Footnote 28. 32Kessel, Op. cit. 28 difference indicated the existence of a liquidity premium at the point in time the forward rate was calculated. Kessel also responded to Meiselman's charge that the existence of an "a" regression estimate from equation (5) close to zero invalidated the liquidity preference theory. Kessel found that the dependentvariable, as de— At+nrl,t' fined would naturally find an "a" estimate close to zero because t-l's premium had been subtracted from t's premium. Cagan found that increasing the maturities of issues held for a set holding period led to increased returns.33 Cagan reasoned that the returns were a result of the liquidity premium. Both Kessel and Cagan supported the money-substi- tute hypothesis Of the liquidity premium; the liquidity premium varies directly with the interest level. Malkiel has offered a plausible explanation for the direct relation- ship between liquidity premiums and the interest level. Dealer risk aversion increases as the interest level in- 34 creases, and widens their Spread. This increased dealer spread imparts a more positive bias to the SIOpe of a yield 33Phillip Cagan, "A Study of Liquidity Premiums on Federal and Municipal Government Securities," reprinted in Essays on Interestpgates, Vol. 1, NBER General Series #88 (1969). 34 p. 143. Malkiel, Term Structure of Interest Rates, 29 curve when interest rates are high. Malkiel's recognition of transactions costs offers some practical explanation of Kessel's liquidity premium. Michaelsen in a test similar to Cagan's found that longer maturities led to both higher average holding period returns and standard deviation Of those returns.35 Theorists believe that the expectations theory and the liquidity preference theory are compatible and complementary. The liquidity preference theory allows the expectations theory to account for real world uncer- tainty. . The existence Of liquidity premiums have implica- tions for the management of debt. Financial risk and trans— actions cost aside, borrowers gain an interest cost reduc- tion through continual finding by short—term debt. The borrower does not incur the liquidity premium and debt cost is reduced by that amount over time. The existence of the liquidity premium may enhance multi-stage financing as op— posed to single-stage financing. If borrowers did issue only short-term debt issues, the liquidity premium would not exist since the demand by investors would equal the supply of borrowers. It is the imbalance Of supply and 5JacOb Michaelsen, "The Term Structure of Interest Rates and Holding Period Returns," Journal of Finance, Vol. 20 (September, 1965), pp. 444-63. 30 demand caused by risk aversion that leads toward the liquidity premium. The liquidity preference theory has not been subject to criticism to the extent of the pure expec- tations theory. Institutional Theory The institutional or hedging pressure theorists state that the interest rate differentials are a function of the relative demand and supply for given maturities. This theory holds that the debt market is segmented by investor and issuer preference for debt maturity. Commer- cial banks desire short—term maturities so as to be able to quickly liquidate debt for additional loans or reserve needs. Insurance companies are more interested in longer term debt because of their long-term liabilities. The theory states that investors are more interested in secu- rity of income over their holding period rather than poten— tial capital gains. Institutions issue debt to parallel asset life. Implicit is the assumption that investors hold the debt to maturity. The institutionalists state that yield differentials are neither a function of expectations nor of liquidity preference but rather of supply and demand for a given maturity. The institutiOnal theory holds that the market for IA ‘1! '- h. d- If ”I 11 5: ’f’ 31 maturities may be dis-continuous. Market participants are constrained by law and tradition in their choice of maturi- ties. The rates of long-term debt do not affect the rates of short-term debt and vice-versa. The linking of yields of various maturities as implied by the mathematics of the expectations theory or the liquidity preference theory is not accepted by the institutionalists. Empirical evidence for this theory has been less substantive than the previous theories discussed. Some market practitioners effectively argue for the institutional approach as reflected by their day to day working experience. Homer and Johannesen (members of a large Wall Street firm specializing in bonds) do not re- gard short and long-term bonds as two ends of the same moustache, but rather... as different from each other as stocks are from bonds, or more 30.36 Since the theories prOposed to explain the term structure are attempting to predict that structure, the above comments from those close to the market are particularly revealing. The practitioners do not agree with the academicians. In addition, Culbertson felt that since holding period returns increased as the maturities of that holding 36Malkiel, "The Term Structure," p. 14. . v- a" (Y) .1 ‘ 32 period increased, the only logical explanation could be institutional. Wallace found that forward rates are influ- enced by the supply of maturities of loans greater than one year.37 The effects prOposed by Wallace were small but sta- tistically significant. Modigliani and Sutch attempted to test the supply effect on term structure of governmental rates and found that changes in the supplies of government debt had little effect on interest rates. Empirical support for the institutional theory has been limited. Sufficiently refined data has not existed for prOper determination of a debt maturity effect. Data does not exist that prOperly reflects private and local government debt. In addition, debt maturity and cost are intertwined. If rates are high borrowers may refrain from issues until a more favorable interest level exists. It is difficult to assume that debt composition is a truly exogenous variable. Malkiel tested the assumption that market partici- pants are rigidly constrained by maturity preference from information of The Treasury Survey of Ownership of Govern— . . 38 . . . ment Securities. The Survey prOVides information on the ————~ 37Neil Wallace, "Buse on Meiselman -- A Comment," Journal of Political Economy, Vol. 77 (July, 1969), pp. 524-70 38Malkiel, The Term Structure of Interest Rates, 33 maturity composition of securities by different financial institutions. The maturity composition by financial insti— tutions is quite variable over time. The strict assumption of an extreme institutional theory is doubtful. The support or non-support of the general institutional theory will be- come clearer with the introduction of more refined debt composition data. Implications for the institutional theory are very clear for the governmental debt manager. Given that supply affects the interest level, the government could shape a yield curve to its preference by debt maturity decisions.39 The corporate manager might attempt to issue that maturity of debt that would least affect the interest level for that maturity. Thus, if many firms were issuing twenty year debt, the manager might find a cost advantage in issuing other than twenty year maturities. Summary Empirical evidence tends to support the expectations and the liquidity preference theories but not the 39See Modigliani and Sutch for a discussion of the Governments Operation Twist where an attempt is made to change the yield curve shape through debt maturity deci- sions. Franco Modigliani and Richard Sutch, "Innovations in Interest Rate Policy," American Economic Review: Papers and Proceedings (May, 1966), pp. 178-97. '(1 :06' ,..- ‘:7' l“' 34 institutional theory. As more debt data becomes available all three theories might be viewed as being complementary. Disagreement exists with regard to any one theory or their combinations for explanatory and predictive value in the term structure of interest rates. The theorists do agree that interest cost reductions may be possible with prOper timing of debt maturities. Baxter notes: Malkiel Although commercial paper and funded liabili- ties are not considered as good substitutes, most issuers indicate that they try to time their long-term issues to get the most attrac- tive rates possible. The expectation of rising interest rates will generally speed up the long-term financing decision and that of falling rates will lead to its postponement. Borrowers utilize short-term debt, both bank loans and commercial paper, to provide funds until the long-term flotation.4O indicates: Thus, there are reasons to suppose the exist- ence of a strong a priori case in favor of funding which would tend to bias the distri— bution of corporate debt toward longer matu- rities. We hasten to point out, that this case for funding in no way rules out the possibility Of anticipatory or delayed funding.41 4ONevins D. Baxter, The Commercial Paper Market (Bankers Publishing Company, 1966), p. 75. Pa 168. 41Malkiel, The TermyStructure of Interest Rates, 35 Historically, the most Opportune times for long-term financing have occurred when the yield curve was steeply upward sloping.42 Limited empirical evidence has supported the idea that the lepe Of the known term structure of interest rates conveys useful knowledge for the management of debt. For such a policy to be feasible, the yield curve must reflect or potentially reflect information not fully explained by the term structure theories. This study places additional in- formation in front of the financial manager for the timing of maturities of a desired amount of debt. Chapter two shows the theoretical decision structure and the research technique for the testing of the hypothesis: information is contained in the lepe of a yield curve for debt manage- ment. A_A 42Malkiel, "The Term Structure," p. 18. CHAPTER II A THEORETICAL DEBT DECISION STRUCTURE AND RESEARCH DESIGN Introduction This chapter presents the research design for a test Of the stated hypothesis. The hypothesis is that a debt issuer may reduce interest costs by issuing combina— tions of debt maturity based on the lepe of a given yield curve. While the research technique tests the prOposition within a macroeconomic framework, the results may be applied within the microeconomic environment. Attention is focused on the maturity composition of a given amount of total debt to be issued. The best method of minimizing debt cost could be determined with perfect foresight of the future interest rate structure. Since this foresight does not exist, we must do with the existing term structure and any historical perspective available with regard to interest rates. This research attempts to provide one such perspec- tive within an interest minimizing debt decision structure. First, however, a debt maturity model is formalized so that 36 37 the decision framework may be more clearly stated. The decision model represents only one of many such models that could be presented. Models may include alternative vari- ables with an objective function other than interest cost minimization. The model selected concentrates on the rela- tionship between the yield curve lepe and the maturity of debt selected. A Theoretical Debt Decision Structure In this section the debt decision is formalized in a theoretical model.1 In the model debt interest costs are minimized subject to certain constraints concerning the maturity Of debt and financial risk which the maturity represents. These constraints may be imposed by management or creditors. Flotation costs associated with a debt issue 2 are assumed to be zero and call provisions are assumed to be absent.3 Debt needs are predicted on the basis Of cash 1For this section's background see Charles R. Carr and Charles W. Howe, Quantitative Decision Procedures in Management and Economics (McGraw—Hill Co., 1964). The theoretical framework centers on the corporation, but is equally applicable to the government. 2Robert H. Litzenburger and David P. Rutenberg, "Size and Timing of Corporate Bond Flotations", Journal of Financial and Quantitative Analysis (January, 1972), pp. 1343-60. 3See Martin H. Weingartner, "Optimal Timing of Bond Refunding", Management Science, Vol. 13, No. 7 (March, 1967), pp. 511-524. Oswald D. Bowlin, "The Refunding Deci- sion: Another Special Case in Capital Budgeting," The Journal of Finance (March, 1966), pp. 55—68. 38 flow for the firm. These limitations are particular to this decision framework and allow full concentration on the hypothesis. The limitations may be removed only with resulting increase in decision structure complexity. Debt alternatives (Xi) are composed of varying debt maturities (xij) at an interest cost (cij) for each matu- rity. The subscript i represents the year of debt issue (i=1,...,p) while the subscript j represents the remaining term to maturity for that issue (j=0,...,n). Once a debt instrument, x.., is issued it continues to carry a cost of 1] cij to retirement. The debt decision model for both a single-stage (i=1) and a multi—stage (i=1,...,p) are shown. The model is formulated in terms of a decision structure consisting of a state space, a feasible decision set, a transformation set and an objective function; and an asso— ciated search process involving these decision structure components. Multi-Stage Decision The components of the decision structure identify the relevant aspects of the decision problem confronting the firm. In a multi-stage setting the financial manager lives in any period, say period t, with the consequence of decisions made previously (period i=1,...,t-l). 39 Discretionary financing in the following period is limited to total debt requirements less the debt maturities exist— ing from past periods. The decision structure components are now examined with greater detail. State Space The state space 9 is a set of elements 6 represent- ing those relevant aSpects which are non-controllable inso- far as the firm's debt decision. The elements may represent such given parameters as the current yield curve facing the firm and total debt requirements of the firm. Examples of possible 6's for period i are: 0 {6 = (61. um 6k. ..-.em)} where 91 A n component row vestor Of interest rates. This vector is simply the yield curve facing the firm in period i for maturities one through n. This vector for period i=1 is simply the current yield curve facing the firm. The manner in which future interest rates are forecast provide the crux of the empirical test of this re— search. The expectations theory projects future interest rates on the basis of mathematical extrapolation while the liquidity premium theory includes a risk premium for increasing maturities. Ob- viously, the yields applicable to future maturities may greatly affect the Optimal decision. 62 = The debt requirement for year i based on cash flow of the firm. 93 = A n component row vector of dollar debt maturity constraints. The constraints 40 may be imposed by management or creditors. The dollar constraint might not exist for all maturities. Since maturity of debt represents risk to the firm, the relative debt constraints may be imposed to main- tain a desired amount of financial risk. HOwever, once these constraints are fixed they become non-controllable in the decision model. Feasible Decision Space The decision Space P refers to the set of feasible and alternative debt maturity decisions. Elements of the decision space are denoted as X which represents a vector of feasible debt dollar amounts within alternative maturi- ties. The decision space is normally constrained so that debt maturity decisions are in fact feasible. The feasi- bility of a decision veCtor X is comprised of real numbers and is made feasible by meeting the constraints ga. For example, the dollar amount of debt maturities selected should equal the total debt requirement. Examples of pos- sible constraints based upon the examples of the state Space previously indicated are: P {X : ga (9.x) = 0, a=l,...,q} where: n 91(9.X) x- - 62 = 0. Hence, constraint jgl 3 one, 91, indicates that total debt requirements are met for year 1. Maturities may proceed to a n year maximum. 41 92(6.X) = X - 03 = 0. Constraint two, 92’ indicates the minimum and/or the maximum dollar amount that may be obtained by the different maturi- ties of debt. State Transformation Function The transformation function T refers to the change in the state space from period i to period i+1 as a result of a decision X being made in a period i. In effect, the transformation function indicates how the state space changes over time. The most significant consequence is that annual debt maturity decisions involving a maturity greater than one year affect the discretionary debt require- ments for subsequent periods. Decision X made in period i affects the state space in period i+1.4 Illustrations for the sample elements Of the state space are: 4Note that for any i # l, ga(ei,Xi) = ga(T(ei_1.X1_1), Xi) = 0 Which in more general form reduces to: ga(Ti-1(Ti-2("°T2(T1(X1'91)'X2)""'Xi_1)xi) which is equivalent to: ga(T(91, X1.X2,...,Xi_l),xi) = 0 where (61, Xl'X2'°"'Xi-l) = 9i and where T = Ti-l‘Ti-Z"'Ti' a composite function of previous trans- formations each Of which is based on a particular decision and state. Thus, state 9i for decision i depends on all previous decisions Xi-l' Xi—2""'Xl and the initial state 61. Certainty exists only if one possible initial state, say 9 = 61 and if all transformation functions are deter- minis ic. A non-deterministic T might be: °i+1 = Ti(9i' Xi' Zi) where Zi is a random variate denoting uncertainty during period i. 42 T(6.X) = e'ee where: 91' -- A new yield curve will face the firm in period i+1. The yield curve will depend on how future interest rates are fore- cast from period i. It is on this area that the empirical research is focused. In particular, the test attempts to note information contained by a yield curve lepe. Statistically significant results of the regression model applied in this study adjust the forecasted rates based on information contained by the slope. 62 -- The discretionary debt need for the firm in period i+1 is equal to the total debt requirement for period i+1 minus the debt provided in the period i of maturity greater than two. Thus, decision X of period i affects the state of nature of period i+1. This relationship establishes the key to the debt maturity decision and the empirical test. Once a longerdterm debt maturity is selected the interest cost is "locked-in" for the maturity of that debt and the feasible debt decision space in the future is limited. ‘ -- The firm faces new debt constraints as im- posed in period zero. HOwever, many managements will provide similar con- straints for all periods of consideration and this element will not change from period i to i+1. Decision X in period i may affect whether constraint 65 becomes binding or not in period i+1. Search PrOblem The search process attempts to locate the maturities of debt and the timing of those maturities over the entire period of consideration so that the maturities are feasible and their cost is minimized. The Objective function ni for 43 the firm in period i yields the present value of interest costs for maturity decisions taken in that period. The value of “i is defined: j n ni(ei.xi) = jgl kgl Cijxj k (1+Cij) The firm attempts to minimize the present value sum of these functions with respect to the alternative and feasible debt decisions. n(91.X) is minimized. . - p . min n(61.X) - 121 “1(ei'xii XEP (1+Cij)l Where X = (x1'OOO'Xi'OOI'Xp)O An Optimal solution may be derived by dynamic programming. Figure 1 schematically indicates the relationship of the decision structure components. FIGURE 1 MULTI-STAGE DECISION STRUCTURE X.€P. i i T ... 6i80 % Period i T(ei'xi) : ei+15(‘, + x -2 3 Ci“ “i(9i'xi) j=1 kzl (l+c--)k 1] 44 The impact of the multi-stage presentation is that todays decisions have an effect on future decisions and the present cost of those decisions. If the pure expectations theory holds, any one debt decision is as costly as any other. The hypothesis of this paper is that the slope of a yield curve may reflect useful information for the debt manager. If this hypothesis is not rejected, then there is basis for including this information in the transformed interest vector 6i of the state 9. Market imperfections which are contained within the yield curve lepe would be introduced for future interest rate forecasts. The search process then selects maturities from the transformed data input. Single-Stage Decision In a single-stage debt model debt funds are provided for one period subject to existing debt, maturity constraints and cost minimization. When i=1 the multi—stage problem reduces to a single stage prOblem. For this special case the search prOblem may be represented as follows: Min {fli(61:X1)} x1 In words the search problem states that management elects those maturities of debt which meet individual maturity constraints and total debt requirements while oifi ”b‘ ' a or, ..n‘ UUQI Wu. u.‘ .‘l. Rho ‘e \l. \ AJ 45 minimizing interest cost. This is equivalent to selecting that maturity from the lowest point of a yield curve until meeting a constraint and proceeding to the next lowest cost and associated maturity. It may be desirable that integer constraints be imposed on debt which might alter the final solution from a strict implementation Of linear programming. The implications Of a one—stage model is that a firm reacts only to the financial environment for the pres— ent year. Decisions made in period i are tolerated in period i+1. If the pure expectations theory best explained interest term structure, such a decision policy would not be economically undesirable since no cost advantage is possible through altering debt maturity. Few decisions of a firm should be made with regard to only one period and the multi-stage decision model is more realistic. The em- pirical test may be introduced now that the theoretical framework for debt maturity decisions has been explained. Research Design A Regression Model The analysis assumes the issuer knows the time span needed for debt funds and is financing this constant amount over n years. Other costs are assumed not to exist. Transactions costs are assumed to be minimal and so do not 46 enter the decision structure. An issuer may provide for debt funds through a single, double or multi—stage issue. As an example, if an issuer needs funds for a twenty year period, n=20, it may issue a single—stage twenty year bond in year zero, or might issue a double-stage issue by a one year note, j=l, in year zero to be funded in year one by a nineteen year bond. Other multi—stage issues of greater than two stages are possible, of course, but are not con- sidered in this study. The issuer is assumed to follow that course of action which promises to minimize interest cost within the financial constraints. The known present cost Of a single-stage issue may be equated to the unknown present cost Of a two—stage issue. The uncertainty of the two-stage issue is due to the un- known future interest cost of the second stage. We may solve this equation for a second stage breakeven interest rate. If the future realized rate for the second stage is above the breakeven rate, the single-stage issue is advan— tageous; for a future realized rate below the breakeven point, the two-stage issue is advantageous. Mathematically, the breakeven problem is as shown below where coupon rates are equal to current interest rates (no bond premium or discount). 47 Interest Cost = Interest Cost Single-Stage Double-Stage g __EEE_T = g ij. + ; m+jrn—jT (7) i=1 (1+mRn)1 i=1 (1+mRn)1 i=j+1 (1+mRn)1 where: mRn = the known current long-term interest rate in period m ij = the known current short-term interest rate in period m and jow Dmeumqmm m mmDOHm whoa momH vmmm p P 11 J xuflu9ume Ham» H l.l.: muHHSDME umm» om Nmma LIXN txv rXO \ ”(Ky N 62 Hulmmma "mQQMHW mfidmommou Qmeumqmm o mmDOHm whoa moma voma coma omma mmma P . a _ wow + momma HmfioumEEOO . . . . muflaflub dd Eumulmcoq.l.l.l. ANN xx + mEAum xsmm .. ... use . o\o .\| / l. / 1: F80 lrxom ARCH 63 TABLE 1 FINANCING PLANS TESTED Two-Stage Alternatives Time Period Debt Covered Single—Stage lst stage/ 2nd stage Government 2 years 0R2 ORl/lrl 5 years 0R5 oRi/lra‘ 0R2/2r3‘ 0R3/3r2; 0R4 4r1 10 years 0R10 0R1/1r9; oRz/zra‘ oRs/Srs 20 years oRzo 0R1/1r19; 0R2/2r18; ORS/SrlS; ORlO/lOrlO Corporate 20 years oRzo 0R1/1r19 where oR20 and 0R19 are equal to the long—term AA utility bond yield and CR1 is equal to the commercial paper yield plus % per cent. 20 years where ORZO and OR19 and 0R1 is equal to R 0 20 0R1/ 1r19 are equal to the long-term AA utility bond yield I the bank prime rate plus a per cent. 64 Interpretation of the Regression Model We are attempting to see if the Slope of the yield curve is useful in eXplaining the difference between a realized rate and a calculated breakeven rate. The signifi— cance of the Sign of the dependent variable was previously noted for use in debt maturity decisions. The regression results indicate two items for the analysis. First, the slope of the regression line, B1, indicates if the SlOpe of the yield curve conveys useful information with regard to possible debt cost reduction. Second, the regression line, B0 + BlZ, Should be able to Offer the debt manager more knowledge about Specific debt issue's alternatives. The regression results may be used within the multi-period decision model framework postulated. Statistically signifi- cant findings could be incorporated into the interest vector of the state space. Specifically, the interest rates within the 6; vector would be adjusted by the addition of the re- gression constant and the regression SlOpe estimate times the yield curve SlOpe: ei'n-j + (BO + B1(mRn — ij)). The process of dynamic programming would then elect the Optimal maturities based on the transformed state. For those deci— sions not made within the rigorous decision model, useful information is available. The regression estimates, based on the period tested, will indicate whether information is 65 contained by the yield curve lepe. For example, a signifi— cantly negative Bl estimate might cause a decision maker to question issuing a single-stage, long-term issue when the yield curve is sharply upward SlOping. Of course, the final decision rests with the debt manager. The regression will merely offer additional information so that the manager may make that decision with more confidence. Assuming linearity exists, the most important infor- mation is gathered from the sign of the B1 regression co- efficient. A B1 coefficient of zero indicates that the lepe Of the yield curve is of no importance in explaining differences in the dependent variable. A positive B1 coef— ficient indicates that as the yield curve SlOpe increases, the realized minus the breakeven rate increases positively. Thus, a positive Bl supports Malkiel's previously quoted statement that an issuer should increase long-term debt financing in periods of a sharply rising yield curve. Single-stage financing is advantageous with a sharply upward SlOping yield curve when the realized rate becomes greater than a breakeven rate as the yield curve SlOpe increases. A negative Bl indicates the dependent variable increases negatively as the independent variable increases. With increasing SlOpe of the yield curve, an issuer would tend to gain by financing in a two-stage process, financial risk 66 and transaction costs aside. The statistical significance of a B1 different from zero is tested by the "F" statistic. H0 B1 = O 1 HA . Bl # 0 The secular rise in the interest level for the time period may possibly bias results toward a positive B However, 1‘ the bias should be uniform with regard to the independent variable and therefore, affect the regression intercept, BO. On average the realized rate should equal the calcu— lated breakeven rate, liquidity premium aside. The break- even rate is dependent on the known yields of period n and period j which may be found from a yield curve of period m. As the n period increases the liquidity premium increases and causes the yield of mRn to increase. By observation of equation (9), the breakeven rate increases as the yield Of mRn increases. However, the realized rate of m+jRn-j has a shorter term to maturity than n and will include a smaller liquidity premium. Due to the above process B is expected 0 to be negative. The B0 should become more negative as the period of refinancing, n-j, becomes smaller and approaches the smallest period considered, one year. The general rise in interest levels over the period of consideration may dominate the liquidity premium effect and Show a less nega- tive (more positive) B0 than originally expected. The 67 significance of the regression intercept is tested by the "F" statistic. 2 2 If the B1 regression estimator points toward a financing plan based on the slope of the yield curve, an issuer would benefit by being able to predict the change in future yield curve lepes. As noted in Chapter one, Macaulay found that time money rates anticipated a seasonal rise in call money rates.15 Peaks and troughs in long-term rates should exist before those in short-term rates. Long-term rates are an average of future short-term rates. If the market can pre— dict short-term turning points, long—term rates should anticipate these short-term movements. However, Kessel found that when the liquidity premium is considered, the market is unable to predict turning points.16 Interest rates reach their peaks and troughs at the same point in time regardless of maturity. The prediction of interest rate turning points appear to be as difficult as the pre- diction of the interest rate level. Cagan noted that 15Macaulay, Op. cit., p. 36. 16Kessel, Op. cit., p. 92. 68 turning points are hard to pinpoint--even with hindsight.17 In addition, Cagan found that turning points of yields for different maturities have clustered closer to each other as time passes. Thus, a lead-lag relationship among rates is decreasing, if not already non-existent, and limits the ability to predict future yield curve slopes. All is not lost. The analysis is designed to assist the manager in debt decisions at a point in time and, as such, makes use of existing information. This analysis finds a historical perspective that may assist in proper debt maturity place- ment. Chapter three presents the results of the empirical test for governmental securities. 17Phillip Cagan, "Changes in the Cyclical Behavior of Interest Rates", reprinted in Essays_on Interest Rates, Vol. II, NBER General Series #93 (1971), pp. 3-34. CHAPTER III TEST OF HYPOTHESIS WITH YIELDS ON GOVERNMENT SECURITIES Introduction The Treasury is responsible for United States debt management and would be interested in potential for interest cost minimization through debt maturity placement. Public debt management takes as "given" the size of the debt and the general conditions prevailing in the money market. The func- tion of public debt management is to estab- lish the terms on which new issues are sold, and maturing public issues are refinanced. Public debt management means, then, making decisions concerning the types of public debt offered, the proportionate amounts of different debt forms to be used, the pattern of debt maturities, the pattern of debt ownership and determination of all other 1 general characteristics of the public debt. Different goals, sometimes of a conflicting nature, . . 2 . have been ascribed to Treasury Operations. First, the Treasury should fund debt to longer-term maturities 1Ansel M. Sharp and Bernard F. Sliger, Public Finance (The Dorsey Press, 1964), pp. 177-8. 2The Treasury goals mentioned are summarized from James M. Buchanan, The Public Finances (Richard D. Irwin, 1970), pp. 331-2. 69 70 whenever possible such that the mere physical burden of continually placing debt may be diminished. The maturity distribution of the debt has shortened almost steadily since the end of the Second World War.3 In 1946 56 per cent of the government debt was of a maturity greater than five years while in 1971 about 18 per cent was greater than five years.4 Thus, the Treasury must now go to the market more often to refinance retiring debt. Second, the Treasury should attempt to minimize the interest costs of govern- mental debt. While debt may be structured so as to minimize present interest costs, the Treasury must pay the "going rate" for its borrowing.5 Third, the timing and maturities of debt Should accommodate the needs of the various classes Of investors. The third goal may be considered a subgoal of interest cost minimization since accommodation allows lower interest costs than would otherwise be available. This goal reflects a possible explanation for the shorten- ing composition of public debt. Corporate Treasurers have become more sophisticated in short-term cash management and 3Tilford C. Gaines, Techniques of Treasury Debt Management (The Free Press of Glencoe, 1962), p. 266. 4Board of Governors of The Federal Reserve System, Historical ChartLBpok 1971 (New York, 1972), pp. 40-1. 5Gaines, Op. cit., p. 259. 71 have demanded safe, short-term investments. Fourth, and perhaps most important, the Treasury should secure an effective coordination between debt management and fiscal policies and the more general monetary policies of the Federal Reserve. Sharp and Sliger note the following: Public debt policy decisions, such as changing the pattern of maturities and ownership, determining the rate of interest,...may have economic effects which offset or foster the policy pursued by fiscal and monetary policies. Not all theorists feel the above mentioned policies should be followed by the Treasury with regard to public debt management. More Specifically, the goal of interest cost minimization is dependent upon the type of Treasury policy followed: countercyclical, pro-cyclical or neutral. Simons and the Committee for Economic Development (CED) both indicated that public debt Should be used as a countercyclical monetary device. Simons took as given the structure Of debt but altered the absolute size of the debt. Consols were to be issued in times of inflation (high interest level) and to be purchased in times of deflation 6Sharp and Sliger, Op. cit., pp. 178-9. 7The alternative Treasury theories of debt manage- ment are summarized from William E. Laird, "The Changing Views of Debt Management," Quarterly-Journal of Economics and Business, Vol. 3 (Autumn, 1963), pp. 7-17. 72 and economic stagnation (low interest level). These Opera— tions in conjunction with the Federal Reserve would tend to reduce the liquidity and money supply in inflationary periods and increase them otherwise. Meanwhile, the CED took as given the Size of the debt, but altered the composi- tion of that debt. The debt was to be lengthened during periods of high interest and shortened in periods of low interest. Either of the countercyclical approaches has the impact Of increasing debt interest costs since long-term issues are increased when the interest level is highest. The pro-cyclical approach has been the policy most Often followed or at least mentioned as a normative Objec- tive by the Treasury. The debt should be "tailored to the market" and issued so as to minimize interest costs. Debt maturity would be lengthened during recessions and low interest rates and shortened during inflationary periods and high interest rates. The third approach has been one of neutrality for debt management. Friedman and Gaines both argue for a dependable system of financing whereby debt Operations would be "regular in timing, reasonably stable in amount and pre- dictable in form."8 Debt management would not be used for 8Milton Friedman, A Program forpMonetary Stability (FOrdham university Press, 1959), p. 65. 73 economic stabilization. Interest costs are neither an objective nor a constraint for the neutral approach. This brief background Of Treasury debt management provides a framework from which the results of this research may be placed. Interest cost minimization is the goal of this study. However, this should not be construed as a bias to a pro-cyclical Treasury approach. Rather, the study should be viewed in the perspective of the potential for interest cost minimization with regard to knowledge of a current yield curve lepe. These results may be useful to the Treasury if interest cost reduction continues to remain one of the several competing goals stated. Regard- less of Treasury objectives advocated, the study will further illuminate term structure theory and is useful within that construct alone. Ordinary Least Squares Empirical Results The following sections present and interpret the regression results based on governmental securities. The ordinary least squares regression Shows high positive auto- correlation as judged by the Durbin-watson d statistic. The time series is positively autocorrelated since the d statistic is less than the lower bound allowed. Kmenta comments: 74 However, if the test indicates autoregres- sion then we have some reason to be con- cerned. One reSponse is to re-estimate the equation, using one of the estimation methods designed for this situation (e.g. maximum likelihood or the two-stage procedure). Alternatively, we may take a second look at the specification of the regression model, since the autoregression of the disturbance may simply reflect the presence of some un- explained systematic influence on the dependent variable... Finally, if the result of the test is inconclusive we may or may not respond.9 Significant regression results could be used to alter the state space of the multi-period decision model. In par- ticular, the forward yield curve (a, would be modified as indicated in Chapter two. Optimal debt maturity decisions might be changed as a result of this state transformation. Changes in debt maturity decisions would identify poten- tially cheaper debt financing alternatives. In addition, the regression model indicates whether the yield curve SlOpe as defined predicts a realized yield minus calculated breakeven yield relationship. We identify cheaper debt financing plans with yield curve lepes for various periods and plans tested. It is important to remember that this identification assumes a position within the multi-period decision framework. 9Kmenta, op. cit., p. 296-7. 75 1952-71 Positive autoregression bias the variances of the regression estimators which invalidates testing of signifi- cance for those estimators. However, the B and the B O 1 estimates are non-biased and present useful information. Table 2 shows the results of the regression for govern- mental securities from 1952-71. To assist the interpreta- tion of results the financing plan of n=2 and j=l is used TABLE 2 RESULTS OF LEAST SQUARES REGRESSION FOR FINANCING PLANS 0F QUARTERLY YIELDS FOR GOVERNMENT SECURITIES: 1952-71 Financing Plan Observa- n yrs 3 yrs tions R B0 B1 Durbin-Watson d 2 l 76 -.146 .0005 -l.3219 .4080 5 1 76 -.058 .0011 -0.1563 .4535 5 2 72 -.054 .0026 -0.2271 .4386 5 3 68 -.l39 .0053 -l.0705 .4369 5 4 64 -.217 .0069 —3.8596 .3664 10 1 76 -.084 .0017 -0.0972 .4707 10 2 72 -.194 .0045 -0.3086 .4646 10 5 60 -.005 .0098 -0.0251 .2647 20 l 76 -.072 .0017 -0.0487 .4960 20 2 72 -.248 .0044 -0.2580 .4634 20 5 60 -.088 .0101 -0.2292 .1907 20 10 40 -.489 .0194 -2.7650 .4999 FA' yl‘ HIV-“ .' In \Doonu ..‘1 3.9: _:a: Oh? 5V. 76 as an example. The B0 = .0005 indicates that when the yield curve is flat, mRn - ij = .0000, the realized rate lies above the breakeven rate by .05 or five basis points. The B1 = -l.3219 indicates that the dependent variable be- comes less positive (more negative) as the slope of the yield curve increases. In particular, for every basis point increase in the yield curve slope, the realized rate minus breakeven rate declines by 1.3 basis points. The yield curve slope may be increased by an increase in mRn or a decrease in ij or a similar combination Of the two yields. The breakeven yield is calculated at the time of the yield curve Observation. Thus, the dependent variable becomes a function Of the change in the realized yield com- pared to a stationary breakeven yield. The relationship for n=2 and j=l is shown graphically in Figure 7. Based on the regression, two stage financing becomes more desir- able whenever the yield for two years is approximately 4 basis points more than for one year. The desirability of stage financing is dependent upon the location in the re- gression graph; top half for single—state, and bottom half for two-stage. From Table 2 note the regression constant B0 is positive for all financing plans. The realized rate should possess a smaller liquidity premium since the time remaining 77 FIGURE 7 GRAPHICAL EXPRESSION OF REGRESSION MODEL RESULTS e) K\ mRn - ij (Independent Variable) .0005 - 1.3219(mRn - ij) m+jrn-j_(Dependent Vari m+jRn-j h') H .u “I r} ..1 't1 filt- uvn " on 78 to maturity is n-j which is less than the entire n period. The general rise in interest rates over the 1952-71 period offsets the expected negative BO resulting from the liquidity premium effect. However, for a given j period the B0 be- comes greater as the n period increases. Equal number of Observations are possible between financing plans when the same j period is used.' The increasing BO estimates indi- cate the existence of an increasing liquidity premium for increasing maturity. The realized rate is greater as the n-j period increases for given j periods. In summary, the increasing trend of interest rates for the time period tested offsets the expected liquidity premium for any one financing plan but the liquidity premium may be Observed when various plans are compared. The regression slope B1 is negative for all financ- ing plans. As the lepe of a yield curve increases, the difference between the realized rate and the calculated breakeven rate increases negatively. Thus, a two—stage financing plan becomes more desirable as the yield curve SlOpe increases. The coefficient of correlation, R, is shown. The coefficient Of correlation measures the linear relationship between the dependent variable and the inde- pendent variable. The negative R indicates the Same inverse linear fit as does the negative Bl estimator. Considering 79 these statistics together note that as the B0 becomes more positive, the B1 estimate becomes more negative. This rela- tionship holds for a given n period plan as the j period increases with the exception of j=5 years. When j=5 years for a n period of both 10 years and 20 years, the R sta- tistic and the B1 estimator "fall out of line." A visual observation of yield curves indicates that more governmental yield curves are humped with peak equal to 5 years that any other period. This fact provides a possible clue to the difference in results with regard to humped and non-humped yield curves. A humped yield curve is defined as a curve where the highest yield occurs at a maturity other than the extremes of the maturities observed. When the basic regression is run on data where humped yield curve variables (30 of 76 data points) are removed, the re- sults are inconclusive. 1952-60 and 1961—71 Dividing the 1952-71 time period into two sub- periods of 1952-60 and 1961-71 uncovers interesting results. The Durbin-Watson d statistic of Table 3 shows the residuals remain autocorrelated and again usefulness Of the estimators is diminished. Particularly noteworthy is the uniform alternating of signs for the coefficient Of correlation 80 TABLE 3 RESULTS OF LEAST SQUARES REGRESSION FOR FINANCING PLANS OF QUARTERLY YIELDS FOR GOVERNMENT SECURITIES: 1952-60 AND 1961-71 Financing: Plan Observa- R B B Durbin- Period n yrs j yrs tions 0 1 Watson d 1952-60 2 l 36 .198 .0064 1.7286 .5960 1961-71 2 l 40 -.411 .0049 -4.1956 .4879 1952-60 5 l 36 .406 .0053 1.0497 .7415 1961-71 5 l 40 -.340 .0041 -1.0178 .4591 1952-60 5 2 36 .304 .0038 1.1317 .5904 1961-71 5 2 36 -.208 .0064 -0.9324 .5156 1952-60 5 3 36 .291 .0026 1.6643 .7405 1961-71 5 3 32 -.464 .0127 -4.ll97 .6081 1952-60 5 4 36 .130 .0014 1.5161 .8508 1961-71 5 4 28 -.504 .0155 -10.5226 .5441 1952-60 10 l 36 .362 .0018 0.3824 .6702 1961-71 10 l 40 -.298 .0030 -0.3933 .4321 1952-60 10 2 36 .207 .0003 0.2599 .4757 1961-71 10 2 36 -.317 .0068 -0.5742 .5049 1952-60 10 5 36 .446 .0030 1.2485 .5855 1961-71 10 5 24 -.219 .0182 -1.1694 .4734 1952-60 20 l 36 .341 .0007 0.2182 .5056 1961-71 20 l 40 -.223 .0024 -0.1731 .4976 1952-60 20 2 36 .079 .0014 0.0666 .3178 1961-71 20 2 36 -.316 .0060 -0.3754 .5659 1952-60 20 5 36 .395 .0046 0.5726 .3653 1961-71 20 5 24 -.371 .0166 -l.2403 .3496 81 between time periods. The correlation coefficient in- creased in absolute amounts from the aggregative period. In effect, single-stage financing becomes more desirable in the first decade as the yield curve lepes more sharply up- ward. Two-stage financing becomes more desirable during the second decade as the yield curve Slopes more sharply upward. However, these "cost benefits" cited are tenuous Since the significance Of the estimators cannot be tested because of autoregression. The last financing plan of n=20 and j=10 is not subdivided since realized yields are not available past 1971. The striking reversals of sign for the statistics between the two decades in Table 3 deserve additional com- ment. A different liquidity premium hypothesis may be applicable for each decade. The BO intercept of equation (11) identifies the point where the yield curve is flat with respect to maturity n and maturity j. The dependent variable is equal to the regression constant plus the re- gression slope times the yield curve slope which is zero where mRn = ij. Hence, the B0 intercept is the point identified with a flat yield curve. Generally, the yield curve is flat when the interest level is high with regard to a normal level. As such, the interest level may decline in the future as it tends toward normality. The money- 82 substitute hypothesis indicates the liquidity premium varies directly with the interest rates. Therefore, when the yield curve is flat and the interest level high, the liquidity premium is greatest according to the money- substitute hypothesis. However, the premium will decline as the interest level falls. The "normal" liquidity premium hypothesis indicates the liquidity premium varies inversely with the interest level. When the yield curve is flat and the interest level high, the liquidity premium is lowest according to the "normal" hypothesis. However, the premium will increase as the interest level falls. The B0 estimates are negative for the decade of the 1950's. When the interest level does fall the liquidity premium declines according to the money-substitute hypoth- esis. There is a greater probability that the realized rate will include a smaller liquidity premium and cause the dependent variable to be negative. The negative BO esti- mates coincide with that expected for the money-substitute hypothesis for the 1950's. This hypothesis agrees with the cyclical liquidity preference research of Kessel and Cagan over similar time periods. The B0 estimates become very much more positive for the decade of the 1960's. The liquidity premium increases as the interest level falls. There is a greater probability that the realized rate will .- -u...ru. ‘va-g—y—quam— .‘ ‘-_ '.' ~ . I ~ .11 _ ... _3£. ;' .,' I'thL, ‘ h 83 include a larger liquidity premium and cause the dependent variable to be positive. The positive BO estimates may substantiate the "normal" hypothesis for the 1960's. The positive B estimates may well be a result of the dramatic 0 rise in interest rates during the 1960's. The rising interest level would, of course, increase the realized interest yields over that expected. In any event, the evi- dence offered is weak since the standard deviations of the estimates are biased and inference making is limited. The autoregression must be reduced to an acceptable level to gain more satisfactory statistical results. Two-Stage Least Squares Empirical Results Rationale Several procedures exiSt to reduce the effect of autocorrelation on residuals such as maximum likelihood, first difference equations or two-stage least squares. Serial correlation indicates a disturbance in period t is not independent but, rather, dependent on period t—l. All three methods attempt to remove period t—l's effect from period t. The convariance, p, among time periods measures the relationship from period t—l to period t. The three lOIbid., p. 282-92. 84 techniques differ with regard to determination of the co— variance. The first difference equations method assumes p is equal to one and as such the resulting BO approaches zero. The maximum likelihood method attempts to locate that p which minimizes the variance of a random variable ut. The two-stage method uses a calculated p which makes it superior to the first difference equations since p may not, in fact, be equal to one. The two-stage method is nearly as efficient as the maximum likelihood method and facilitates ease of computation: hence, its use. The covariance may be calculated from residuals of a first-stage least squares re“gression as follows where et is the residual for period t: n 2 p = t=2 etet-l n z t=2 et-12 Normally, least squares' regressions assume that p is equal to zero. Once p is calculated, the value is used to reduce the serial disturbance. The logic £0110W3° For Period t the regression is: Yt : B0 ‘1" Blzt + at (15) and for period t-l the regression is: (16) Yt-l = Bo + Bth-l + et-l Multiplying (16) by p and subtracting from (15) results with: Y t r~ th_1 = B0(1-p) + B1(Zt - pZt_l) + (et - et_1) (17) ‘53...“ Wt“ a?“ “ ‘—_ fi“r‘:?:“‘-7~'.—ri‘jr—.-T a: 85 It may be shown that et - et-l = ut is normally and inde- pendently distributed.11 The basic assumptions of the ordinary least squares model are satisfied. The second stage least squares is run on the following equation: Yt - th_1 = BO(1-p) + Bl(Zt - pZt-l) + ut t=2,...,n (18) This second stage may be run if p is known. The coeffi- cient p is estimated from the residuals of the first stage regression. One observation, t=l, is lost from the second Stage regression and the resulting estimators are nearly BLUE. Table 4 shows the covariance p for the following selected financing plans: short-term, n=2 and j=l: inter- mediate-term, n=5 and j==l, n=5 and j=2; long-term, n=20 and j=l, n=20 and j=lO. The plans are representative of financing alternatives available to the government. How- ever, it must be remembered that a majority of Treasury financing is confined to short-term maturities, especially bills that carry a maturity less than one year. The re- sults are applicable to maturities greater than one year and the Treasury does finance with these maturities. Re- sults of Table 4 indicate that the assumption of p=0 or pal is false and serial correlation does exist. with esti- m . . ates of covariance known the second stage regreSSion of the two-stage least squares technique may be performed. \ llIbid.. p. 284. 86 TABLE 4 COVARIANCE AMONG RESIDUALS FROM FIRST- STAGE REGRESSION OF QUARTERLY GOVERNMENTAL YIELDS Financing Plan n yrs j yrs Covariance, p 2 l .7825 5 l .7551 ET; 5 2 .7445 E 20 1 .7124 E 20 10 .7519 , i] 1952-71 Results for the transformed two—stage least squares for: the time period 1952—71 are shown in Table 5. The estimates presented are for the transformed data as indi— cated by equation (18) . Therefore, both B0 and its Standard deviation must be corrected by the amount l/(l-p) £017 (estimates of a non-transformed nature. Since p is approximately equal to .75 for the government securities, the values for B0 and its standard deviation should be multiplied by a factor of approximately four. However. t}u3 F'statistic and the significance remain the same beQEUSe the numerator and the denominator are multiplied by a constant. The major objective Of the regression model 87 TABLE 5 RESULTS OF TRANSFORMED TWO-STAGE LEAST SQUARES FOR FINANCING PLANS OF QUARTERLY YIELDS FOR GOVERNMENT SECURITIES: 1952-71 Financing Plan Observa- 1 ‘I ,. ; ti yrs j yrs tions R B0 B1 Durbin-Watson d 2 l 75 —.125 -.0003 -0.7740 1.0942 5 l 75 -.035 .0001 -0.0852 1.2537 5 2 71 -.134 .0007 -0.4848 1.6446 (.0008) (.4330) (.384*) (.267*) 2(3 1 75 .045 .0003 0.0350 1.5291 (.0004) (.0918) (.403*) (.704*) 2C) 10 39 -.238 .0047 -1.0073 1.8920 (.0006) (.6759) (.001*) (.l45*) *Indicates the significance of the estimator based on the F test. is a test of parameters significantly different from zero. . 12 Thls may'be obtained from the transformed data as presented. However, if the regression estimates were statistically sig- nificant, the el' vector must be corrected using the non- traIlsformed data; the use of BO/(l-p) not BO as reported in t:he tables. The two-stage least squares does not elimi- natlea autocorrelation with two financing plans: n=2 and j=1. \ AH . 44 12The R statistic will also change when applied to -,,_.-—.. umm-.-——.—~ \._ __ .. . I .- . .' ‘WI _ '5 t 8}}3 non-trans formed data . QICDII model is predictive. n (3r1\feys little information. Since the intent Of the regres- ot explanatory, the R statistic r :. ... 43th . haw];— 88 n=5 and j=l. For these plans the d statistic is less than the acceptable lower bound at the one per cent level. For these two plans we may only note the best regression esti- mators not the variances. The serial correlation is re- duced to an acceptable level for the remaining plans. The standard deviations of non-biased estimates are noted F“. within parentheses. Where the assumptions of least squares have been met, the familiar F statistic is employed for the ’1” exit"? Tn-::.’fua—a~i- m determination of the significance of the B0 intercept and the B1 SlOpe. The SlOpe H 1- B = O 0 ' 1 H 1- B a o A ' 1 2 ._ The constant HO : BO - 0 2 The significance found is reported with an asterisk so that investigators may attach their own interpretation of the restilts. However, this study regards significance at the '1 level for expository purposes. The alpha level of .1 indicates a 10 per cent chance of rejecting the null hYF><>thesis H when, in fact, the null hypothesis is true 0 (tYpe I error) is accepted. In general, the results are non-significant at the '1‘ level. Significance is found only in the B0 intercept f . or n=20 and j=10 plan with a positive constant. This last 89 result leads the debt manager to prefer one long-term 20 year issue over two 10 year issues when the yield curve is flat or nearly so. The Significance of the one BO inter- cept may be a result of the rising interest structure of the 1960's. 1952-60 and 1961—71 The total period is again subdivided into sub- periods of 1952-60 and l96l-7l.13 Table 6 shows the results for the transformed data. Autocorrelation continues to exist for plan n=2 and j=l. From Table 6 note that only one estimator is significant; n=20 and j=l during 1952-60 with a positive Bl slope. This one statistic indicates that Single-stage financing becomes more desirable as the SlOpe of the yield curve increases. The forward interest Vec tor could be corrected on the basis of the regression model using non-transformed variables. Immediate long-term financing via a single-stage would be more greatly favored. Since the autoregression has been reduced to an acceptable 1eVel confidence exists for the non-significance of regres- sion estimators. Additional information is not uncovered \ ll. 4_l A deb 13For a review of the effectiveness of Treasury Re t management see Thomas R. Beard, "Debt Management: Its Relationship to MOnetary Policy, 1951-63," National Banking w, Vol. 2 (September, 1964), pp. 61-76. '-7_ A's-l.“ on. .'u 4. ‘1‘41 1 ..9' “ELL. 90 TABLE 6 RESULTS OF TRANSFORMED TWO-STAGE LEAST SQUARES FOR FINANCING PLANS 0F QUARTERLY YIELDS FOR GOVERNMENT SECURITIES: 1952-6O AND 1961-71 Financing Plan Observa- R B B Durbin- Period :1 yrs :1 yrs tions 0 1 Watson d 1952-60 2 35 -.098 -.0005 -0.5194 1.0721 1961—71 2 40 -.165 .0000 -l.3210 1.1894 1952-60 5 35 .138 -.0005 0.2879 1.4250 (. 0010) (. 3591) (. 648*) (.428*) 1961—71 5 40 -.212 .0005 -0.6201 1.2550 (.0010) (.4633) (. 631*) (.189*) 1952—60 5 35 -.043 -.0001 -0.1131 1.5024 (.0010) (.4494) (. 951*) (. 803*) 1961-71 5 36 -.219 .0013 -l.l372 1.6668 (.0012) (. 8699) (. 289*) (. 200*) 1952—60 20 35 .379 -.0002 0.2461 1.6483 (.0005) (.1047) (.591*) (.025*) 1961-71 20 40 -.169 .0005 -0.1564 1.5274 (.0005) (.1483) (. 365*) (. 298*) —\ i: Indicatzes the significance of the estimator based on the F test. rs.) ... an ‘.\.‘.’o"—I.. .41.; my”! .7' v}! .~ ,‘..‘~n“fs 'Q vt' - I 91 by eliminating the humped yield data points from the re- gression. Since the two-stage least squares reduced the effect of autocorrelation the testing of hypotheses is valid. However, based on the F statistic tests we cannot reject the hypothesis that B0 or B1 estimators are differ- ent from zero. The low coefficients of correlation (— - 17f the two financing plans. Hence, the resulting relation- Eflaip of realized minus calculated breakeven yield becomes nuare positive (less negative) and the cost advantage of the tnvo-stage issue diminishes. A two-stage least squares re- SIression might then be run on the corporate yield data com- Efiared with the new breakeven yield. While the above analysis a-ppears to be academically pleasing at this stage of devel— c>pment, the pragmatic usefulness for the corporate manager iss less obvious. The treatment for uncertainty involves a Errocess similar to utility preference theory.4 How much . 4Ralph O. Swalm, "Utility Theory-~Insights into Iilsk Raking," Harvard Business Review (November, 1966), pp. 123-36. I “‘9”! 109 should the discount rate be decreased to account for what degree of uncertainty? The implementation of the process involves many problems. However, the framework does pro- vide an area for additional study. Summary The two—stage least squares reduces positive auto- correlation to acceptable limits and the null hypothesis of the regression s10pe equal to zero may be rejected. A cor- sxoration may effect potential interest cost benefits by :financing via a multi-stage framework as a current yield (narve lepes more steeply upward. The information provided lay a yield curve lepe is ascribed to be a result of par- 1:icipant overreaction and market inefficiency. Multi-stage :Einancing increases financial risk of a firm since funding (Df debt must be accomplished more often. The increase in Ifinancial risk may be accounted by adjustment of the dis- Cnount rate used for the breakeven yield computation. Addi— tZional empirical research may be attempted as corporate iASSues for various maturities become available. CHAPTER V SUMMARY'AND IMPLICATIONS FOR FURTHER RESEARCH Summary Theories of Interest Rate Term fitructure and Yield Curve SlOpe This section summarizes the research technique, empirical results and interpretation of those results. The Summary section may be omitted without loss of continuity by the faithful reader of the previous four chapters. Im- Plications with regard to the theories of interest rate term structure and debt management applications are made. Several theorists have mentioned that debt interest cost benefits may be obtained by judicious timing of long-term issues based on the slope of a yield to maturity curve. This analysis represents a serious attempt to discover Vflaat information, if any, is contained within a yield curve SlOpe. If information has historically been contained in the lepe, use of that information may be profitably made in the future. Various theories have been proposed to explain the 110 111 interest rate term structure. The pure expectations theory implies long-term interest rates are a geometric average of expected future short-term rates. All interest rate move— ments are accounted for by the SlOpe of the yield curve. Accordingly, the expectations theory indicates that a par- ticular slope does not contain information applicable for E'W debt management. The liquidity preference theory implies a natural increase in interest yields as maturity increases. Implications for information contained by the lepe depend upon the liquidity preference hypothesis posited. The money-substitute hypothesis indicates the liquidity premium is greatest when the interest level is high and the premium is smallest when the interest level is low. When the interest level is high the SlOpe of the yield curve is flat or declining while the curve is upward sloping when the interest level is low. Accordingly, future liquidity premiums increase as the future interest level increases as implied by a present upward sloping yield curve. The future liquidity premiums decrease as the future interest level declines as implied by a present downward leping yield curve. Note the increase or decrease in the liquidity premium does not occur in the period the yield curve is observed. An upward sloping yield curve implies interest rates will increase as time passes. As the interest level 112 increases which is implied by an upward SlOping yield curve, the liquidity premium increases such that future realized yields are greater than expected. The converse is true for downward sloping yield curves. Alternatively, the "normal" liquidity premium hypothesis indicates the liquidity premium is greatest when the interest level is low. Thus, a down- ward leping yield curve indicates the future liquidity premium will increase as the future interest level declines as implied by a downward sloping yield curve. The converse is true for upward leping yield curves for the "normal" hypothesis. Either hypothesis of the liquidity preference theory implies information is contained by the slope since the premium changes with regard to the interest level. The institutional theory indicates that yield differentials are neither a function of expectations nor of liquidity prefer- ence but rather of supply and demand for a given maturity. The slope of the yield curve is inconsequential for poten- tial interest cost benefits according to the institutional theory. In summary, if information is contained by the yield curve lepe, market imperfections exist or one hypothesis of the liquidity preference theory is supported. If no information is contained by the lepe, the expecta- tions theory gains additional support. 113 Research Technique The research hypothesis is that the lepe of the yield curve contains information useful for debt management. Funds for a given amount of time may be financed through a single-stage issue or double-stage issue. Larger number of issues are possible but are not considered. A decision model minimizes debt interest costs by electing the Optimal debt maturities based upon the debt needs, debt maturity constraints and forecasted interest structure. If infor- mation is contained by the yield curve sIOpe, the interest vector of the issuer's state space may be profitably altered. The interest cost associated with a single-stage issue is known with certainty as is the first stage of a two-stage issue. Uncertainty and possible interest cost gain or loss exists with the yield realized for the second stage of the two-stage issue. By equating the present interest cost of the single-stage issue to the two-stage issue, a breakeven rate for the second stage may be calcu- lated. The realized future rate is compared to the calcu- lated breakeven rate. The slope of the yield curve is measured by the difference in yields between two different maturities at a point in time. Thus, the slope is the yield for a single—stage issue minus the SlOpe of a first stage of a two-stage issue. An ordinary least squares 114 regression is run between the realized yield minus the breakeven yield (dependent variable) and the sIOpe (inde— pendent variable) over time. The time period for analysis is 1952-71. Quarterly yields are analyzed for various governmental and corporate financing plans. Yields are Obtained from Salomon Brother's An Analytical Record of Yields and Yield Spreads. Time series regressions are subject to autoregression which invalidates hypothesis testing. Therefore, two-stage least squares is employed in order to reduce the autoregression effect. Multicollinearity is not a problem since only one independent variable is indicated. The regression estimate of the intercept B0 is expected to be negative due to the existence Of liquidity premiums. The realized rate for the second stage should contain a smaller liquidity premium since the time remain— ing to maturity is smaller. The liquidity premium changes with regard to maturity and over time--depending on the liquidity preference hypothesis. The general increase in the interest level over the period of 1952-71 does bias the results. The regression estimate of the slope B1 indicates which type of financing plan may benefit, if any, as the lepe of the yield curve changes. A B of zero indicates 1 no information is contained by the lepe of the yield curve 115 for prediction of the dependent variable. A negative Bl indicates two—stage financing becomes more favorable with an upward leping yield curve while a positive B1 indicates single-stage financing becomes more favorable with an up- ward sloping yield curve. Significance of the regression estimates is tested by the F statistic. Significant results 5' 3 would justify a change in the interest vector facing the % 27m! firm. A change in this state might allow a more Optimal debt maturity selection by a dynamic programming process 5 j 1 for the issuer. Empirical Results Governmental Autoregression as shown by the Durbin—Watson d statistic exists for the ordinary least squares regression for the governmental plans tested. Although hypothesis testing is invalid, interesting points exist from the re- gression estimates. Generally, the negative B regression l estimates indicate that a two-stage financing plan becomes cheaper with an upward sloping yield curve. The existence of increasing liquidity premiums with increasing maturities is substantiated. For a given first stage financing period (j), the regression intercept B0 increases as the time financing is needed (n) increases. The realized minus 116 breakeven relationship increases as the length of time remaining to be financed increases. Thus, the realized yield increases as the maturity increases which is what the liquidity preference theory indicates. More useful information is provided by subdividing the twenty year period into decades of 1952-60 and l96lé7l. Autoregression continues to exist and inference making is again limited. Striking reversals of sign exist between the decade of the 1950's and the 1960's in the regression estimates and the correlation coefficients. A single-stage issue becomes cheaper in the 1950's while a two-stage issue becomes cheaper in the 1960's as the yield curve slopes more positively. The existence of an increasing liquidity premium with increasing maturity shows for both time periods. However, different liquidity preference hypotheses may be at work for the two sub-periods. The BO intercept is nega- tive or less positive in the 1950's than it is in the 1960's. When the yield curve is flat at the B intercept, interest 0 rates are generally high and are expected to decline some- time in the future. As the interest rates do decline the realized rates include a smaller liquidity premium accord- ing to the money-substitute theory. Thus, the realized yield has a greater probability of being less than the breakeven rate and the fact is demonstrated by the results 117 for the 1950's. This hypothesis agrees with the cyclical liquidity preference research of Kessel and Cagan over similar time periods. However, during the 1960's the B0 regression estimate becomes much more positive. According to the "normal" liquidity premium hypothesis the premium is low when interest rates are high but increases as :17 interest rates decline. This fact would cause the realized rate to increase more than the breakeven rate at the point of a flat yield curve and is evidenced by the positive B O regression estimates for the 1960's. However, standard deviations of the estimates are biased and the evidence offered is weak. In most cases the two-stage least squares eliminates the effects of positive autoregression to acceptable limits and hypothesis testing is valid. Significance in regression estimates is lacking. This statistical evidence does not support the existence of information being contained by the sIOpe of the yield curve. Again, as noted by the ordinary least squares results, a liquidity premium exists for the sub-periods tested. The money-substitute hypothesis gains weak support for the 1950's and the "normal" hypothe- sis for the 1960's. However, the rapid interest level in- crease of the 1960's may explain the positive B regression O estimates, not the "normal" hypothesis. 118 In summary, the governmental results indicate knowl- edge of a yield curve lepe is immaterial for proper debt management. The null hypothesis of B1 equal to zero cannot be rejected and the expectations theory gains additional support. The yield curve lepe does not, by itself, exhibit any other information than expected. Weak evidence sup- ports the existence Of a liquidity premium and a change in the cyclical liquidity premium from the money-substitute hypothesis in the 1950's to the "normal" hypothesis in the 1960's. Results do not diaprove the institutional theory since relative supply and demand is not measured. Corporate Limited data exists for corporate maturities and only two plans are tested: a commercial paper alternative and a bank prime alternative where both issues are funded in year one by a nineteen year AA long-term Utility issue. The regression and the time period are similar to that tested for the governments. Autoregression exists for the ordinary least squares regression. Implications are similar to those of the governments. However, with regard to either the entire time period of 1952—71 or the sub- period decades, two-stage issues become cheaper as the slope of the yield curve increases. This is particularly .‘n-*. ".9.- .. (1‘44 _ ’2}: ‘ fp';}r.p . t’ueqk .. --‘4 119 interesting since the period is one of generally increasing interest rates which bias the regressions toward single- stage financing. The two—stage least squares eliminates positive autoregression to acceptable limits. The regression slopes of the corporates are negative and significantly negative 1“ rate—q —V ' ! ya! 3“.- in all periods except 1952-60 for the commercial paper i alternative. Two-stage financing is indicated for steeply upward leping yield curves. The regression intercepts are positive but not significantly different from zero. The regression intercept increases from the 1950's to the 1960's offering weak evidence for a change in the liquidity premium hypothesis. Knowledge of the yield curve slope offers potential interest cost reduction for the corporate financial manager. The existence of statistically significant negative B1 regression estimates have implications for the market perfection of corporate securities. The negative regres- sion slope may be explained by market participant over- reaction. For example, a sharply upward leping yield curve, long-term yields two per cent greater than short- term yields, indicates future interest rates are expected to increase. On the basis of this lepe corporations may attempt to increase long-term debt issues so as to avoid a 120 further yield increase. This increased demand for long- term maturities will generate additional pressure on the yield curve and increase the lepe. The slope may be in- creased by an increase in long-term rates or a decrease in short-term rates. For either case the calculated breakeven rate necessary for comparison with the second stage realized yield will increase. Thus, once market overreaction has subsided there exists a greater probability that the realized rate will be less than the inflated breakeven rate. A similar circumstance exists when the yield curve lepe is downward leping. Corporations would issue short- term debt until long-term rates do, in fact, decline. These actions tend to accentuate the negative SlOpe of the yield curve and decrease the calculated breakeven rate. The realized rate has a greater probability of being larger than the breakeven rate once market overreaction subsides. Therefore, a market overreaction phenomena may explain the corporate results and negative regression slope of this research. The results for the commercial paper alternative are much closer to the governmental results than the bank prime alternative. The commercial paper rate reflects mar- ket conditions much more rapidly than the administered bank prime rate. However, now that some banks tie the prime to 121 weekly movements in commercial paper yields, the effect may be pertinent only to historical debt needs. Market ineffi- ciencies increase the chance that information may be con- tained by a yield curve lepe. Application of Corporate Results Debt maturity decisions are not made on the sole basis of interest cost reduction. Maturity of debt repre- sents risk to the issuer. Shorter debt maturity carries a greater potential for economic loss and cash insolvency as a result of being unable to continually fund debt. Longer debt maturity carries a greater potential for an Opportunity loss from having unneeded long-term debt. Over the long run the maturity of debt should parallel that of its assets, although short run variations allow interest cost benefits. This analysis indicates a two-stage issue is most profit- able when the yield curve is steeply upward SlOping. A two-stage issue Offers the firm additional risk. First, the average maturity of debt is shorter and this in- creases potential for economic loss. Second, uncertainty remains with a realized yield of the second stage. Risk and uncertainty increase as the maturity of the first stage decreases. Average maturity of debt is smaller and any variations in the realized yield compared to expected yield 122 affect the firm for a longer period of time. Risk is also present for the single-stage issue: the risk future interest rates may decline which would make the single-stage issue more expensive. Risk may be accounted for by a utility preference adjustment for debt maturity in the original breakeven rate calculation. Risk may also be judged by discounting the expected present cost benefit (loss) and its standard deviation Over the debt need life relative to a single-stage issue. The expected present cost and standard deviation may be obtained from the regression estimates. The process allows the financial manager to make decisions on the basis of more information within a rational framework. An estimate may be made as to the prObability of the two- stage interest cost being less than the single—stage cost based on a given yield curve lepe. Implications for Additional Research Normative This research indicates governmental interest rate term structure may be explained by the expectations theory in addition to weak evidence Of a liquidity preference with regard to maturity. The cyclical liquidity premium is best explained by the money-substitute theory for the 1950's which substantiates other theorists' research. The liquidity lurl Ii. 0 L. 123 premium may be best explained by the "normal" hypothesis in the 1960's and offers a challenge to the previously support- ed hypothesis. As such, economists may wish to further ex- plore this apparent shift for the liquidity premium and its implications for a normative Federal debt management model. This research indicates the corporate debt manager 5‘ .1 ._.._.._. ' 'v.a may Optimize debt costs with respect to the slope of the yield curve. First, the research technique of this analysis should be continued for other possible debt maturities as h“? —~—r- —-—~.— -‘ ~—.——-T—- 13.5. .4. \ ..I. .Fr-t s'.vh.'. ...- !4 I sufficient information becomes available. Second, the em- pirical results of this exercise represent a small portion of necessary inputs for an Optimal debt policy. These results must be incorporated with existing research efforts for a more total corporate environment. This analysis ab— stracts from flotation costs and bond refunding which should be considered for a total representation of rational policy. A more Optimal policy with respect to issuing debt maturity appears possible. Given that interest costs are currently high we might expect two-stage financing to Offer greater rewards in the 1970's if the interest level declines to a more 1 I 0 normal range. However, a seeming paradox ex15ts. Future 1Lindley H. Clark, "The OuthOk". The Wall Street Journal, Vol. LII, No. 185, July 3, 1972, p. l. 124 rates are expected to decrease with a declining or flat yield curve. Based on this research a single-stage not a two-stage issue would be advantageous when the yield curve is flat or declining. Two-stage financing becomes cheaper when the yield curve is sharply upward leping which indi— cates interest rates are expected to increase. In general a firm would benefit by multi-stage financing when the interest level declines. In particular the existence of market overreaction offers the firm an additional area for potential interest cost reduction from debt maturity deci- sions and yield curve slope analysis. Positive The question of how corporations have actually placed debt maturity has not been addressed or answered. A positive study relating debt maturity and debt composition with regard to yield curve lepe appears to be in order. Have corporate financial managers responded in a manner similar to that Offered as more Optimal by this empirical research? Debt policy may be measured by either average debt maturity or debt composition: percentage of total debt placed in short—term (0—1 year), intermediate-term (1-10 years) and long-term (10 years and longer). For either or both debt policy definitions it is important to note l-_. m... ~m4nu.m-1 - an”; N‘Dx“\ ..l.‘ «w . o ‘ ' l 9‘ 125 reliance on creditor funds so as to avoid spurious correla— tions of those firms with very small or large total debt usage. A particularly intriguing point Of study is sales finance companies. These firms have the ability to quickly change debt policy in addition to possessing a large debt capacity. Utilities lie on the other side of the spectrum of firms with large long-term debt usage and, as such, pro- vide a good balance with sales finance companies for a posi— tive study of debt policy and yield curve analysis. ‘q‘rfllq‘wtnne ' 5‘"! 4.3 ss.:nn.mu..am ...-non” .5 The entire area of debt/equity study may be enhanced by recognition of maturity Of debt rather than total debt. Maturity of debt does affect the financial risk of the firm. Therefore, financial managers may be able to lower cost of capital by formally introducing debt maturity to the total debt component of a firm's capital structure. Recognition of debt maturity offers another dimension of risk to that of debt itself. Additional research is necessary fOr analyzing basic data used in construction of yield curves. Are the points generated for a yield curve plot similar in all but remain- ing term to maturity? Obviously, if this condition is not met impr0per empirical conclusions may result. Certain yield curve shapes such as the humped curve may not trully exist. Further rigorous examination of the assumptions 126 behind yield curve data points may prove especially useful. Government Implications for Yield Curve Analysis Government, in the most general sense of the word, may affect the basic interest rate term structure. The 1951 "accord" between the Treasury and the Federal Reserve marked the inception of modern public debt management. Under the accord, the Federal Reserve continued to ensure that the government would be able to finance its cash needs ”35‘“ while maintaining the Opportunity to promote economic sta- bility and growth through judicious use of its monetary policies. Without the Federal Reserves support for pegging of prices for public debt, the Treasury began to pay the "going rate" for its issues. No longer was the government yield curve static in shape and level from period to period. Flexible interest rate policies allow financial managers an Opportunity to time debt maturities so as to minimize interest costs. The Treasury has Often included interest cost minimization as a goal; increasing long-term issues in recessions and short-term issues in inflationary periods. However, these pro-cyclical Operations run counter to those monetary policies of the Federal Reserve: providing liquidity in recessions and restraint in inflationary periods. As a result, a neutral and more systematic debt management policy 127 is emerging as the guideline for Treasury management. How— ever, given that the Treasury is not fully certain of cash needs, an opportunity remains for partial interest cost minimization. Additional pursuit is deserving a policy that minimizes interest costs relevant to the uncertain Federal debt needs. Interest cost reduction, even in a . . xu-_“ -U’M . i partial sense, frees budget dollars for more worthwhile society demands. While this study does not statistically indicate the sloPe of a current yield curve is useful for [F .3 present value interest cost minimization, other variables may. These variables appear worthy of pursuit. Interest cost minimization need not be a historical relic nor need it run counter to the intent of a general neutral debt management policy. Meanwhile, private sectors of the financial com- munity are being encouraged to artificially restrain interest rate movement. More specifically, commercial banks are being asked to maintain and isolate bank prime rates from those of the more volatile market.2 The committee on interest and dividends feel that limiting bank prime in- creases will slow inflation. Artificial constraints by 2Edward P. Foldessy, "Interest Panel Warning Bankers to Keep Loan Charges Down or Face Rate Controls". The Wall Street JOurnal, Vol. CLXXX, No. 88, November 6, 1972, p. 3. 128 government affect current interest rates and the perception of future interest rate term structure. The financial man- ager must be able to anticipate governmental interference with regard to calculating a forward interest rate vector. The corporate data of this study may be inapprOpriate for future use given potential governmental intervention. A definite need exists for a more general qualitative and quantitative analysis of government Operations on interest rate term structure for corporate and governmental secu- rities. Conclusion In conclusion, this study has attempted to see if information is contained within a yield curve's Slope. The government market was more orderly and information contained by the lepe is that anticipated by a combination of the expectations and the liquidity preference theory. Addi- tional research may be warranted for a study of a possible shift of the cyclical liquidity premium of governments be- tween the decade of the 1950's and the decade of the 1960's. Initial evidence supports the fact that information was present and may be usefully applied for a corporate finan— cial policy. Additional research is warranted for both normative and positive implications of corporate debt 129 maturity management and yield curve analysis. A continuing study of the financial return and risk for debt maturity is necessary. Finally, the impact of different government Operations on the term structure must be ascertained. The existence of market imperfections resulting from participant overreaction allowed the astute financial manager a chance to lower the overall cost of creditor funds. SELECTED BIBLIOGRAPHY SELECTED BIBLIOGRAPHY Books Baxter, Nevins D. The Commercial Paper Market. Bankers Publishing Company, 1966. Board of Governors of the Federal Reserve System. 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