'- ' THE RISKLESS RATE OF RETURN IN RISK PREMIUM STUDIES. Eugene F~ Brigham and Di1ip K. Shame

Transcription

1 '- ' THE RSKLESS RATE OF RETURN N RSK PREMUM STUDES Eugene F~ Brigham and Di1ip K. Shame May 1980

2 THE RSKLESS RATE OF RETURN N RSK PREMUM STUDES EugeneF. Brigham and Dilip K. Shome Public Utility Research Center University of Florida May 1980 PURC Working Paper No. -80

3 -1- One question that rises immediately in a study of risk premiums is the best choice for the riskless rate. The principal alternatives are (1) the rate on short-term u.s. Treasury securities (Treasury bills) and (2) the rate on long-term Treasury bonds. Both types o~ securities are free of default risk, but neither is completely riskless because both are exposed to interest rate risk (the risk of a decline in the value of the outstanding bonds as a result of an increase in interest rates) and to purchasing power risk (the risk of a decline in the real value of interest and principal due to an increase in inflation). Long-term bonds are more exposed to both interest rate and purchasing power risk than are Treasury bills and other short-term government debt. Therefore, bills are closer to being truly riskless than are bonds, and for this reason a number of people have argued that risk premiums on common stocks should be based on bills rather than on Treasury bonds~l However, there is a fundamental problem with basing common stock riskpremiums on short-term Treasury bills, namely, the fact that bill rates are subject to short-term phenomena that do not affect long-term rates, or at least affect long-term rates differently. First, consider inflation. Nominal security returns are equal to a pure rate of This is particular-ly true of advocates of the CAPM. See Willard T. Carleton, "Comment on the Use of the CAPMin Public Utility Rate Cases," Financial Management, Autumn 1978, pp. 57-S9,for a more complete development of this point. Carleton noted the points we expressed below and strongly opposed using bills in common stock risk premium studies.

4 -2- return (RR), plus a premium for expected inflation (P), plus a risk premium (RP), plus an error term (e) which reflects random market factors which cause temporary disequilibrium: Nominal expected return = RR + P + RP + e. (1) There is no reason to think that RR will be different for Treasury bonds or bills, but there is a very good reason to think that P, RP, and e will be different for bonds versus bills. First, P reflec~s expected inflation over the life of th.e security. Therefore, the yield on a 3D-day Treasury bill reflects expected inflation during the next 30 days, while the yield on a 30-year bond reflects the average rate of expected inflation over the next 30 years. short-term inflation rates are rarely identical. For Long and example, in May, 1980, the long-term expected inflation rate (average rate over the next 5 to 10 years) is generally regarded as being in the 8 to 9 percent range, but the short-term (1 year) expected rate is about.12 percent. Thus, long and short-term interest rates are often quite different, as they are in theu. s. today. Also, because short-term inflationary.expectations are more volatile than long-term inflation, short-term interest rates are much more volatile than long-term-interest rates. The risk premium, RP, also differs between bills and bonds: Because of their much greater exposure to interest rate and purchasing power risk, bonds have a larger "liquidity risk premium" than do bills. Finally, consider the "error term."

5 -3- Random movements in interest rates are caused by such factors as the current level of corporate liquidity, Federal Reserve monetary policy, u.s. Treasury surpluses or deficits, and the activity of,foreign and domestic currency dealers and speculators. These random movements are probably larger (in either a positive or a negative direction for bills than for bonds because bills are the securities that the Treasury, the Federal Reserve, corporate treasurers, and currency dealers and speculators all use.in their normal operations. The larger error term for bills also helps explain why bill rates are so much more volatile than bond rates. Now consider the implications of all this for the choice of short-term or long-term government debt instruments as.the basing point in a study of common stock risk premiums. We are seeking a risk premium which can be added to the current observed and quoted market rate on debt securities which can then be used to obtain an estimate of the current cost of equity capital. Bonds and common stocks are both long-term securities, so their returns should reflect long-term inflation. Further, neither type of security is used as an instrument of monetary policy, or by currency speculators, or asa buffer for temporary changes in corporate liquidity, or by international currency speculators. Treasury bills are, of course, used for all these purposes. Therefore, it is far more logical to think that the cost of common equity is correlated with interest rates on long-term

6 bonds than with those on bills, and for this reason we based our common stock risk premiums on long-term bonds rather than on short-term bills. The Government Bond Rate There are a number of different issues of long-term Treasury securities, and they sell at different premiums or discounts depending on their coupon interest rates. -4- Further, certain deep discount, or "flower" bonds, sellon a lower yield basis because they may be surrendered at par value to pay estate taxes. (These bonds are called "flower bonds" because they are associated with funerals.) n other words, a $1,000 par value, 3 percent coupon, 20 year bond would have a theoretical value of $505 if the going rate of interest on 20 year government bonds were 8 percent, but to a wealthy individual with terminal cancer and a one-month expected life, the bonds would be worth approximately $1,000 because they could be used to pay $1,000 of estate taxes. Therefore, these bonds sell at high prices, and their yields are far below the yields on new bonds that.sel1 at close to their par value. Because of the flower bond phenomenon, indices of U.S. Treasury bond yields may be distorted, so one must exercise care in selecting the best index. Our choice was the U.S. Treasury "Constant Maturity Series," which gives relatively

7 -5- little weight to flower bonds. l This particular series has been published in the Federal Reserve Bulletin since 1977; earlier editions of the FRB used a series that was heavily weighted with flower bonds. To get some idea of the effects of including flower bonds, consider the following set of data for the period 1973~1975: Long-term Treasury Bond Yields As reported in the FRB during the 'year in question Difference % 7.12% '0.82% Average 1.03% Using the yield data as reported in the Federal Reserve Bulletin would have resulted in an overstatement of the risk premium of approximately one full percentage point. Because the constant maturity series prior to 1977 is not readily available, a set of tables, and a memo describing the series prepared by the Federal Reserve Board staff, is attached her~with as Appendix A. We also show, as Appendix B, yield differentials on various types of bonds from 1960 through lf flower bonds were used in the series, the effect would be to lower the reported yield on long-term governments and,therefore, to increase the reported risk premiums. Since we have chosen a series 'which excludes these bonds, our calculated risk premiums are smaller than would otherwise be the case.

8 -6- APPENDX A ATTACHMENT TO THE H.15 AND G.13 STATSTCAL RELEASES 4/19/77 nformation About the Treasury Constant Maturity Yield Series Yields on Treasury securities at constant maturity are constructed by the Treasury Department, based on the most active1y traded marketable Treasury securities. To obtain these yields, personnel at the Treasury Department construct a yield curve each day (see below), and yield values are then read from the curve at fixed maturities. -- presently 1,2,3, 5, 7, 10,20, and 30 years. By this technique, a yield may be estimated for, say, the 5-year maturity, even if no outstanding marketable Treasury issue currently has exactly 5 years remaining to maturity. Jj Constant maturity yields have been constructed by the Treasury Department since 1962 for maturities of 1,3,5, 10, and 20 years. The 7-year series was begun in July 1969; the 2-year series, in June 1976; and the 30-year series, in February The Federal Reserve Board has recently constructed comparable data for the pe"ri od Apri to December 1961, so that conti nuous month ly constant maturi ty yield series (averages of daily data) now exist for five of t~e maturities for nearly a 24-year period. Copies of the back data are attached. To construct a yield curve for any given day, the Treasury Department first plots the closing market bid yields of outstanding Treasury securities on a graph. (These yields are based on composite quotes reported by five U.S. Government securities dealers to the Federal Reserve Bank of New York. ) The horizontal axis of the graph shows the maturity date of each security, and the vertical scale measures the yield. A single, continuous yield curve is then drawn, either by hand or by computer, through the plotted points, with the heaviest weight given to the most recent, actively traded Treasury issues. n particular, very little weight is now given to the low-coupon, deep discount Treasury bonds commonly known as flower u bonds. A warning should be given in the.case of the 20-year constant maturity yield series. During the period from roughly May 1965 to January 1973, the 20-year yield series fell increasingly below what may be thought of as its Ucorrectll level. When it was returned to its "correctll level in January an upward correction of about 75 basis points was required. 2/ Jj y The yield curves constructed by the Treasury Department are used as a basic input, along with other market data, in estimating "the yield the Treasury would have to pay if it sold a new marketable security of given maturity. Between June 1965 and August 1971, the Treasury sold no new marketable securities which had more than 7 years to maturity (because of a 4-1/4 per cent Congressionally-legislated ceiling on all new Treasury bonds). Therefore, each yield curve constructed during that entire 6-year period was necessarily based -- at least in the long-term maturity area -- on low yielding Treasury securities issued prior to June Between March 1971 (When the 4-1/4 per cent ceiling was partially relaxed) "and the end of 1972, the Treasury sold five new bonds -- with maturities between 9-3/4 years and 15 years -- and a new 20-year Treasury bond was auctioned on January 4, Moreover, a number of new Treasury bonds have been sold since then. Based on this renewed flow of information about Treasury borrowing costs in the long-term area, the 20-year series has beenata higher, more "correct" level since January 4,1973.

9 Market Yields on U.S. Government Securities at Constant Maturity (Monthly averages of daily data, in per cent per annum) 1-yr 2-yrs 3-yrs '5-yrs 7-yrs 10-yrs 20-yrs 1-yr 2-yrs 3-yrs 5-yrs 7-yrs 10-yrs 20-yrs l.ill 1955 Jan. NOT AVALABLE Jan Feb.... NOT AVALABLE.. Feb Mar. NOT AVALABLE Mar Apr Apr May May 1.90' Jun Jun i Jul Jul Aug Aug Sep Sept Oct Oct ' J Nov Nov Dec Dec lli.6. Jan Jan Feb Feb Mar Mar Apr ' Apr M.ay May Jun Jun., Jul ~O 2.57 Jul Aug ' Aug , Sep , Sept Oct Oct Nov Nov Dec Dec "J:Tli" Sources: , Federal Reserve Board; 1962 to present, Treasury Department.

10 ... Market Yields on U.S. Government Securities at Constant Maturity (Monthly averages of daily data, in per cent per annum) 1-yr 2-yrs 3-yrs 5-yrs 7-yrs 10-yrs 20-yrs 1-yr 2-yrs 3-yrs 5-yrs 7-yrs 10-yrs 20-yrs Jan. 5., Jan. ' ~8 Feb Feb Mar Mar , Apr Apr , May May , Jun ' ;'06 Jun Jul Jul Aug ,.62 Aug , '8 050 Sept i Sep Oct Oct Nov Nov '~ Dec Dec lli 1976 Jan Jan Feb Feb ' 8.03 Mar Mar Apr Apr. ' May ' 8.14 Hay Jun Jun; Jul ' Jul Aug Aug. ' Sep ' Sep Oct ; :" Oct Nov Nov Dec Dec CT5 -T:86 Sources: , Federal Reserve Board; 1962 to present, Treasury Department. (X)

11 .- Market Yields on U.S. Government Securities at Constant Maturity (Monthly averages of daily data, in per cent per annum) 1-yr 2-yrs 3-yrs 5-,yrs 7-yrs 10-yrs 20-yrs 1-yr 2-yrs 3-yrs 5-yrs 7-yrs 10-yrs 20-yrs Jan Jan ' Feb Feb Mar Mar Apr Apr ~ 6.00 May May Jun _ Jun Jul. 7~60. ' Jul Aug Aug ' Sep Sep Oct '6~50 Oct ~ Nov Nov Dec Dec Jan Jan Feb Feb Mar ' Mar ~ Apr Apr May May Jun Jun Jul. 7.10, Jul Aug Aug S ep Sep Oct ~ Oct Nov Nov Dec Dec ~ Sources: , Federal Reserve Board; 1962 to present, Treasury Department.

12 t. Market Yields on U.S. Government Securities at Constant Maturity (Monthly averages of daily data, in per cent per annum) Jan Jan Feb Feb Mar ' Mar Apr Apr May May Jun Jun ; ~ Jul Jul Aug Aug Sep Sep Oct Oct ' 0 Nov Nov Dec Deco Jan Jan, Feb Feb Mar Mar Apr Apr May May ;>5 Jun Jun Jul Jul Aug Aug Sep Sep Oct Oct Nov Nov Dec Dec Sources: ZClr , Federal Reserve Board; 1962 to present, Treasury Department.

13 :Harket Yields on U.S. Government Securities at Constant Maturity (Honth1y averages of daily data, in per cent per annum) 1-yr 2-yrs 3-yrs 5-yrs 7-yrs 10-yrs 20-yrs 1-yr 2-yrs 3-yrs 5-yrs 7-yrs 10-yrs 20-yrs Jan Jan Feb Feb Mar Mar Apr Apr May May Jun Jun Jul Jul ' Aug Aug Sept Sept Oct Oct Nov Nov Dec Dec Jan Jan Feb Feb Mar Mar Apr Apr May May Jun Jun Jul Jul Aug Aug Sep Sept Oct Oct Nov Nov Dec Dec ' -' Sources: , Federal Reserve Board; 1962 to present, Treasury Department.

14 ". Market Yields on U.S. Government Securities at Constant Maturity (Monthly averages of daily data, in per cent per annum) Jan Jan Feb Feb Mar , Mar , Apr Apr May May " Jun Jun ~. 52 ' Jul ' Jul Aug Aug Sept ~ Sept ' 4.29 Oct Oct ' 4.72 ' ~ N Nov Nov ~0 Dec Dec ~ Jan Jan Feb Feb. 4., Mar Mar Apr ,, Apr May May Jun Jun Jul Jul Aug Aug Sept Sept Oct Oct Nov Nov Dec ' Dec ' :L..2L 1":48" Sources: , Federal 'Reserve Board; 1962 to present, Treasury Department.

15 Market Yields on u.s. Government Securities at Constant Maburity (Monthly averages of daily data, in per cent per annum)

16 Appendix B. YELD DFFERENTALS ON VAROUS TYPES OF BONDS (Average of Monthly Values) GOVERNHENT BONDS UTLTY BONDS YELD SPREADS :ace.... AAA SHORT LONG -L.T. AA A BBB A BBB BBB YEAR TERN TERN AAA AA A BBB GOVT'S -AAA -AAA -AAA -AA -AA -::.A / ~ , lch ~72.52 AVERAGE STANDARD DEVATON Source: Standard & Poor, Security Price ndex, 1979.

17 Figure B-1 RSK PREMUMS ON TRPLE B BONDS BBB-AAA % Spread: Baa-Aaa... U q