The Market Risk Premium: Expectational Estimates Using Analysts' Forecasts

Robert S. Harris and Felicia C. Marston

Us ing expectatwnal data from f711a11cial a 11 a~r.11s. we e~ t ima t e a market risk premium for US stocks. Using the S&P 500 a.1 a pro1·1•.fin· the market portfolio. the Lll'erage market risk premium i.lfound to be 7. 14% abo1·e yields on /o11g-ter111 US go1·ern 111 e11t honds m·er the period I 982-l 99X. This ri~k premium 1•aries over time; much oft his 1·aria1io11 can he explained by either I he /e1 1el ofi11teres1 mies or readily availahle fonrard-looking proxies for ri.~k . Th e marke1 ri.1k p remium appears to 111 onz inversely with gol'ern111 e11 t interes1 ra/es .rngges1i11g Iha/ required rerurns 011 .~locks are more stable than interest rates themse!Pes. {JEL: GJI. G l 2]

Sfhc notion of a market ri sk premium (th e spread choice has some appealing chara cteri sti cs but is between in vestor required returns on safe and average subject to many arb itrary assumptions such as the ri sk assets) has long played a central rol e in finance. 11 releva nt period for tak in g an average. Compound ing is a key factor in asset allocation decisions to determine the difficulty or usi ng historical returns is the we ll the portfolio mi x of debt and equity instruments. noted fa ct that stand ard model s or consum er choice Moreover, the market ri sk premium plays a critica l ro le would predi ct much lower spreads between equity and in th e Capital Asset Pricing Model (CAPM ), the most debt returns than have occurred in US markets- the widely used means of estimating equity hurdle rates by so ca lled equity risk premium puzzle (sec Welch, 2000 practitioners. In recent years, the practical signifi ca nce and Siegel and Thaler, 1997). ln addition. theory call s of estimating such a market premium has increased as fo r a forward-l ook in g risk pre mium th at could well firms, financi al analysts. and in vestors empl oy fin ancial change over time. fram eworks to analyze corporate and in vestment This paper takes an alternate approach by usin g pe rform ance. For in s tance. th e increased use of expectational data to estimate the market risk premium. Economi c Value Added (EVA') to assess corp orate The a pproach has two major advantages for prac titioners. First, it provides a n independ ent performance has provided a new impetus for estimating estimate that can be compared to historical averages. capital costs. Al a minimum. this can help in understanding likely The most prevalent approach to estimating the market ranges for risk premi a. ccond, expectati onal data al low ri sk premium relies on some average of the historical in vestigation of changes in risk premia over time. uch spread between returns on stocks and bonds. 1 This time variations in risk premia serve as important signal s from investors th at should affect a host of financia l ·Robcn S. lla rr i ~ is 1he C. Ste\\ an Sheppard Professor of Business decisions. Th is paper provides new te ts of whether Administration and l·chcia C. Ma rston 1, an Associate l'mfcs,or changes in ri k premia over time are li nked 10 forward­ a1 1hc Uni' crsi1y of Vi rg in ia. Charlo1tcsv11lc. VA 22906. looking measures of ri sk. Specifica ll y, we look at the The a uthors tha nk Eri k Bcnrud. a n ano nymous re\ icwcr. and ,cmin a r participants a l the Universi ty or Vi rgi n ia. th e 113 run.:r. Ea des. Ha rris. a nd Higgins ( 1998) pro1 idc suncy University of Con nec tic ut and a 1 the SEC for co m ment~. c1 idene.: on hoth te\thuo1' advice and prac11110ncr 111c1hods T ha n!..;, to Darden Sponsors. TVA. the Walker Family Fund, for es11n1:11111g c.:a1lital eos1s. As tcs1:1n11.:n1 10 1hc market for and Mcintire A~'ociatco, for sup port t•I' this research and 10 cost of c;1p11al estimmc'. lbho1,on Assm:1a1cs ( 1998) publishes IBF.S, Inc. fo r s upplying data. a "( 0,1 of Capital Quarterly.''

6 OPC 002716 FPL RC-16 HARRIS & MARSTON-THE MARKET RISK PREMIUM 7 relationship between the risk premium and four ex­ et al. ( 1998) point out, few respondents cited use of ante measures of ri sk: the spread between yields on expectational data to supplement or replace hi storical corporate and government bonds, consumer sentiment ret urns in estimating the market premium. about future economic conditions, the average leve l Survey evidence also shows substantial variation or dispersion across analysts as they forecast in empirical es tim ates. When respondents gave a corporate earnings. and the implied volatility on the precise estimate of th e market premium, they cited S& P500 In dex derived from options data. figures from 4% to over 7% (Bruner et al., 1998). A Section I provides background on the estimation of quote from a survey respondent highl ights the range equity required returns and a brief di sc ussion of in practice. " In 1993, we polled various investment current practice in estimating the market ri sk premium. banks and academic studies on the issue as to th e In Section II , models and data are discussed. Following appropriate rate and got anywhere between 2 and 8%, a comparison of the results to historical returns in but mos t we re between 6% and 7.4%." (Bruner et al.. Secti on 111. we examine the time-series characteristics I 998 ). An informal sampling of current practice also of the estimated market premium in Section IV. Finally, reveals la rge differences in assumptions about an conclusions are offered in Section V. appropriate market premium. For instance, in a 1999 application o f EVA analysis, Goldman Sachs I. Background In vestment Research specifics a market risk premium of"3% from 1994-1997 and 3.5% from I 998- l 999E for The notion of a ··market" required rate of return is a the S&P lndustrials" (Goldman Sachs, 1999). At the conveni ent and widely used construct. Such a rate (k) same time, an April 1999 phone call to Stern Stewart is the minimum level of expected return necessary to re vea led that their own applicati on of EVA typically compensate investors for bearing the average risk of employed a market risk premium of6%. In its application equity investments and receiving dollars in the future of the CAPM. Ibbotson Associates ( 1998) uses a market rather than in the present. In general. k wi ll depend on risk premium of7.8%. Nol surprisingly, academics do not returns available on a lternative investments (e.g., agree on the ri sk premium either. Welch (2000) surveyed bonds). To isolate the effects of ri sk, it is useful to leadin g financial economists at major universiti es. For a work in terms of a market risk premium (rp), defined as J O-year horizon, he found a mean ri sk premium of 7. I% but a range from 1.5% to 15% with an interquartile range Ip = k - i, ( I ) of2.4% (based on 226 responses). To provide additional insight on estimates of the where i = required return fo r a zero ri sk in ve tment. market premium , we use publicly avail able Lacking a superior alternati ve, in vestigators often expectational data. This expectational approach use averages of hi storical reali za tio ns to estimate a employs the di vidend growth model (hereafter referred market risk premium. Bruner. Eades. Harris, and Higgins to as the discounted cash now (DCF) model) in which ( 1998) provide recent_s urvey results on best practices a consensus measure of financial analysts' forecasts by corporati ons and financial advisors. While almost (FAF) of earnings is used as a proxy for in vestor all respondents used some average of past data in expectations. Earlier work has used FAF in DCF mode l s ~ estimatinu a market risk premium. a wide range of but generall y has covered a span of only a few years approaches emerged. "While most of our 27 sample due to data avai la bi lity. compan ies appear to use a 60+ year hi stori cal peri od to estimate returns, one cited a window of less than II. Models and Data ten years, two cited windows of about ten years, one began averaging with 1960, and another with 1952 data" The simplest and most commonl y used version of (p. 22). Some used arithmetic averages. and some used the DCF model is employed to estimate shareholders' geometric. Thi s hi stori cal approach requires the required rate of return, k, as shown in Equation (2): assumptions that past reali zati ons are a good surrogate for future expectations and, as typically app li ed. that th e risk premium is constant over tim e. Carl eton and :sec Malkicl ( 1982), Orighum, V in ~o n. an d Shorn.: ( 1985), Lakoni shok ( 1985) demonstrate empirica lly some of the Harris ( 1986), a nd Ha rris and Ma rston ( 1992). The DCF problems wit h such historical premia when th ey are approach w ith analysis· forecasts has been used frequently in disaggregated fo r different time periods or groups of reg ulator) settings. Ibbotson Associates ( 1998) use a varia nt firms. Siegel ( 1999) cites additional problems of using of the DCF mode l "ilh forn ard-lool..ing gro\\ th rate~; however. they do this as a separate tech nique nnd not as part of the hi storical returns and argues that equity premium C APM For their CAPM esllmntt:s. I hey UM! his1orical averages e ti mates from past data are likely too hi gh. As Bruner for the market ri sk premium.

OPC 002717 FPL RC-16 8 JOURNAL OF APPLIED FINANCE - 2001

a market required rate of return is calculated using (2) each dividend-paying stock in the S& P500 index for which data are available. As additional sc reens for re liability ofdata , in a given month we eliminate a firm where D, = dividend per share expected to be received if there are fewer than three analysts' forecasts or if at time one, Pn=c urrent price per share (time 0), and g the standard deviation around the mean forecast = expected growth rate in dividends per share.3 A exceeds 20%. Combined, these two screens eliminate primary difficulty in using the DCF model is obtaining fewer than 20 stocks a month. Later we report on the an estimate of g, since it should reflect market sensitivity of the results to various screens. The DCF expectations of future performance. This paper uses model in Equati on (2) is applied to each stock and the published FAF of long-run growth in earnings as a results we ighted by market value of equ ity to produce proxy for g. Equation (2) can be applied for an the market-required return. The risk premium is individual stock or any portfolio of companies. We constructed by subtracting the interest rate on focus primarily on its application to estimate a market government bonds. premium as proxied by the S&P500. We weighted 1998 results by year-end 1997 market FAF comes from IB ES Inc. The mean value of va lues since the monthly data on market value did not individual analysts' forecasts of five-year growth rate extend through this period. Since data on firm-specific in EPS is used as the estimate of gin the DCF model. dividend yields were not avai lable for the last four The fi ve-year horizon is the longest horizon over which months of 1998 at the time of this study, the market such forecasts are avai lable from IBES and often is the di vidend yield for these months was estimated using longest horizon used by analysts. I BES requests the dividend yield reported in the Wall Street Journal "normalized" five-year growth rates from analysts in scaled by the average ratio of this figure to the order to remove short-term distortions that might stem dividend yield for our sample as calculated in the first from using an unusually high or low earnings year as eight months of 1998. Adjustments were then made a base. Growth rates are available on a monthly basis. using growth rates rrom !B ES to calculate the market Dividend and other firm-specific in formation come required return. We also estimated results using an average dividend yield for the month that employed from COMPUSTAT. D1 is estimated as the current indicated annual dividend times (/+g). Interest rates the average of the price at the end of the current and (both government and corporate) are from Federal prior months. These average dividend yield measures Reserve Bulletins and Moody's Bond Record. Exhibit I led to simi lar regression coefficients as tl1ose reported describes key variables used in the study. Data are later in the paper. used for all stocks in the Srandard and Poor 's 500 For short-term horizons (quarterly and annual), past stock (S&P500) index fo ll owed by IBES. Since five­ research (Brown, 1993) finds that on average analysts' year growth rates are first available from !BES beginning forecasts a re overl y optimistic co mpared to in 1982, the analysis covers the period from January realizations. However, recent research on quarterly 1982-December 1998. horizons (Brown, 1997) suggests that ana lysts' The approach used is generally the same approach forecasts for S&P500 firms do not have an optimistic as used in Harris and Marston ( 1992). For each month, bias for the period 1993-1996. There is very little research on the properties or five-year growth forecasts, as opposed to shorter horizon predictions. 'Our method• follow llarris ( 1986) and II ams and Marston Boebel (J 991) and Boebel, Harri s, and Gultekin ( 1993) ( 1992) who discuss earlier research and the approach employed here. including comparisons of single versus multistage growth examine possible bias in analysts' five-year growth models. Since analysts' forecast growth in earnings per share, rates. These studies find evidence ofoptimism in !BES their projections should incorporate the anticipated effects of growth forecasts. In the most thorough study to date, share repurchase programs. Dividends per share "ould grow at Boebel ( 1991) reports that this bias seems to be getting the same rate as EPS as long as companies manage a constant nitio of dividends to earnings on a per share basis. Ba!.ed on smaller over time. Hi s forecast data do not extend into S&P500 figures (sec the Standard and Poor's website for their the 1990s. procedures), the ratio or DPS to EPS was .51 during the period Analysts' optimism, if any, is not necessarily a 1982-89 and .52 for the pe riod 1990-98. Lamdin (200 I) problem for the analysis in this paper. If investors share discusses some issues if share repurchases destroy the equivalence of EPS and DPS growth rates. Theoretically, i is a analysts' views, our procedures will stil l y ield risk-free rate. though its empirical proxy is on ly a "least risk"' unbiased estimates of required returns and risk premia. altemati~e that 1s itself subject 10 risk. For instance. Asness In light of the possible bias. however, we incerpret the (2000) shows that over the 1946-1998 period, bond volatility estimates as "upper bounds" for the market premium. (in monthly reali7ed returns) has increased relati\e to stock volalil ity. which would be consistent wiih a drop in the equity This study also uses fou r very different sources to market premium. create ex ante measures of equity risk at the market

OPC 002718 FPL RC-16 HARRIS & MARSTON-THE MARKET RISK PREMIUM 9 Exhibit 1. Variable Definitions k = Equity required rate rewm.

Po Price per share. o, = Expected di vidend per share measured as current indicated annual dividend from COM PUST AT multiplied by ( l + g). g Average financial analysts' forecast of fi\•e-year growth rate in earnings per share (from IB ES).

= Yield to maturity on long-term US government obligati ons (source: Federal Reserve. 30-year constant maturi1 y series). rp Equity risk premium calculated as rp = k- i.

BSPREAD spread between yields on corporate and government bond5, BSPREAD = yield to maturity on long-term corporate bonds (Moody's average acros bond rating categories) minus i.

CON Monthly consumer confidence index reported by the Conference Board (divided by I 00).

DfSP Dispersion of analysts' forecasts at the market level.

VOL Volatility for the S+P500 index as implied by options data.

level. The first proxy comes from the bond market and around the mean of individual forecasts for that is calculated as the spread between corporate and company in that month. DISP also was estimated using government bond yields (BSPREAD). The rationale is a value-weighted measure of analyst dispersion for that increases in this s pread s ignal investors' the firms in our sample. The results reported use the perceptions of increased riskiness ofcorporate activity equall y weighted version but similar patterns were that would be translated to both debt and equity obtained with both constructions.5 Our final measure, owners. The second measure. CON, is the consumer VOL. is the implied volatility on the S&P500 index. As confidence index reported by the Conference Board at of the beginning of the month, a dividend-adjusted the end of the month. While the reported index tends Black Scholes Formula is used to estimate the implied to be around I 00, we rescale CON as the actual index volati lity in the S&P500 index option contract, which divided by I 00. We also examined use or CON as of ex pires on the third Friday of the month. The call the end of the prior month; however, in regression premium , exercise price, and th e level of the S&P500 analysis, this Jagged measure generally was not index are taken from the Wall Street Journal. and statistically significant in explaining the level of the treasury yields come from the Fede ral Reserve. market risk premium.4 The third measure, DISP, Dividend yield comes from DRI. T he option contract measures the dispersion of analysts ' forecasts. Such that is closest to being at the money is used. analyst disagreement should be positively related to perceived ri sk since hi gher levels of un certainty would Ill. Estimates of the Market Premium li kely generate a wider distribution of earnings forecasts for a given firm. DlSP is calculated as the Exhibit 2 reports both required returns and ri sk average of firm-specific standard deviations for each premia by year (averages o f monthly data). The stock in the S&P500 covered by IBES. Tbe firm-specific estimated risk premia are positive, consistent with standard deviation is calcu lated based on th e equity owners demanding additional rewards over and dispersion of individual analysts· growth forecasts above returns on debt securities. The average expectational ri sk premium ( 1982 to 1998) over 'We e xamined two o ther proxies for Cons umer Confidence. The Conference Board's Consumer Ex pectations Index yielded ~ Fo r the r egression s r eported in Ex hi bit 6, the value­ essentia ll y th e same results as th ose reponed. The University weighted dis p e rsion meas ure actually exh ibited mo r e of Michigan's Consumer Sentiment Indices tended to be less explanatory power. For regressions us ing the Prais-Winsten significantly linked to the mar ket ri s k premium, though method (see footnote 7), the coefficient on DI SP was not coefficients \I ere still negativc. signi ficant in 2 o f the 4 cases.

OPC 002719 FPL RC-16 10 JOURNAL OF APPLIED FINANCE - 2001

Exhibit 2. Bond Market Yields, Equity Required Return, and Equity Risk Premium, 1982-1998

Va lues are averages of monthly figures in percent. / is the yield 10 maturity on long-tem1 government bonds. k is the required return on the &P500 estimated as a value weighted average using a discoumed cash now model with analysis· growth forecasts. The risk premiu m rp = k - i. The average of ana lysts' growth fo recasts is g. Div yield is expected dividend per o; harc divided by price per share.

Year Div. Yield g k rp = k - i

1982 6.89 12.73 19.62 12.76 6.86

1983 5.24 12.60 17 .86 11. 18 6.67

1984 5.55 12.02 17.57 12.39 5.18

1985 4.97 11.45 16.42 10.79 5.63

1986 -1.08 11 .05 15. 13 7.80 7.34

1987 3.64 11.01 14.65 8.58 6.07

1988 4.27 11 .00 15.27 8.96 6.31

1989 3.95 11 .08 15.03 8.45 6.58

1990 4.03 11 .69 15.72 8.61 7.11

1991 3.64 11 .99 15.63 8.14 7.50

1992 3.35 12. 13 15.47 7.67 7.81

1993 3. 15 11 .63 14.78 6.60 8.18

1994 3. 19 11.47 1-1.66 7.37 7.29

1995 3.04 I I .S I 14.55 6.88 7.67

1996 2.60 11.89 14.49 6.70 7.79

1997 2. 18 12.60 14.78 6.60 8.17

1998 1.80 12.95 14.75 5.58 9.17

A11erage 3.86 11 .81 15.67 8..53 7.14 government bonds is 7. I 4%, sli ghtly hi gher than the Ex hibit 2 shows the estimated risk premium changes 6.47% average for I 982 to I 99 I reported by I larris and over time, s uggesting changes in th e market's Marston ( 1992). For comparison purposes, Ex hibit 3 perception of the incremental risk of investing in equity contains historical returns and ri sk premia. The average rather than debt securities. Scanning the last column expectati onal ri sk premium reported in Exhibit 2 is of Exhibit 2, the ri sk premium is higher in the 1990s approx imately equal to the arithmeti c (7 .5%) long-term than earl ier and especially so in late 1997 and 1998. di ffe rential between returns on stocks and long-term Our DCF results provide no evidence to support the government bonds.6 noti on of a declin ing risk premi um in the 1990s as a driver of the strong run up in equi ty prices.

" l n l crc~ting l y. for the 1982-1996 period the arithmetic ~pread A striking feature in Ex hibit 2 is the relative stabili ty between large company stocks and long-term go\ crnment or th e estimates of k. Afler dropping (along wi th bonds was on ly 3.3% per year. The down\\ ard trend in interest interest rates) in the early and mid- I 980s. the average rates resulted in average annual returns of 14. 1% on long­ annual value ofk has remained within a 75 basis po int term government bonds over thi s horizon. Some (e.g .. Ibbotson. 1997) argue that only the income (not total) return range around 15% fo r over a decade. Moreover, th is on bonds 'houlcl be: subtracted in calculating risk prcmrn. stability arises despite some variabi lity in the

OPC 002720 FPL RC-16 HARRIS & MARSTON-THE MARKET RISK PREMIUM 11

Exhibit 3. Average Historical Returns on Bonds, Stocks, Bills, and Inflation in the US , 1926-1998

Historical Return Realizations Geometric Mean Arithmetic Mean

Cornrron Stock (Large Col1l'Jlly) 11.2% 13.2%

Long-1cnn C1ovcrnn-x:n1Bonds 5.3 5.7

Trca,ury Bill-, 3.8 3.8

Inil at ion Rate 3.1 3.2 Source: lbbotslln Associates. Inc .. 1999 Srocks. 8011d~ . /111/s 1111d /11jla1io11 . 1999 Yenrbook.------

underlying dividend yield and growth components of IV. Changes in the Market Risk k as Exhibi t 2 illustrates. The results suggest thal k is Premium Over Time more stable than government interest rates. Such relative stability of k translates into parallel changes With changes in the economy and fin ancial markets, in the market risk premium. In a subseq uent secti on, equity investments may be perceived to change in ri sk. we examine whether changes in our market risk premium For instance, investor sentiment about future business estimates appear linked to interest rate conditi ons and conditions likely affects attitudes about the riskiness a number of proxies for risk. of equity investments compared to investments in the We ex plored the sensiti vity of the resul ts to our bond markets. Moreover, since bonds are ri sky screening procedures in se lecting compani es. The investments themselves. equity ri sk premia (relati ve reported results screen out all non-dividend paying to bonds) could change due to changes in perceived stocks on the premise that use or the DCF model is riskiness of bonds, even irequities di spl ayed no shifts inappropriate in such cases. The di vid en d screen in ri sk. eliminates an average of55 companies per month . In a In earlier work covering the 1982- 199 1 period, Harri s give n month, we also screen out firms with fewer than and Marston ( 1992) re po rt ed regression results th ree analysts· fo recasts. or if the standard deviation indicating that the market prem ium decreased with th e arou nd the mean forecast exceeds 20%. When th e level of government interest rates and increased with analysis is repeated without any of the three screens, the spread between corporate and government bond th e average risk premium over the sample period yields (BSPREAD). This bond yield spread was increased by only 40 basis points, from 7 .14% to 7.54%. interpreted as a time series proxy for equity ri sk. In The beta of the sample firms al so was estimated and this paper. we introduce three additiona l ex ante the sample average was one. suggesti ng that th e screens do not systematically remove low or hi gh-risk measures of risk shown in Ex hib it I: CON, DI S P. and fi rms. (Specifically, using lirms in the screened sample VOL. The three measures come from three independent as of December 1997 (the last date for which we had se1s of data and are suppl ied by different agents in the CRSP return data). we used ord inary least sq uares economy (consumers, eq uity analysts, and investors regressions to estim ate beta for each stock using the (via opti on an d share price darn)). Ex hibit 4 provides prior 60 months of data and the CRSP return (SPRTRN) summ ary data on all four of these ri sk measures. as the market index. The value-weighted average of the Exhibit 5 replicates and updates earlier analysis by 7 individual betas was 1.00.) Harris and Marston ( 1992). The results confirm 1he The results reported here use firms in the S& P500 as ea rlier pattern s. For the entire sample period, Panel A reported by COM PUSTAT in September 1998. Thi s shows that risk premia arc negati ve ly related to interest could create a survivorship bias, especially in 1he earlier rates. This negative relationship is also true for both months of the sample. We compared our current results to th ose obtained in Harris and Marston ( 1992) for "OLS regression> " ith le' eb of variables genera lly sho11 cd which th ere was data to upda te the S&P500 SC\ ere a utocorrelation. As a result. 11 c used Lhe Pra1s-Wins1c n method (on le,·els of variable>) and also OLS regressions on compositi on each month. For the overlapping period, fir,t differences of 'ariables. Since bmh methods yielded similar January 1982-May 1991, the two procedures yie ld the results and the latter had more stable coc1T1c1cn rs across same a\erage mark et ri sk premium, 6.47%. This specilications. we rcpor1 only the results us ing first ddTc:renccs. suggests that the firms departing from or enteri ng the Tests u~ 111 g Durbi n-Watson s tatistics from regressions in S&P500 index do so for a number of reasons with no l:.x h1 bits 5 and 6 do not accept the hypothesis of autocorrelarcd errors (tests al .01 s ignificance level. sec Johnston, 1984). discern able effect 0 11 the overall estimated S&P500 We ali.o cstimnred the first di fTcrencc model without an intercept market risk premi um. and obtained estimates almost idcnllcal to those rcponed.

OPC 002721 FPL RC-16 12 JOURNAL OF APPLIED FINANCE - 2001

Exhibit 4. Descriptive Statistics on Ex Ante Risk Measures Entries arc based on monthly data. BSPREAD is the spread between yields on long-term corporate and government bonds. CON is the consumer confidence index. DISP measures the dispersion of analysts· forecasts of earnings growth. VOL is the volatility on the S&P500 index implied by options data. Variables are expressed in decimal form, (e.g.. 12% = .12).

Panel A. Variables are Monthly Levels Mean Standard Deviation Minimum Maximum

BSPREAD .0123 .0040 .0070 .0254

CON .9504 .2242 .473 1.382

DlSP .0349 .0070 .0285 .0687

VOL .1599 .0697 .0765 .6085

Panel 8 . Variables are Monthly Changes Mean Standard Deviation Minimum Maximum

BSPREAD -.00001 .0011 -.0034 .0036

CON .0030 .0549 -.2300 .2 170

DISP -.00002 .0024 -.0160 .0154

VOL -.0008 .0592 -.2 156 .4081

Panel C. Correlation Coef{icie111s for Mo111hly Changes BSPREAD CON DISP VOL

BSPREAD 1.00 -.16** .054 .22*

CON -.16** 1.00 .065 -.09

DISP .054 .065 1.00 .027

VOL .22* -.09 .027 1.00

••Significantly d11Tercni from ?Cro nl the .05 level. •Significantly different from Lero at the .0 1 le,el. the 1980s and 1990s as displayed in Panels B and C. investing in equities as opposed to government bonds. For the entire 1982 lo I 998 period, th e additio n of the O ne striking feature is the large negative coefficients yield spread risk proxy to the regressions lowers the o n government bond yields. The coefficients indicate magnitude of the coefficient o n government bond the equity ri sk premium declines by over 70 basis yields, as can be seen by comparing Equations (I) and points for a I 00 basis point increase in government (2) of Panel A. Furthermore. the coefficient of the yield interest rates.8 This inverse relations hip suggests s pread (0.488) is itself significantly positive. T his pattern suggests that a reduction in the risk differential ' The Exhibit 5 coefficients on i arc signilicantl y different between investment in government bonds and in from -1. 0 suggesting that equity required returns do respond corporate bonds is trans lated into a lower equity lo interest rale changes. Ho..,.cvcr, the large negative coefficients imply only minor adjustments of required returns market risk premium. lo interest rate changes since the risk premium declines. In In major respects, the results in Exhibit 5 parallel earlier work (Harris and Marston. 1992) the coefficient was earlier findings. The market risk premium changes over significantly negative but not as large in absolute value. In that time and appears inversely related Lo government earlier work, \\e reported rc~u l ts using the Prais-Winsten estimators. When we use that estimation technique and recreate interest rates but is positively related to the bond yield the second regression in Exhibit 5. the coefficient for i is -.584 (1 s pread. which proxies for the incremental ris k of - - 12.23) for the enure sample period I 982- I 99R.

OPC 002722 FPL RC-16 HARRIS & MARSTON- THE MARKET RISK PREMIUM 13

Exhibit 5. Changes in the Market Equity Risk Premium Over Time The exhibit repons regression coefficients (1-values). Regression estimates use all variables expressed as monthly changes to correct for autocorrelation. The dependent variable is the market equity risk premium for the S&P500 index. BSPREAD is the spread between yields on long-tenn corporate and government bonds. The yield to maturity on long-term government bonds is denoted as i. For purposes of the regression, variables are expressed in decimal form, (e.g.. 12% = .12).

Time Period Intercept BSPREAD

A. 1982- 1998 -.0002 -.869 .57 (- 1.49) (- 16.54)

-.0002 -.749 .488 .59 (- 1.1 I) (- 11.37) {2.94)

8. 1980s -.0005 -.887 .56 (- 1.62) (- 10.97)

-.0004 -.759 .508 .57 (- 1.24) (-7.42) ( 1.99)

c. /990J -.0000 -.840 .64 (-0.09) (- 13.78)

-.0000 -.757 .347 .65 (0.01) (-9.85) ( 1.76)

Exhibit 6. Changes in the Market Equity Risk Premium Over Time and Selected Measures of Risk

The exhibit reports regression coefficients (I-values). Regression estimates use all variables expressed as monthly changes to correct for autocorrelation. The dependent variable is the market equity risk premium for the S&P500 index. BSPREAD is the spread between yields on long-tem1 corporate and government bonds. The yield to maturity on long-term government bonds is denoted as i. CON is the consumer confidence index. DISP measures the dispersion of analysts' forecasts of earnings growth. VOL is the volatility on the S&P500 index implied by options data. For purposes of the regression, variables are expressed in decimal form, (e.g .. 12% = . 12).

Time Period Intercept BSPREAD CON DISP VOL Adj. Ff

A. 1982-1998 (I) 0.(X)(}2 -0.014 0.05 (.97) (-3.50)

(2) -0.0001 -0.737 0.453 -0.007 0.60 (-.96) (-11.3 1) (2.76) (-2.48)

(3) O.CXl02 0.224 0.02 (.79) (2.38)

(4) -0.0001 -0.733 0.433 -0.007 0. 185 0.62 (-.93) (- 11.49} (2.69) (-2.77) (3. 13)

8. Muy 1986-1998 (5) 0.0000 -0.818 OA20 -0.005 0.378 0.68 (.06) (-11.21) (2.52) (-2.23) (3.77)

(6) 0.0001 0.0 11 0.05 (.53) (2.89)

0.0000 -0.831 0.326 -0.005 0.372 0.006 0.69 (.Cl2) (- 11.52) ( 1.95) (-2.12) (3.77) (2.66)

OPC 002723 FPL RC-16 14 JOURNAL OF APPLIED FINANCE - 2001 much greater stability in equ ity required returns than the average value of i for January, Februa ry. and March is often assumed. For instance. standard appli cation is subtracted from the March va lue of k. This approach of the CAPM suggests a one-to-one change in equity assumes that, in March, k stil l reflects values of g that returns and government bond yields. have not been updated from the prior two months. Ex hibit 6 introduces three additional proxies for risk The quarterly measure of risk premium then is paired and explores whether these variables. either with the average values of the other variables for the indi viduall y or collectively. are correlated with the quarter. For instance, the March 1998 "quarterly" risk market premium. Since the estimates of implied volatility premium wo uld be paired with averaged va lues of start in May 1986. the exhibit shows results lor both BSPREAD over th e January through March period. To th e entire sample period and for the period during whi ch avoid overlapping observations for th e independent we can introd uce all va riables. Entered indi vid uall y variables, we use only every third month (March. Jun e, each of th e three variables is significa ntl y lin ked to September, December) in the sample. th e risk premium with the coe fficient ha ving the As reported in Exhibit 7, sensi ti vi ty ana lysis using expected sign. For in stance, in regression ( I) the "'quarterly" observations suggests that delays in coefficient on CON is -.0 14. which is significantl y updating may be responsible for a portion, but not all, different from zero (t = -3.50). The negative coe ffi cient of the observed negative relationship between the signals th at hi gher consumer confidence is linked to a market premium and interest rates. For example, when lower market premium. The positive coefficients on quarterly observa ti ons are used, the coe ffi cient on i in VOL and DISP indicate the equity ri sk prem ium regression (2) of Exhibit 7 is -.527. well below the earlier increases with both market volati lity and disagreement estimates but sti ll significantly negative. '° among ana lysts. The effects of the three va riables appear As an additional test. mo vements in the bond ri sk largely unaffected by addin g oth er variables. For premium (BSPREAD) are examined. Si nce BSPR.EAD is instance, in regression (4) the coefficients on CON and constructed directly fr om bond yield data. it does not DISP both remain significant and arc similar in magn itude have the potential fo r reporting lags that may affect to the coefficients in single variable regressions.'1 ana lysts' growth fo recasts. Rt:gression 3 in Exh ibit 7 Even in the presence of th e new ri sk variables. shows BSPREAD is negatively lin ked to government Exhibit 6 shows that the market ri sk premium is affected ra tes and significantly so.11 While th e equ ity premium by interest rate conditions. The large negati ve need not move in the same pattern as the corporate coefficient on government bond rates impli es large bond premium, the negative coe ffi cient on BSPREAD reducti ons in the equity premium as interest rates rise. suggests th at our earlier results are not due solely to One fea ture of our data may contribute to th e observed "stickiness"' in measurements of market req uired returns. negati ve relati onship between the market ri sk premium The results in Exhibit 7 suggest that the in verse and the level of interest rates. Specilically, if analysts re lationship between interest rates and the market risk are slow to report updates in their grov. th forecasts. premium may not be as pronounced as suggested in changes in th e estimated k would not adjust full y with ea rlier exhibits. Sti ll, there appears to be a significant changes in the interest rate even if the true risk premium negati ve link between the eq uity risk premium and were constant. To address the impact or "'stickiness" gove rnment interest rates. The quarterly results in in th e measurement or k. we fo rmed "quart erly'" Ex hibit 7 would suggest abou t a 50 basis poi nt change measures of the risk premium that treat k as an average in ri sk prem ium fo r each I 00 basis point movement in over the qu arter. Specifica ll y, we take the value or k at interest rates. the end of a quarter and subtract from it the average Overall , the ex ante estimates of the market ri sk va lue of i for the months ending when k is measured. premium are significantly linked to ex ante proxies for For instance. to form the risk premium for March 1998, ri sk. Such a link suggests that investors modify their required returns in response to perceived changes in the environment. The findings prov ide some comfort "Rcali1ed cqull} return, arc difficull to predict out of 'ample (sec Goyal und Welch. 1999). Our approach is ddTcrcnt in that our ri sk premium estimates are capturing. at least that "e loo" at c:1.pcc tational risk prcmi.1 "hich un.' much m o re stable. For in ~tance. ''hen "e esumatc rt.'gres\1011 cocflic1cnts (usin g the specification sho" n 111 regression 7 of '"Scn.,llh Hy analysis for the I 9X2- l 989 and 1990-1998 E'hihll 6) and apply them oul of sample \\I.! ohtain subpcriods yields results similar to those reported. ""predictions"' of e:1.pecta11 o nal r1 k premin thal are " We thank Bob Conroy for suggesting use of BSPREAD. s ign11icantly more accurate (beuer than the .0 I level) than a R.: gn:~sion 3 1n Exhibit 7 appears to ha\C autocorrelau.:d no c hange forecasl. We use a ··roll ing regression·· approach error': lhe Durbin-Watson (DW) ~ta t ist i c rejects the hypothc>is using data th rough December 1991 w get coefli c icnb to predict of no a utocorre la tion. Ho\\ ever, 1n subpcriod 11 nulys1s. the the rbk premium in January 1992. We repeat th.: proc.:dure D\\ s ta tistic for the 1990-98 period 1s consistent with no llH)\ ing fornard a month and dro pping the o ldcsl monlh of uutocorrclation and lhc co.:flicicnl on i 1s cs>cntially the same data from the regression. Details ;ire •wadablc from the au1hor, . (-.24, 1 = -8.05) a> reported in Exhibit 7.

OPC 002724 FPL RC-16 HARRIS & MARSTON-THE MARKET RISK PREMIUM 15

Exhibit 7. Reg ressions Using Alternate Measures of Risk Premia to Analyze Potential Effects of Reporting Lags in Analysts' Forecasts The exhibit reports regression coefficients (1-values). Regression estimates use all variables expressed as changes (monthly or quarterl y) to correct for autocorrelation. BSPREAD is the spread between yields on long-term corporate and government bonds. rp is the risk premi um on the S&P500 index. The yield to maturity on long-term government bonds is denoted as i. For purposes of the regression, variables are expressed in decimal form. (e.g., 12% = .12).

Dependent Variable Intercept BSPREAD Adj. Ff

(I) Equity Risk Premium (171) -.0002 -.749 .488 .59 Monthly ObservaLions (- 1. 11) (- 11 .37) (2.94) (same as Table V)

(2) Equity Ri~k Premium (rp) -.0002 -.527 .550 .60 '·Quanerly"' nonoverlapping (-.49) (-6.18) (2.20) ob~ervations to account for lags in analyst reporting -.000 1 -.247 .38 (3) Corporate Bond Spread (BSPREAD) (-1.90) (-1 1.29) Momhly Observation\ in part, underlying changes in the economic of equity returns implied by options data. The significant environment. Moreover. each of th e risk measures economic links between the market premium and a wide appears to contain relevant information for in vesrors. array of ri sk variables suggests that the notion of a The market ri sk premium is negatively related to the constant risk premium over time is not an adequate level of consumer confidence and positively linked to explanation of pricing in equ ity versus debt markets. interest rate spreads between corporate and These results have implications for practice. First, government debt, disagreement among analysts in their at least on average, the estimates suggest a market forecasts of earnings growth. and the implied volatility premium rough ly comparable to long-term historical of equity returns as revealed in options data. spreads in returns between stocks and bonds. Our conjecture is that, if anything, the estimates are on the V. Conclusions hi gh sid e and thus establi sh an upper bound on the market premium. Second. the results suggest th at use Shareholder required rates of return and risk premia of a constant ri sk prem ium will not full y capture should be based on theories about in vesto rs' changes in in vestor return requirements. As a speci fie expectations fo r the future. In practi ce, however, ri sk example, our findings indicate that common application premia are typically estimated using averages of of models such as the CAPM will overstate changes historical returns. This paper applies an alternate in shareholder return requirements when government approach to estimating risk premia th at empl oys interest rates change. Rather than a one-for-one publi cly available expectational data. The resultant change with interest rates implied by use of constant average market eq uity risk premium over government ri sk premium, the results indicate that equity required bonds is comparable in magnitude to long-term returns for average risk stocks likely change by half differences ( 1926 to 1998) in historical returns between (or less) of th e change in interest rates. However, the stocks and bonds. As a result, our evidence does not picture is considerably more compl icated as shown by resolve the eq uity premi um puzzle: rather. the results th e linkages between th e risk premium and other suggest ill\ estors still expect to receive large spreads attributes of ri sk. to inve t in equity versus debt instruments. Ultimately. our research does not resolve the answer There is strong evidence, however, that the market 10 the question ·· what is the right market ri sk ri sk premium changes over time. Moreover. these premium?'" Perhaps more importantly. our work changes appear linked to the level of interest rates as suggests that the answer is condit ional on a number we l I as ex ante proxies fo r risk drawn from interest rate of fea tures in th e economy-not an absolute. We hope spreads in the bond market. consumer confidence in that future research will harness ex a111e data to provide future economic conditions, disagreement among additional guidance to best practice in using a market fi nancial analysts in their fo recasts and the vo latility prem ium to improve financial decisions. •

OPC 002725 FPL RC-16 16 JOURNAL OF APPLIED FINANCE - 2001

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OPC 002726 FPL RC-16