Market Risk Premium and Interest Rates

Market Risk Premium and Interest Rates Professor Robert G. Bowman Dr J. B. Chay Department of Accounting and Finance The University of Auckland Private Bag 92019 Auckland, New Zealand February 1999

Market Risk Premium and Interest Rates Executive Summary Estimating the cost of equity capital is an important task for a firm as it has investment and performance evaluation implications. The preferred method of estimation is to use the Capital Asset Pricing Model. This model requires an estimate of the forward-looking market risk premium ( MRP ). This estimation has proved to be difficult. The MRP is an expectation and hence is not observable. The conventional procedure is to collect historical information on MRP over long time periods and to then use this ex post data to estimate a reasonable range for the ex ante MRP. The usual procedure is then to choose a point estimate near the middle of the range under the assumption that this is the best estimate of the forward-looking MRP. However, this procedure assumes there are no predictable time-varying properties to MRP. As the span of the reasonable range may be substantial, the choice of a point within the range can be very important economically. Therefore, it is important to examine the assumption, usually implicit, about the intertemporal behaviour of the MRP. A substantial literature, both theoretical and empirical, has developed in financial economics on the time-varying properties of returns and variance of returns. As the research progressed, attention began to focus on the MRP. Studies by Ferson and Harvey (1991) and Evans (1994) recognise the importance of understanding the behaviour of the MRP over time. These papers examine whether the variation of portfolio returns over time is attributable to time-varying betas (systematic risk) or to time-varying risk premia. Both studies conclude that most of the time-variation in returns can be attributed to time-varying risk premia, and that betas are relatively constant over time. The MRP varies inversely over time with the level of short-term interest rates. i

In addition to the many studies on other datasets, there have been a number prominent studies of risk premiums in the electric utility industry in the United States. In an early study, Carleton, Chambers, and Lakonishok (1983) provide empirical evidence that regulatory lags induced risk premiums for utility stocks to rise with inflation and interest rates, contrary to theory and empirical observations in the absence of regulatory lag. They investigated the 1970s and early 1980s in the United States when regulatory lag severely hampered earnings from keeping pace with inflation. At least three other studies [Brigham, Shome and Vinson (1985), Shome and Smith (1988) and Harris (1986)] all find an inverse relation between interest rates and ex ante risk premium measures for the utilities. A study by Bellamy and Heaney (1997) analysed the time-varying characteristics of MRP in Australia. This study was largely unsuccessful in detecting significant factors. Unfortunately, the combination of limited data, substantial changes to the regulatory and economic environment, and the 1987 Stock Market decline make it unlikely that significant results can be found in such a study. Taken as a whole, the theoretical and empirical research provides substantial evidence to support predictable time-variation in MRP that is inverse to nominal interest rates. When short-term interest rates are low, the MRP is high. An implication of this research is that an ex ante estimate of MRP for Australia today, when nominal interest rates are at historically low levels, should be toward the top of a reasonable range for MRP. This research has important implications for commercial and regulatory estimates of MRP in Australia. ii

Market Risk Premium and Interest Rates This is not a story that the market is screwed up. This is a story of how investors behave when their wealth changes. Say I tell you the relative risk premium is 120 --- you ll get 120% of normal expected return for bearing risk. If that was the only thing I told you, you d say let s buy stock. But what if I also told you the reason for that is we re in a recession and someone in your family is out of work. If you re average, you ll say, I guess these are offsetting. I ll stay with what I ve got. In fact, that s what has to happen in an efficient market. The risk premium has to adjust to where the average investor doesn t want to do anything. Nobel Laureate William Sharpe, quoted in Beros (1990, p 78) 1. Introduction Applications of the Capital Asset Pricing Model ( CAPM ) to the task of estimating the cost of equity capital for firms require the estimation of the market risk premium ( MRP ). This estimation has proved to be difficult. The MRP is an expectation and hence is not observable. The conventional procedure is to collect historical information on MRP over long time periods, and to then use this ex post data to estimate a reasonable range for the ex ante MRP. 1 Once a reasonable range has been established for MRP, a point estimate within the range must be chosen. The usual tendency, not surprisingly, is to choose an estimate near the mid-point of the range under the assumption that this is the best ex ante estimate of MRP. However, this procedure assumes there are no predictable timevarying properties to MRP. As the span of the reasonable range may be substantial, the choice of a point within the range can be very important economically. Therefore, 1 See Bowman (1999) for a discussion of the estimation of the reasonable range in Australia.

it is important to examine the assumption, usually implicit, about the intertemporal behaviour of the MRP. A substantial literature has developed in financial economics on the time-varying properties of returns and variance of returns. Early developments in theory by Litzenberger and Budd (1972), Merton (1973, 1980), Friend and Blume (1975), Black (1976) and Landskroner (1977) predict a positive relation between the MRP and conditional market variance (where both MRP and market variance vary over time). Early empirical studies by Fama and Schwert (1977), Engle (1982) and others made important advances both in terms of evidence and statistical techniques. Studies by Ferson and Harvey (1991) and Evans (1994) recognise the importance of understanding the behaviour of the MRP over time. These papers examine whether the variation of portfolio returns over time is attributable to time-varying betas (systematic risk) or to time-varying risk premia. Both studies conclude that most of the time-variation in returns can be attributed to time-varying risk premia, and that betas are relatively constant over time. The sections that follow review the literature on time-varying properties of returns, with a particular focus on the ex ante MRP. The message of this research is that there is substantial empirical evidence to support predictable time-variation in MRP that is inverse to nominal interest rates. This research has important implications for commercial and regulatory estimates of MRP in Australia. 2. Relation between the MRP and conditional market variance The early theory on MRP and conditional market variance pointed to a positive relation between the two. Yet, empirical studies fail to agree on the sign of this basic relation. Most papers on the intertemporal behaviour of the MRP employ a conditional single factor model 2 motivated by the static CAPM. These conditional 2 The model is called conditional because market variance expected for time t is estimated by using the information available at time t-1 such as past conditional market variance (which, in turn, is based 2

single-factor models imply a simple linear relation between the MRP and conditional market variance. Estimates of the simple risk-return relation range from significant positive 3 to significant negative. 4 Recently, Scruggs (1998) resolves the issue by using a conditional two-factor model of the MRP motivated by Merton s (1973) intertemporal CAPM. In the conditional two-factor model, the MRP is a function not only of conditional market variance but also of conditional market covariance with a variable that describes the state of investment opportunities in the economy. If the true model is a conditional multifactor model, then conditional single-factor models are misspecified, and estimates of the simple risk-return relation are subject to an omitted variable bias. Scruggs found that the partial relation between the MRP and conditional market variance is positive and significant when long-term government bond returns are included as a second factor in the conditional two-factor model. The conditional two-factor model used by Scruggs is well motivated theoretically by Merton (1973) and empirically by Chen, Roll and Ross (1986) and Shanken (1990). Merton interprets the effects of a changing interest rate as a state variable capturing shifts in the investment opportunity set. Long-term bonds are a natural instrument for hedging interest rate risk because their returns are negatively, albeit not perfectly, correlated with changes in interest rates. Long-term bond returns have been used in empirical studies of multifactor asset pricing models. Chen, Roll and Ross find that exposure to interest rate risk is significantly priced in the stock market. Shanken tests a conditional two-factor version of the ICAPM and finds that both stock and bond market exposures are priced. Scruggs results suggest that a conditional two-factor model explains the intertemporal behaviour of the MRP better than the conditional single factor models used in the previous literature. Based on US monthly data for the period from 1950 to 1994, Scruggs establishes that the partial relation between the MRP and conditional on past conditional market variances) and lagged return innovations (or surprises in returns). The model is call single factor because the MRP is a function of only one factor, market variance. 3 For example, see Harvey (1989), Turner, Startz and Nelson (1989). 4 For example, see Campbell (1987), Glosten, Jagannathan and Runkle (1993). 3

market variance is significant and positive. He shows that estimates of the simple risk-return relation obtained from conditional single-factor models are biased downward due to the omission of an interest rate-related state variable from the conditional MRP equation. He demonstrates that the magnitude of the bias is sufficient to distort the estimated sign between MRP and market variance. 3. Relation between the MRP, conditional market variance and the shortterm interest rate Campbell (1987) and Glosten, Jagannathan and Runkle (1993) both report a strong negative relation between the MRP and conditional market variance when the nominal one-month Treasury bill yield is included in the conditioning information set that explains conditional market variance. When the Treasury bill yield is removed from the conditioning information set, the significant negative risk-return relation disappears. Campbell describes these results as perverse as they are not consistent with the theory for the relationship. Scruggs results show that including the nominal risk-free rate in the conditional market variance equation distorts estimates of the simple risk-return relation suggested by the conditional single-factor model. The strong negative relation between the MRP and the nominal risk-free rate appears to dominate the estimation of the simple risk-return relation, giving significant and negative results. To understand this, we need to consider two distinct interest rate effects that are well established empirically. The first effect is the empirical relation between market volatility and the level of short-term interest rates. Campbell (1987), Breen, Glosten and Jagannathan (1989), Shanken (1990) and Glosten, Jagannathan and Runkle (1993) all report a significant positive relation between market variance and the nominal one-month Treasury bill yield. The second effect is the direct relation between the MRP and short-term interest rates. Fama and Schwert (1977), Campbell (1987), Ferson (1989), Shanken (1990) and 4

Brennan (1997) all find that nominal Treasury bill yields are negatively correlated with future stock returns. Using an Arbitrage Pricing Theory factor approach, Elton, Gruber and Mei (1994) show that in a case study of nine New York utilities companies, about 16% of the MRP is related to interest rates. The combination of the above two relationships gives a negative relation between MRP and market variance. This in turn suggests that the strong negative relation between the MRP and the nominal Treasury bill yield dominates the estimation of the simple MRP-market variance relation. If there are two distinct interest rate effects, then including the interest rate only in the conditional variance equation (and thus excluding it from the conditional mean equation that relates the MRP with conditional market variance) could distort estimates of the conditional mean equation parameters. Scruggs explores this by estimating an ad hoc model in which the short-term interest rate enters directly into both the conditional mean and conditional variance equations. He finds that including short-term interest rates as a second factor in the conditional mean equation restores the positive relation between the MRP and conditional market variance. In summary, there is a significant positive relation between the MRP and conditional market variance. There is also strong evidence that the MRP varies over time with a significant and negative relation with the short-term interest rate. The latter relation is so strong that it distorts the estimation of the relation between the MRP and market variance, if estimated naively. We discuss this inverse relation between MRP and interest rate in more detail in the following section, based on the studies relying on expectational data. 4. Theory of the inverse relation between ex ante MRP and interest rates The theoretical developments of the relations between MRP and interest rates generally involve consideration of rates of inflation. Perhaps the first direct theory on the issue was Gordon and Halpern (1976). They assumed that the risk-free asset s nominal returns are fixed so that its real returns vary with inflation, whilst real returns 5

on equities are independent of inflation so that they are perfect inflation hedges. Then the MRP will vary negatively with the expected rate of inflation. Because of the theoretical (and empirical) link between inflation and nominal interest rates, the MRP will also vary with nominal interest rates. If the assumption is relaxed that the riskfree asset s nominal returns are fixed, the relationship between MRP and interest rates will still hold as long as stocks are a better inflation hedge than bonds. Fama (1981) used money demand theory to demonstrate a strong negative relation between expected inflation and anticipated real activity. Stock returns are shown to be positively related to future real variables. However, he assumes that money supply does not move with real shocks. Geske and Roll (1983) argue that stock returns signal changes in inflationary expectations because of a chain of macroeconomic events. When stock prices decline in response to an anticipated slowdown in real economic activities, the government, given largely fixed expenditures, will tend to run a deficit. To the extent that the deficit is monetised, an increase in money growth will lead to increased expected inflation. Perhaps the most rigorous theoretical piece in this literature is Stulz (1986). He shows that, in a simple representative agent model, increases in expected inflation due to worsening productivity can lead to a decrease in the return differential between stocks and nominal bills. Given the stylised empirical fact that nominal interest rates are strongly positively related to inflation, the above arguments can explain the negative relation between the MRP and nominal interest rates. In a different vein, Gordon and Gould (1984) show analytically that MRP will vary inversely with interest rates if the marginal personal tax rate on interest payments is greater than the rate on returns from investment in equity securities. Finally, by employing the concept of temporal risk aversion (i.e., risk aversion over consumption at different periods), Ahn (1989) derives optimal consumption rules and the equilibrium interest rate in a general equilibrium setting. As temporal risk aversion (i.e., marginal time impatience) increases, current consumption increases and future consumption decreases. With a sufficient level of temporal risk aversion, the expected level of optimal consumption is decreasing over time. Ahn s results indicate 6

that the equilibrium interest rate decreases as temporal risk aversion increases - the higher the time impatience, the lower the equilibrium interest rate. He also shows that the MRP increases as temporal risk aversion increases. Ahn s results are robust and intuitively appealing. As temporal risk aversion increases, the optimal proportion of wealth invested in the risk-free asset increases. A temporally risk-averse consumer is extremely averse to the situation where he has to consume very little in all periods. To avoid this undesirable possibility, the consumer can buy more of the risk-free asset, which promises certain payoffs at maturity dates. Consequently, as temporal risk aversion increases, the demand for the risk-free asset increases and the price of the asset increases. Accordingly, the equilibrium interest rate decreases, and the MRP will increase. Although Ahn does not directly examine the relation between interest rates and the MRP, his results imply that the interest rate is negatively related to the equity premium. 5. Empirical evidence of the inverse relation between ex ante MRP and interest rates As mentioned in section 3 above, there is now extensive empirical evidence that the MRP varies over time with the level of short-term interest rates. When short-term interest rates are high, the MRP is low and vice versa. The inverse relation between the MRP and interest rates is also apparent in studies that use expectational data to assess the risk premium. 5 In these studies, a risk premium model that relies on the expected cost of equity capital, rather than realised returns, has been proposed as the appropriate basis for measuring risk premiums. Generally, studies supporting an ex ante MRP approach are based on data from as early as the mid-1960s through the mid-1980s. The ex ante measurement of MRP holds conceptual appeal because it is consistent with the valuation of equity investments based on expected returns. 5 For example, see Brigham, Shome and Vinson (1985), Harris (1986), Shome and Smith (1988), Harris and Marston (1992) and Maddox, Pippert and Sullivan (1995). 7

An ex ante risk premium study by Brigham, Shome and Vinson (1985) supported the existence of an inverse relation between interest rates and risk premiums of electric utility stocks from 1980 through the first half of 1984. To determine these risk premiums, they employed a two-stage discounted cash flow model to obtain monthly cost of equity estimates for utility stocks. Risk premium measures for each month were then derived by deducting an appropriate Treasury bond yield. Shome and Smith (1988) obtained similar results, finding an inverse relation between interest rates and electric utility risk premiums that continued through 1985. Harris (1986) also finds an inverse relation between interest rates and ex ante risk premium measures during the early to mid-1980s, based on utility and broader stock market indices. In a more recent study, Harris and Marston (1992) find an inverse relation between interest rates and ex ante risk premiums for stocks in the S&P500, based on data from 1982 to 1991. Shome and Smith note that while stocks and bonds are both considered hedges against anticipated inflation, common stocks are considered to offer a partial hedge against unanticipated inflation. Therefore, Shome and Smith argue that during periods of greater inflation uncertainty, it is reasonable to expect MRP to decline as interest rates rise. 6 Stated another way, the risk and required return of the less complete hedge (i.e., debt) would increase at a relatively greater rate than the more complete hedge (i.e., equity), thereby reducing the risk premium during periods of higher uncertainty. However, Carleton, Chambers, and Lakonishok (1983) provide empirical evidence that risk premiums for utility stocks tend to rise with inflation and interest rates if regulatory lag severely hampers earnings and prevents dividends from keeping pace with inflation. Brigham, Shome and Vinson (1985) and Shome and Smith (1988) also find a positive relation between equity risk premiums and interest rates in their sample covering the 1970s. In an attempt to explain the shift of positive relation during the 1970s to negative relation between debt and utility stocks during the 1980s, both studies discussed factors that reduced the impact of regulatory lag on utility stocks 6 This is consistent with the theory of Gordon and Halpern (1976). 8

from the late 1970s into the early 1980s. Both studies concluded that reduced regulatory lag contributed to shifting positive relation to negative. These studies were by and large an outgrowth of the market climate of the early 1980s. During that time, the risk of debt instruments rose in an absolute sense and became comparable to stocks. This led many to conclude that the risk premium had narrowed and some to even argue it was negative. In summary, there is ample evidence that ex ante MRP is inversely related to interest rates. Some early evidence of a positive relation found in utility stocks can be attributed to the impact of regulatory lags. 6. Economic interpretations To assess economic significance of the inverse relation between ex ante risk premiums and interest rates, we consider a study of the electric utility industry in the US. Maddox, Pippert and Sullivan (1995) estimated the ex ante risk premium for the electric utility industry by using a constant-growth discounted cash flow (DCF) model. Risk premium for each electric utility company was obtained by subtracting the threemonth average yield on 30-year Treasury bonds from the ex ante cost of equity capital calculated using the DCF model. Finally, Maddox, Pippert and Sullivan averaged these ex ante risk premiums of 30 electric utility companies to construct an industry risk premium. Based on quarterly data from 1980 to 1993, they found there were major shifts in the level of the risk premiums over time. They interpret these as changes regarding the market s evaluation of relative risk between debt and equity. After taking these shifts into account by a dummy variable regression, Maddox, Pippert and Sullivan found a 9

stable inverse relation between long-term interest rates (30-year Treasury bond yield) and ex ante risk premiums over their sample period. Maddox, Pippert and Sullivan s results indicate a measure of the magnitude of the relationship. Their research shows that there is approximately a 37 basis points inverse change in risk premium for each 100 basis-point change in Treasury bond yields. This result is consistent with Harris and Marston (1992), who found a 36 basis point inverse relation between long-term government bond rates and risk premiums for a broader sample over the 1982 to 1991 period. In a related study, Marston and Harris (1993) suggested that a one percentage point increase in long-term interest rates would cause the MRP to decrease by approximately one half of a percentage point. 7. Other macroeconomic variables affecting the MRP The MRP will change when there are changes in the mix of investors or changes in risk aversion resulting from changes in aggregate wealth as the economy grows. It may also change as a result of shifts in the attitude of investors toward risk and investment over the business cycle. Fama and French (1989) document that risk premiums are inversely related to long-term business conditions. Ferson and Harvey (1991) also find empirical evidence that the expected risk premium increases during economic contractions and peaks near business cycle troughs. These results compliment the results discussed above on the relationship between interest rates and MRP. 8. Evidence in Australia A recent study of the time-varying properties of MRP in Australia is Bellamy and Heaney (1997). They use daily data for the Australian All Ordinaries Share Price Accumulation Index during the period July 1985 to December 1994. They find some evidence of volatility effects in the MRP, but only in the post-crash period. They do not find any other consistently significant effects, including for interest rates. 10

The probable explanation for the lack of results is provided by the authors (p 26). The study period is clearly unusual in terms of the level of the risk premium with an average ex-post risk premium over the period prior to October 1987 of 29.1% p.a., and an average risk premium for October 1987 onwards equal to 8.0% p.a. I might add that over the four years since the end of their study, the annual equity premium in Australia has been about 10% and at a time when interest rates have been quite low by historical standards. The time period that Bellamy and Heaney studied is characterised by a number of significant economic events affecting both debt and equity markets. To even attempt to estimate ex ante equilibrium MRP relationships on the 1985 to 1994 ex post data is dubious at best. A standard way to attempt to bolster the analysis is to increase the size of the dataset. Unfortunately, there is little historical time-series data on MRP in Australia that is likely to be useful. Bellamy and Heaney (p 24) note that in selecting their data they exclude the early 1980s where major deregulatory changes occurred in Australian financial markets. Data drawn from before the early 1980s will be of limited relevance to the current MRP in Australia because of the major regulatory changes to which they allude. I do not believe it is possible to use Australian historical data to meaningfully assess the time-varying properties of MRP or, more specifically, the relationship between MRP and interest rates. The evidence from other markets, particularly the US, must be used to make reasonable inferences about the relationships. 9. Conclusions The research reviewed above has important implications for the application of the CAPM to estimate the cost of equity capital for firms. The well established procedure is that when an estimate is made of MRP for purposes of applying CAPM, a reasonable range is identified. A point estimate near the mid-point of the range is 11

then chosen under the assumption that this is the best ex ante estimate of MRP. However, this procedure implicitly assumes there are no predictable time-varying properties to MRP. The above discussion shows that such an assumption is not appropriate. There is strong evidence that the MRP varies over time. Consistent with theory in financial economics, the MRP is positively related to conditional market variance. It has also been established that the MRP rises during business contractions and falls during more prosperous periods. The most pronounced empirical evidence is that the MRP varies inversely with nominal interest rates. The best existing evidence suggests that a one percent decrease in nominal interest rates implies about 35-50 basis points increase in the ex ante MRP. An implication of this research is that an ex ante estimate of MRP for Australia today, when nominal interest rates are at historically low levels, should be toward the top of a reasonable range for MRP. 12

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