Is there a Positive Risk‐Return Tradeoff? A Forward‐Looking Approach to Measuring the Equity Premium

Published date01 November 2015
Date01 November 2015
Is there a Positive Risk-Return
Tradeoff? A Forward-Looking
Approach to Measuring the
Equity Premium
Dimitrios Koutmos
Worcester Polytechnic Institute, Worcester, MA, USA
This article revisits the puzzling time-series relation between risk and return on the
stock market portfolio. It replaces the standard ex post mean returns with forward-
looking calculations of the equity risk premium derived from the classic Gordon
stock valuation model. The article estimates the equity premium for several
industrialised markets and nds that conditional market risk is signicantly priced
in the context of asset pricing theory both in the short- and long-run using various
specications for volatility. Findings herein lend credible support for the presence
of a positive intertemporal risk-return relation and suggest that perhaps ex post
realised returns are unjustiably used to make ex ante inferences regarding
expected returns and to motivate asset pricing tests.
Keywords: asset pricing, intertemporal risk return tradeoff, GARCH, realised
volatility, fed model, earnings-yield, dividend-yield
JEL classification: C50, G10, G11, G12, G15, G17
1. Introduction
A fundamental challenge in modern empirical nance is quantifying the intertemporal
tradeoff between risk and return on the aggregate stock market portfolio. Although
intuition dictates that investors demand higher compensation in order to take on higher
risks, the empirical evidence provides mixed conclusions despite recent advancements in
the sophistication of modelling techniques. This is problematic from a theoretical
standpoint since it dees the predictions of general equilibrium asset pricing models
I am grateful to John Doukas (the Editor), two anonymous referees for their comments and
suggestions, Christian T. Lundblad and Rossen I. Valkanov kindly provided discussions
that have improved materially the content of this article. The usual disclaimer applies.
European Financial Management, Vol. 21, No. 5, 2015, 9741013
doi: 10.1111/eufm.12043
© 2014 John Wiley & Sons Ltd
which postulate a positive and linear relation between expected market returns and
market risk (cf., Sharpe, 1964; Lintner, 1965; Merton, 1973). It is furthermore
troublesome in practice given that the risk-return tradeoff is an important ingredient in
cost of capital estimations and optimal portfolio allocation and risk management
decisions (cf., Graham and Harvey, 2001).
To circumvent the problem that expected returns are not readily observable, the
convention in literature has been to use historical realised mean returns as a proxy for
investorsexpected risk premium. Dozens of papers utilise this approach to explore the
time-series nature of the risk-return tradeoff yet the evidence remains inconclusive, with
inferences that are highly sensitive to econometric specications or sampling periods.
They justify the practice of using ex post mean returns on grounds that, for long enough
time horizons, realised mean returns convergeto ex ante expected returns. Thus, ex post
mean returns provide an empirically tractable alternative to motivating asset pricing
Despite its widespread use however, there are at least two fundamental limitations to
using ex post realised returns as an estimate of investorsex ante risk premium; rst,
since the risk premium is time-varying and linked to uctuations in the business cycle,
any inference drawn concerning ex ante expected returns is naturally determined by the
sampling period considered. Second, investors are forward-looking and estimate future
risks on the basis of current volatility and news regarding future volatility. Their resultant
discount factor (required rate of return) which they apply to future streams of income
therefore adjusts accordingly and may not be reected in ex post realised mean returns.
The prevailing hypothesis which attempts to reconcile much of the conicting
aforementioned ndings is known as the volatility feedback effect,originally proposed
by French et al. (1987) and formalised by Campbell and Hentschel (1992). It states that a
negative shock in returns (unexpected drop in price) leads to higher future volatility than
a positive shock (unexpected increase in price) which is of equal magnitude. The reason
for this is straightforward; since volatility is persistent (cf., Mandelbrot, 1963), an
increase in volatility today signalsthat volatility will be higher in the future. This raises
investorsrequired rate of return and the discount factor they use to discount future
streams of income. Assuming that corporate earnings and dividends are not rising, prices
will obviously fall since investors sell off their positions and wait until expected returns
rise again to the appropriate level. The declining prices produce a lower historical mean
return leading one to erroneously believe that the expected ex ante required rate of return
is falling when, on the contrary, the required rate of return is rising commensurate to
higher perceived risk (as theory predicts) and hence to lower prices.
See for example Baillie and DeGennaro (1990), Bauer et al. (2010), Bekaert and Wu (2000),
Campbell and Hentschel (1992), Chou (1988), French et al. (1987), Glosten et al. (1993),
Harvey (1991, 2001), Lundblad (2007), Masset and Wallmeier (2010), Nelson (1991),
Schrimpf et al. (2007) and Subrahmanyam (2010), to name but a few.
This argument can be expressed in the context of a cost-of-capital problem; if a rise in
volatility raises investorsrequired rate of return for bearing systematic risk, this will lead to a
higher cost of equity capital for rms and may result in a reduction in investment and output
and possibly a rise in future volatility and uncertainty. Thus, realised stock market returns
tend to be historically low during recessionary periods since investorsrequired rate of return
(discount rate) rises commensurate to the rise in systematic risks.
© 2014 John Wiley & Sons Ltd
A Forward-Looking Approach to Measuring the Equity Premium 975
In this paper I argue that the fundamental problem in estimating the time-series
relation between risk and return may not be the result of econometric (miss-)
specication of the variance, but is rooted in the use of ex post realised returns as an
appropriate proxy of investorsex ante risk premium. Sharpe (1978) and Elton (1999)
also warn of the pitfalls associated with using ex post realised returns to test asset pricing
theories and to estimate expected returns. In particular, Elton (1999) maintains that
future work in asset pricing should strive to consider alternative ways to measure
expected returns instead of focusing on the development of new statistical procedures
that continue to rely on ex post realised returns. More recently, Lundblad (2007)
illustrates that an extremely large time-series of historical market returns is required
nearly two centuries worth of data in order to see convergencebetween ex post returns
and expected returns.
To attack the problem directly, I empirically explore the risk-return tradeoff using a
variant of the Merton (1973) intertemporal capital asset pricing model in conjunction
with proxies for expected returns that are forward-lookingand can be derived
theoretically from the classic Gordon (1962) dividend constant growth model. These
proxies are the dividend yield and the earnings yield, which is the inverse of the price-to-
earnings ratio. Both these yields serve as time honored market valuation measures and, to
some extent, can be likened to the yield to maturity on bonds. Consider, for example, why
the expected returns on bonds are computed as yields as opposed to the logarithmic rst-
difference of their price as is the case when computing returns on stocks. It is because this
yield reects investorsrequired rate of return and reveals insights about their forward-
looking expectations about the state of the economy as well as the prospects for other
investments. It is no surprise, therefore, that while historical mean returns in the stock
market may slump during recessions and periods of increased uncertainty, the yields on
bonds (and their spreads with other bond classes) rises (cf., Campello et al., 2008). Bond
yields are computed on the basis of forward-looking internal rates of return and their
yields rise along with increases in investorsrequired rate of return (discount factor) and,
thus, bonds of rms with higher systematic risk have higher yield spreads in relation to
saferbonds. As Campello, Chen and Zhang (2008) argue, averaging ex post realised
returns only seems to hide investorsconditional forward-looking expectations about
future returns and states of the economy.
In terms of forecasting capabilities, the dividend and earnings yields, respectively,
have proven to be sound predictors of future returns and economic conditions and are
frequently cited by practitioners in order to ascertain whether market prices are over- or
under-valued. In their timeless classic, Graham and Dodd (1940) warned that if investors
buy stocks with relatively high prices in relation to the respective rmsaverage
earnings, they are more likely to lose money in the long run. This message is echoed by
Shiller (2000) who identies that the P/E ratio is a strong proxy for future expected
returns and nds that when it rises above its long-run average, it signals irrational
exuberancein the stock market and a probable likelihood of an imminent correction in
stock prices. Campbell and Shiller (1998, 2001) nd that the dividend and earnings
yields, despite their shortcomings, are useful in forecasting future stock price
movements. Lamont (1998) argues the earnings yield contains useful information
about the future and is a good forecaster of expected returns. Fama and French (2002)
estimate expected stock market returns using dividend and earnings and growth rates.
They argue that the use of such fundamental factors can help to determine whether
realised stock returns diverge from their true values. Most recently, Pastor et al. (2008)
© 2014 John Wiley & Sons Ltd
976 Dimitrios Koutmos

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