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

• Published date: 01 November 2015
• Author: Dimitrios Koutmos
• Date: 01 November 2015
• DOI: http://doi.org/10.1111/eufm.12043

Is there a Positive Risk-Return

Tradeoff? A Forward-Looking

Approach to Measuring the

Equity Premium

Dimitrios Koutmos

Worcester Polytechnic Institute, Worcester, MA, USA

E-mail: DKoutmos@WPI.edu

Abstract

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 finds that conditional market risk is significantly priced

in the context of asset pricing theory both in the short- and long-run using various

specifications 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 unjustifiably 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 finance 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 defies 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, 974–1013

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

investors’expected 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 specifications or sampling periods.

1

They justify the practice of using ex post mean returns on grounds that, for long enough

time horizons, realised mean returns ‘converge’to ex ante expected returns. Thus, ex post

mean returns provide an empirically tractable alternative to motivating asset pricing

models.

Despite its widespread use however, there are at least two fundamental limitations to

using ex post realised returns as an estimate of investors’ex ante risk premium; first,

since the risk premium is time-varying and linked to fluctuations 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 reflected in ex post realised mean returns.

The prevailing hypothesis which attempts to reconcile much of the conflicting

aforementioned findings 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 ‘signals’that volatility will be higher in the future. This raises

investors’required 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.

2

1

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.

2

This argument can be expressed in the context of a cost-of-capital problem; if a rise in

volatility raises investors’required rate of return for bearing systematic risk, this will lead to a

higher cost of equity capital for firms 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 investors’required 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-)

specification of the variance, but is rooted in the use of ex post realised returns as an

appropriate proxy of investors’ex 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 ‘convergence’between 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-looking’and 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 first-

difference of their price as is the case when computing returns on stocks. It is because this

yield reflects investors’required 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 investors’required rate of return (discount factor) and,

thus, bonds of firms with higher systematic risk have higher yield spreads in relation to

‘safer’bonds. As Campello, Chen and Zhang (2008) argue, averaging ex post realised

returns only seems to hide investors’conditional 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 firms’average

earnings, they are more likely to lose money in the long run. This message is echoed by

Shiller (2000) who identifies that the P/E ratio is a strong proxy for future expected

returns and finds that when it rises above its long-run average, it signals ‘irrational

exuberance’in the stock market and a probable likelihood of an imminent correction in

stock prices. Campbell and Shiller (1998, 2001) find 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