Understanding Short‐ versus Long‐Run Risk Premia

• DOI: http://doi.org/10.1111/j.1468-036X.2013.12027.x
• Published date: 01 September 2014
• Date: 01 September 2014

Understanding Short‐versus Long‐Run

Risk Premia

Andrea Buraschi and Andrea Carnelli

The University of Chicago and Imperial College London

E-mails: andrea.buraschi@chicagobooth.edu; andrea.carnelli08@imperial.ac.uk

Abstract

This paper studies the link between short‐and long‐run risk premia. We extract

short‐term risk premia from contemporaneous information on short‐term futures

and cash equity markets under the assumption of no arbitrage. Predictability

regressions reveal that short‐term risk premia capture different information from

long‐run risk premia. Counter to the intuition that a high price of risk commands

high returns, high short‐run risk premia on dividend claims predict low returns on

the index. While inconsistent with models featuring either habit persistence or long‐

run risk, the results may be reconciled with some models of uncertainty aversion.

Keywords: equity risk premium, predictability, dividend prices, asset pricing models

JEL classification: G10, G12, G13

1. Introduction

This paper investigates the relationship between risk compensation on equity claims of

different maturities: we construct a measure of expected excess returns on claims to one

year dividends (the ‘short term’asset) and assess its forecasting power for index excess

returns (the ‘long term’asset). Understanding the properties of risk premia is one of the

most important yet challenging tasks in asset pricing. One of the challenges is related to

the fact that, in general, it is difficult to identify risk premia demanded by investors: they

cannot be directly observed when the timing and magnitudes of dividends are unknown. A

stock index pays uncertain dividends at uncertain times over a life of uncertain duration.

Investors form expectations about future cash flows and use a set of discount rates to

determine the value. All information is then aggregated by a tatonnement and the

econometrician can only observe a time series of stock prices. This loss of information is a

binding constraint for our understanding of asset prices; its limits are laid bare when

We would like to thank John Doukas (the editor), an anonymous referee, Davide Silvestrini

(JP Morgan), Paul Whelan (Imperial College Business School), and conference participants

at FEBS (London, June 2012), EFMA (Barcelona, June 2012), and FMA (Atlanta,

October 2012) for useful comments and suggestions. The usual disclaimer applies.

European Financial Management, Vol. 20, No. 4, 2014, 714–738

doi: 10.1111/j.1468-036X.2013.12027.x

© 2013 John Wiley & Sons Ltd

contrasted to our understanding of discount rates in fixed income markets. In the fixed

income literature, the term structure of interest rates is an observable entity with two

important roles. First, it encodes information about the dynamics of the stochastic

discount factor (yields are risk adjusted expectations of future short rates). Second, it

provides a host of restrictions that allow to better discriminate among alternative models.

If equity discount rates were observable, we could learn about their dynamics and

generate additional restrictions that asset pricing models have to satisfy.

How can we identify risk premia on short term assets? Following the pioneering work

of Van Binsbergen et al. (2010, 2011), we address this challenge by using observations on

dividend prices. Dividend prices can be obtained by imposing a simple no‐arbitrage

pricing restriction on cash and derivatives markets. Unlike stock prices, the prices of

dividends carry information about future expected dividend and risk premia over fixed

horizons. By projecting excess returns of dividend claims on their price to dividend ratio,

we are able to identify the level of compensation required by investors to bear equity risk

of finite duration. Since the dividend prices we focus on are claims on one year dividends,

we label the risk premia we obtain as short term (STRP). Next, we investigate the

empirical properties of STRP and their relationship to LTRP, the risk premia earned by

holding the equity index (the long term asset). We explore this relationship indirectly by

running predictive regressions of realised excess returns on lagged STRP. Since realised

excess returns reveal changes in equity discount rates at all maturities, these regressions

allow us to uncover the dynamic link between short‐and long‐term discount rates. Finally,

we ask to what extent the dynamics of risk premia on short‐term dividends help to explain

index returns and which asset pricing model can be consistent with some of its basic

properties.

Our main empirical exercise is a regression of excess returns on one year risk premia:

can theory say something about the sign and magnitude of the slope coefficient? The

problem can be best understood by means of an analogy to fixed income securities. We

can think of an equity index as a long maturity bond (say, 30 years) that pays coupons (i.e.

dividends), and we can think of STRP as the yield on a short maturity (say, 1 year) zero

coupon bond. The issue we address is akin to the question: can one year yields predict one‐

year holding period returns on a 30 years maturity bond? A rigorous answer to the

question involves specifying a term structure model that: i) derives the price of a bond as a

function of state variables, and ii) determines risk premia by modelling the covariance

between shocks to bond prices and shocks to the stochastic discount factor. To the extent

that the yield on the 1 year bond reveals the state variable, it is also possible to form

expectations about the 1 year holding period return of the 30 year maturity bond. An

equity index is like a coupon‐bearing bond, except that it has infinite maturity and cash

flow risk. Just like a coupon‐bearing bond can be thought of as a portfolio of zero coupons,

an equity index is a portfolio of ‘zero coupon’dividend strips, i.e. claims to dividends

payable at future dates. The term structure model of dividend strips we adopt is the one

developed in Lettau and Wachter (2007). Lettau and Wachter (2007) show that short term

risk premia (our regressor) identify the price of risk up to a scaling factor, and that

expected returns on dividend strips with longer maturities are positive functions of the

price of risk. Since the return on the index is a weighted average of returns on dividend

strips of all maturities, the model provides a tight link between the left and right hand side

variables of our regression, and motivates its predictive power.

Our results can be summarised as follows. We find that short term expected returns

predict realised returns over short horizons in an economically and statistically significant

© 2013 John Wiley & Sons Ltd

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