Understanding Short‐ versus Long‐Run Risk Premia

Published date01 September 2014
Date01 September 2014
Understanding Shortversus LongRun
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
This paper studies the link between shortand longrun risk premia. We extract
shortterm risk premia from contemporaneous information on shortterm futures
and cash equity markets under the assumption of no arbitrage. Predictability
regressions reveal that shortterm risk premia capture different information from
longrun risk premia. Counter to the intuition that a high price of risk commands
high returns, high shortrun 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 termasset) and assess its forecasting power for index excess
returns (the long termasset). 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 difcult 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 ows 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, 714738
doi: 10.1111/j.1468-036X.2013.12027.x
© 2013 John Wiley & Sons Ltd
contrasted to our understanding of discount rates in xed income markets. In the xed
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 noarbitrage
pricing restriction on cash and derivatives markets. Unlike stock prices, the prices of
dividends carry information about future expected dividend and risk premia over xed
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 nite 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 shortand longterm discount rates. Finally,
we ask to what extent the dynamics of risk premia on shortterm dividends help to explain
index returns and which asset pricing model can be consistent with some of its basic
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 coefcient? The
problem can be best understood by means of an analogy to xed 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 couponbearing bond, except that it has innite maturity and cash
ow risk. Just like a couponbearing bond can be thought of as a portfolio of zero coupons,
an equity index is a portfolio of zero coupondividend 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 nd that short term expected returns
predict realised returns over short horizons in an economically and statistically signicant
© 2013 John Wiley & Sons Ltd
Understanding Shortand LongRun Risk Premia 715

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