The Role of Return Predictability and Rare Disasters in

A large body of empirical literature has documented the long-term predictabil- ity of asset returns and the linkages between wealth and other macroeconomic variables. An important reason for the interest in this relation is that expected excess returns on assets appear to vary with the business cycle. For instance,

Chen (1991) studies the relation between changes in the financial investments opportunity set and the macroeconomy. Chen (1991) finds that state variables such as the dividend-price ratio, the default premium, the term premium etc are good indicators of recent and future economic growth. Importantly, he finds that these variables are positively correlated with expected excess return and future economic growth; and negatively correlated with recent economic growth. The counter-cyclicality of risk premium is found to hold even when post 1990 stock market data is considered, see Henkel et al.(2011).

Different explanations have been offered for this empirical result, namely: in- efficiencies of financial markets (Fama and French(1988,1992) andFama(1998)); the rational response of agents to time-varying investment opportunities driven by variation in risk aversion Campbell and Cochrane(2000) or in the joint distri- bution of consumption and asset returns.

One area where return predictability has profound implications is asset allo- cation. For long-term investors the static Markowitz Mean-Variance model will only be suitable under very strict assumptions, one of them being that investment opportunities are constant over time, meaning that returns are unpredictable. If this is not the case, long-term investors can benefit from the return predictability, both in the form of market-timing and in the form of intertemporal hedging of fu- ture return risk. Neither of these effects are captured by the static Mean-Variance model.

Lynch (2001) assesses the impact of return predictability on portfolio choice

for a multi-period investor by characterizing the intertemporal hedging demand in a continuous time setting. Lynch finds that parameters such as the persistence of the return predicting process can have a large impact on the optimal risky share of asset allocation. He attributes the variation in the risky share to hedging motives. However, his model is highly stylized and abstracts from life-cycle dynamics, labour income, any durable good or short sales constraints. Nevertheless, these results are consistent with what we find.

There have been a few recent papers which argue how ”rare disasters” in the economy can resolve several puzzles in the finance literature including but not limited to the equity premium puzzle (Mehra and Prescott(1985)), the risk free rate puzzle (Weil (1990)) and the excess volatility puzzle (Shiller (1981)).4 _This 4_{The risk free rate puzzle emerges out of the equity premium puzzle: why are the risk free} rates so low if the agents are so averse to intertemporal substitution. The excess volatility puzzle is the stylized fact that volatility of dividends (fundamentals) cannot explain the much larger volatility in stock returns.

strand of literature can be traced back toRietz(1988) who models the possibility of a low probability depression like state and shows how such a state can explain these puzzles. The motivation is that Risk-averse equity owners demand a high return to compensate for the extreme losses they may incur during an unlikely, but severe, market crash. To the extent that equity returns have been high with no crashes equity owners have been compensated for the crashes that happened not to occur.

An open question has therefore been whether the risk is sufficiently high, and the rare disaster adequately severe, to quantitatively explain the equity premium. Recently, Barro (2006) revitalized this literature by analysing 20th century dis- asters using GDP and stock market data for 35 countries and showed that it is possible to explain the high equity premium when the disaster probability is set at roughly 2% per year. The framework of his model is based on Lucas’ representative-agent, fruit-tree model of asset pricing with exogenous, stochastic production with tractable elements of closed economy and complete markets. The investor is allowed to hold two assets, one of which is risky and the other riskless. At every date, the agent faces a constant exogenous probability of disaster risk, and an associated size of this collapse. These parameters act as determinants in the analytical closed form solutions of Barro’s optimal expected risky premium and risk free return.Since Barro (2006), several papers have come out and have been successful in explaining several asset market puzzles such as the excess stock return volatility (Wachter (2013))

If rare economic disasters can solve the pricing puzzles, intuitively they should also explain the observed household portfolio holdings (quantity) and/or the lim- ited rates of equity market participation. In other words, perceived risk associated with a disaster in stock markets should be revealed in household portfolios. How- ever, such endeavours have been by and large unsuccessful.

For example Alan (2012) examines whether such rare economic disasters as argued byBarro (2006) can explain the asset allocation and stock market partic- ipation puzzles. Alan(2012) finds that it is difficult to reconcile the results of the calibrated model with observed levels of limited asset allocation and participation rates unless an implausible level of labour market stress is assumed at the time of the disaster.

In a related exercise Fagereng et al. (2013) develop and numerically simulate the standard life-cycle model of portfolio allocation incorporating labour income risks and IID investment opportunity sets adding a small subjective probability of a large loss when investing in stocks (a ”disaster” event) where the parameters

are calibrated to Norwegian Household Panel Data. Their study predicts a joint pattern and level of participation and the risky asset share over the life cycle similar to the one observed in the data, with early rebalancing of the risky share before retirement. However, the stock market participation rate is found to be, counter-factually, 100% for most part of the agent’s life.

Michaelides and Zhang(2015) who solve for optimal portfolio choice and con-

sumption in a standard life-cycle model without housing but with recursive pref- erences and undiversable labour income risk and importantly accommodating a predictable time varying equity premium. They find that in the presence of return predictability ignoring market information can lead to substantial welfare losses. In this chapter we model return predictability following Michaelides and Zhang

(2015) but we do not focus on welfare analysis.

Some recent papers have investigated the impact of return predictability in house prices on optimal portfolio choice. For instance,Fischer and Stamos(2013) study the decisions of households facing time varying expected growth rates in house prices and show that homeownership rates, as well as the sizes of housing and mortgages, increase during good periods of housing market cycles. Their results do not point to a statistically significant impact of the regime of housing market cycles on stock holding. However,Corradin et al.(2014) find that the share of wealth invested in risky assets is lower during periods of high expected growth in house prices and that the decrease in risky portfolio holdings for households moving to a more valuable house is greater in high-growth periods. Unlike these papers, we do not model return predictabiity in house prices but assume that excess stock returns are predictable. There is considerable empirical evidence that house prices and stock prices are uncorrelated and that return predictability in stock prices crucially affects risky portfolio choice.