Disaster risk and asset pricing

Jerry Tsai, Jessica Wachter

11 June 2015

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A persistently puzzling feature of the US stock market is the high return to holding a diversified equity portfolio. On average, over the last 60 years, equities have outperformed short-term bonds by 7.5% a year. The difference, when cumulated over time, is dramatic. Figure 1 shows that $1 invested in 1947 in a value-weighted portfolio of equities traded on major exchanges would have increased 100-fold (in 1947 dollars), while a strategy of rolling over short-term Treasury bills would have barely kept up with inflation. The 2008 Global Crisis resulted in a very temporary dip in this performance. 

Figure 1. Long-run returns to investing equities versus Treasury Bills

Why do equities earn such a high rate of return?

The most obvious possibility is that this high return is a compensation for risk.   However, while equity markets are very risky (the standard deviation of the above portfolio is 18% per year), this risk is not reflected in the broader economy. For long-run investors who are willing to ride out the ups and downs of the stock market, the risk that matters is the risk in actual consumption. And that standard deviation has historically been less than 2% a year, even when taking the Great Recession into account. This disconnect between the return to holding stocks and the risk of the overall economy, is known as the equity premium puzzle (Mehra and Prescott 1985).

In a recent article (Tsai and Wachter 2015), we argue that this equity premium reflects the risk of an economy-wide disaster. Our argument builds on work by Robert Barro (2006), further developed with co-authors Emi Nakamura, John Steinssen and Jose Ursua (Barro and Ursua 2008, Nakamura et al. 2011). Using international data from the last 100 years, these authors document a number of episodes with striking declines in consumption growth. One of these, the Great Depression, occurred in the US. But the Great Depression was, relatively speaking, a minor event. During the Great Depression, consumption declined by 21%. Compare this to the catastrophic effect of World War II on countries in Europe; consumption declined in Austria by 44% and in France by 58%. Figure 2 shows a histogram of these consumption disasters. Figure 2 is not a complete description of consumption disasters. Disasters not shown in Figure 2 (because of limited data availability) include the Russian Revolution and the Civil War in the US. These authors conclude that events of the last 100 years suggest a probability of a disaster of between 2 and 3% per year.

Figure 2. Distribution of consumption declines in the event of a disaster

If investors implicitly understand that the distribution of consumption growth includes these rare disasters, then we can rationalise why equities generate such apparent outsized returns – these returns compensate investors for bearing the risk of a catastrophic decline in the stock market during an economy-wide disaster. While this idea is simple and intuitive, it is only now gaining widespread attention. This may be because many economics models have at their core risk that is normally distributed. Such risk, described by the famous bell curve, suggests that large fluctuations such as those in the intermediate aftermath of World War II should occur far more rarely than they actually do.

Viewed through the lens of the normal distribution, the last 60 years or so of US data are very convincing that economy-wide risks are low.

The reason is that the thin tails of the bell curve make risk appear deceptively easy to measure. Rare disasters appear impossible, and what may be a period of unusual stability appears to be a permanent feature of the economy.

However, taking a broader view of the data leads to the conclusion that the thin-tailed normal distribution cannot account for everything.

Coupled with the inevitable sample-selection problems (the US economy is the subject of study because it has been successful), the last 60 years of US data do not provide a basis for ruling out large negative events, nor do the last 100 years of US data rule out an event that is more significant than the Great Depression. 

Once we account for the possibility of rare disasters, the equity premium is no longer a puzzle. High equity returns do not represent a ‘free lunch’ in which investors receive high returns without taking on risk. On the other hand, equities do not represent something that prudent investors should avoid. Rather high returns on equities reward investors for bearing the risk of a large decline in stock prices during an economic disaster. 

Stock market volatility

Another basic question about the stock market pertains to the level of volatility.   Various studies, beginning with Shiller (1981) have concluded that the volatility in the stock market is too great to represent forecasts of future dividends or other measures of cash flows of corporations. As memorably described by Shiller, the stock market appears to exhibit ‘excess’ volatility, namely volatility that cannot be attributed to rational factors and rather reflects (in the words of Keynes) the ‘animal spirits’ of investors. 

Rare disaster models offer an alternative way to understand excess volatility. Rather than reflecting the day-to-day whims of investors, stock market fluctuations could reflect investors' changing views of the probability of a rare disaster. An increased probability of a disaster implies that future earnings are likely to be both lower and more risky. These effects combine to lower equity prices, even if a disaster itself does not take place. Thus, stock returns, which incorporate these probabilities, can be far more volatile than dividends or consumption, which reflect (primarily) the disaster itself. 

An example of how probabilities can influence stock prices can be found in the recent Global Crisis. As shown in Figure 3, both stock prices and consumption were down significantly at the end of 2008 relative to where they were in 2007. However, the decline in consumption is far smaller than in stock prices (note that consumption is shown on a different scale than prices). Events such as the collapse of Lehman brothers represented a positive shock to the probability of a rare disaster, lowering stock prices beyond what could be justified by relatively small shifts in the risk of fundamentals like consumption. The fact that the Crisis was followed by higher than usual stock returns is also not surprising, as higher risk premia were necessary to induce investors to hold equities during a period of greater disaster risk. This is exactly what one would expect to observe if a disaster were anticipated and did not take place.

Figure 3. Consumption and equity prices during the Great Recession

Low interest rates

As is well-known, the Global Crisis and its aftermath have been characterised by interest rates that are extremely low by historical standards. Figure 4 shows the yield on the 3-month Treasury bill; while already low in 2007, it falled in 2008, and has stayed near zero since. Of course, many factors influence interest rates. However, the same model that can explain a high equity premium and high stock market volatility, can also explain this seemingly anomalous interest rate behaviour. When the risk of a rare disaster rises, investors want to save to protect their assets for the future. This lowers the required return on savings, namely the interest rate, even as it raises the implicit rate of return on equities. This could contribute to the challenge facing central banks when conducting monetary policy. According to this view, raising interest rates may not be a matter of a simple policy decision, and may require the far-harder task of altering investors' perceptions of risk.

Figure 4. Three-month Treasury bill returns during the Great Recession

Conclusion

Recent research demonstrates how rare disasters can explain both a high equity premium and high stock market volatility. Time-varying disaster risk offers a compelling explanation for the patterns in equity values, consumption, and interest rates during the recent Global Crisis and its aftermath. While significant attention has rightly been paid to reducing or eliminating risk in the aftermath of the Crisis, research on disasters suggests that this is a risk that, to some extent, has long been present and accounted for in equity markets. While policymakers struggle with strategies to avoid crises, investors may have decided that a risk of a crisis can never be truly eliminated, and have acted accordingly.

References

Barro, R J (2006) “Rare disasters and asset markets in the twentieth century”, Quarterly Journal of Economics 121(3), 823–866.

Barro, R J, and J F Ursúa (2008) “Macroeconomic crises since 1870”, Brookings Papers on Economic Activity no. 1, 255–350.

Mehra, R, and E C Prescott (1985) “The equity premium: A puzzle”, Journal of Monetary Economics 15(2), 145–161.

Nakamura, E, J Steinsson, R Barro, and J Ursúa (2013) “Crises and recoveries in an empirical model of consumption disasters”, American Economic Journal: Macroeconomics 5(3), 35–74.

Shiller, R J (1981) “Do stock prices move too much to be justified by subsequent changes in dividends?”, The American Economic Review 71(3), 421–436.

Tsai, J, and J A Wachter (2015) “Disaster risk and its implications for asset pricing”, NBER Working paper #20926.

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Topics:  Financial markets Global crisis

Tags:  asset prices, external shocks, risk, equities

University Lecturer in Economics in the Department of Economics, University of Oxford; Fellow, Oxford-Man Institute of Quantitative Finance

Richard B. Worley Professor of Financial Management at the Wharton School of Business, University of Pennsylvania

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