Roberto Pancrazi received his PhD (in economics) from Duke University in 2010. Since then, he is an assistant professor (Junior Chair) in TSE. His research is primarily oriented towards empirical macroeconomics, econometrics and finance. He is currently teaching
the DEEQA courses “Quantitative Techniques in Economics” and “Financial Macroeconomics”
Imagine that you were a little child receiving $100 from your grandmother in 1946. Suppose also, that you were a wanna-be economist who tried to do the best long-run investment decision at the very early stage of your life. At that time, say, you had two options: you could have invested in safe risk-less government bond, or in a riskier stock market. What was the best option? What would you have done?
If you had invested the $100 in government bonds, it would have become (adjusting for inflation) $153 65 years down the line. Instead, if you had kept your money in stocks, it would have become $6473. In other words, historically, investing in stocks gave a 8.2% average annual return, whereas the government bonds only a 0.7% average annual return. The difference in returns between a safe asset and a risky asset can easily be explained with the following argument: given their risky nature, stocks are able to attract investors only if they are compensated with a risk-premium, which is an additional price that investors ask for bearing the risk of holding unsafe assets. In fact, if the returns of government bonds and stocks were the same, no investor would hold stocks. However, it is very important to clarify what "risky" means. It is not possible to predict the return of stocks, given the underlying uncertainty in the performance of the firms. On the other hand, investors know what is the return of the government bonds once they buy them (ignoring possible defaults). Investors also use assets as an insurance device, hence they evaluate the performance of the assets relative to other sources of wealth.
Suppose you are hit by an unexpected negative shock on your income, if for example you lose your job. In that moment, you could sell your assets to get resources to use as a substitute for the reduced income. However, if the value of assets is low at the time, these assets are even less appreciable than assets that have low value in "good times". In other words, investors care about the degree of co-movement of asset prices and their consumption.
With this notion in mind, we should ask the following question: what can rationalize a historical 7.5% equity premium? Is the risk associated with stocks large enough to justify such an equity premium? This question was proposed by Mehra-Prescot in 1985. By using a standard Consumption based Asset Pricing Model (CAPM) with agents having constant relative risk aversion (CRRA) utility function, they showed that only a very high coefficient of risk aversion (greater than 50) could generate an observed value of the risk premium. Plausible values of the relative risk aversion are thought by economists to be less than 3. This is the equity premium puzzle: real investors in real world value risk as requiring a 7.5% premium with respect to safe assets. However, macroeconomic models need agents to be adverse to risk at an implausible degree to rationalize the observed equity premium. A large branch of macro-finance literature have been trying to study departures from the standard CAPM model in order to explain the equity premium with a lower and plausible level of risk aversion. In particular, most of the literature has explored how different preferences and different assumptions on consumption data generating process might help on solving the puzzle. I will briefly give you a summary of these two lines of research. The standard CRRA model assumes time-separable utility across periods. That means that the utility an agent obtains in a period depends only on the consumption in that period. Economists have introduced non-separability in order to solve the equity premium puzzle. For example Abel (1990) showed that habit in consumption with utility depending not just on the level of present consumption, but on its value relative to past consumption, can partially solve the puzzle. However, even with the assumption of non- separability, the risk aversion needed to generate the observed risk-premium is still very large. Instead, Epstein-Zin (1990) proposed recursive preferences, where an agent obtains utility from a non-linear combination of present consumption and future utility. These preferences have received a large amount of attention in the recent literature, given its ability to disentangle the coefficient of risk aversion from the inter-temporal elasticity of substitution (how much an agent like to smooth consumption across time). The tight relationship between these two parameters is one of the primary sources of the puzzle, thus it implies that the recursive preferences are good candidates to provide solutions to the same.
A second line of research on the equity premium puzzle focuses on the assumptions on the data generating process. Then the
puzzle can be formulated as the following: given the pattern of macroeconomic variables that we have observed in the last century, only an implausible value of risk aversion can generate the large risk premium. But what if there is something more than "what we observed in the data"? Barro (2006) proposed a model that is able to generate a large equity premium by assuming that the economy can be subject to rare disasters. A disaster is able to ruin the economy, but it happens with a very low probability. Even though in the post-war period there has not been a disaster, investors still take that probability into account.
As a consequence, they require a large premium for bearing a risk, because holding the risky asset might be terribly bad when a disaster hits. On the other hand, Bansal and Yaron (2004) suggests that macroeconomic variables are characterized by a small (and hidden) component that is very persistent, the so called long- run risk. Therefore, when a bad shock hits, it has very long lasting implications. Agents are adverse to this small long-run risk which explains the large premium. To conclude, the macro-finance literature has been focusing on the equity premium puzzle for a couple of decades now. Explaining how to link macroeconomic variables with financial variables is challenging, but at the same time very important as the recent financial crisis reminded us.
- ABEL, ANDREW B., 1990. “Asset Prices Under Habit Formation and Catching Up With the Joneses”. American Economic Review, May, 80(2), pp. 38–42.
- Bansal, R., Yaron, A., 2004. Risk for the long-run: a potential resolution of asset pricing puzzles. The Journal of Finance, Vol. LIX, No.4, August, pp. 1481- 1509.
- Barro, R.J, 2006. “Rare Disasters and Asset Markets in the Twentieth Century.” Quarterly Journal
of Economics, 121(3): 823–66.
- EPSTEIN, LARRY G. AND ZIN, STANLEY E., 1990. '‘First Order’ Risk Aversion and the Equity Premium Puzzle,” Journal of Monetary Economics, 26(3), pp. 387–407.
- Mehra, Rajnish and Prescott Edward C., 1985. “The Equity Premium: A Puzzle”, Journal of Monetary Economics, 15(2), pp. 145–61.