The 2013 Nobel Prize in economics has been awarded to Lars Hansen, Eugene Fama and Robert Shiller "for their empirical analysis of asset prices." These were three important actors in the asset-pricing literature whose contributions are given context herein.

# CAPM and the efficient market hypothesis

Asset pricing theory shows that stock prices reflect expected dividends, discounted at risk-adjusted rates. Fama (1970) coined the "market efficiency hypothesis" to emphasise the assumption that investors' expectations were rational – that is, they optimally use all available information.

In 1969, to test this hypothesis, Fama – with Lawrence Fisher, Michael Jensen and Richard Roll – developed a new methodology called "event studies," that is still used to this day in many fields, including finance, accounting and industrial economics. In this study and others, Fama presented evidence in support of the hypothesis that investors immediately and optimally use new information, and that higher returns to investment could only come at the cost of higher risk.

In a one-period setting, the principal model is the Capital Asset Pricing Model (CAPM), developed by Sharpe (1964) and Lintner (1965), which predicts that differences in expected returns across assets can only be justified by differences in their exposures to aggregate market risk. In his 1973 paper with James McBeth, Eugene Fama offered one of the first tests of this theory, and found support for the CAPM. Contrary to previous methods, theirs can account for time variations in the risk exposures (the *ß*s), and for cross-sectional correlations, and became the standard for cross-sectional analysis of stock returns.

# Econometric methods

Theoretical asset pricing then moved on to dynamic models. The Consumption based-CAPM model shows how the discount factor depends on the ratio of marginal utilities of future consumption relative to today's consumption. The idea is simple – investors value assets with payoffs in states where they are already consuming a lot less than assets with payoffs in states where they are consuming very little.

Testing this model turned out to be challenging, and was made possible by the path- breaking econometric methodology Lars Hansen developed in 1982, the Generalized Method of Moments (GMM). GMM tackles the estimation of non-linear functions with constraints on their expectations (in the case of the Consumption-CAPM, the non-linear function to estimate is the ratio of marginal utilities, the constraints being that their covariations with the payoffs determine the prices). GMM’s impact on model testing in both the microeconomics and the macroeconomics literature cannot be emphasised too strongly.

In 1982, in collaboration with Ken Singleton, Lars Hansen offered the first structural econometric analysis of the dynamic Consumption-CAPM theory, starting from the condition expressing the optimality of an agent's portfolio choice. Hansen and Jagannathan (1997) formally specified which conditions the discount factor (the ratio of marginal utilities in the Consumption-CAPM framework) has to satisfy in order to explain observed returns. These approaches have become the workhorse of asset pricing.

# Empirical puzzles

Relying on these methods, a literature starting with Hansen and Singleton (1982) and Grossman and Shiller (1981) found the estimates of risk-aversion implied by the theory were unrealistically large. This gave rise to the ‘excess-risk premium puzzle.’

Robert Shiller also started from the theoretical premise that prices should be (appropriately weighted) expectations of future dividends, and found evidence in his 1981 paper that challenged this theory. If prices reflect rational expectations of dividends, then their changes should reflect changes in these expectations. In contrast, Shiller found prices were far more volatile than dividends. This gave rise to a second puzzle, the ‘excess volatility puzzle.’ Campbell and Shiller (1988) demonstrated that the ‘excess volatility puzzle’ could be linked to the predictability of long-horizon returns, which was observed in the data.

In their 1992 paper, Eugene Fama and Kenneth French presented another puzzling empirical result. They found small stocks had higher returns than large ones, and ‘value stocks’ (with low market capitalisation relative to their book value) had higher returns than ‘growth stocks’ (with large market to book ratio), without having higher s. The evidence on the ‘value premium’ has proved to be robust to out of sample testing (in contrast to the ‘small firm effect,’ which was likely spurious).

Altogether, this set of results was damning for the theory. At the same time it showed this was a pretty good theory – one that could be quantified, confronted to the data and rejected. But it left us in need of a theory which could better fit the facts.

# New theories

Since the CAPM and its dynamic counterpart were based on perfect and complete markets and rational investors, a natural solution to relax some of these assumptions. Robert Shiller advocated for the repeal of the rationality assumption, and became a leader of the ‘behavioural finance’ school of thoughts, insisting we should take on board the insights from psychology to model irrational beliefs. This led to his 2000 book, *Irrational Exuberance*, offering a timely prediction of the collapse of the dot-com bubble.

Another branch of research argues the empirical puzzles do not imply that investors are irrational – they simply call for richer models. Lars Hansen has been a major contributor to these new theoretical developments. His 2001 paper on robustness with Thomas Sargent analysed the pricing of assets in markets where investors are uncertain about their model of the world. His 2008 paper with John Heaton and Nan Li suggested the large returns of value stocks could be justified by their high exposure to long-term risk.

# Data

None of the econometric and empirical developments summarised above would have been possible without the availability of reliable data. Fama played a decisive role in this respect, by inspiring and leading the development of the Center for Research in Securities Prices database at the University of Chicago. Shiller also contributed to the development of databases, with the Case Shiller Weiss real estate index.

# Concluding remarks

Thanks to their careful investigation of data, informed by their deep understanding of theory, the 2013 Nobel prize winners in economics have taught us a lot about asset pricing. The good news for researchers is we still have much to learn. The methodologies as well as the example of Fama, Hansen, and Shiller will guide us on this path.

# References

Campbell, J Y and R J Shiller (1988a), “The dividend-price ratio and expectations of future dividends and discount factors,” *Review of Financial Studies* 1, 195-227

Fama, E F (1970), “Efficient capital markets: a review of theory and empirical work,” *Journal of Finance* 25, 383-417.

Fama, E F, L Fisher, M Jensen and R Roll (1969), “The adjustment of stock prices to new information,” *International Economic Review* 10, 1-21.

Fama, E F and K R French (1992), “The cross-section of expected stock returns,” *Journal of Finance* 47, 427-466.

Fama, E F and J D MacBeth (1973), “Risk, return and equilibrium: empirical tests,” *Journal of Political Economy* 81, 607-636.

Grossman, S J and R J Shiller (1981), “The determinants of the variability of stock market prices,” *The American Economic Review* 71, 222-227.

Hansen, L P (1982), “Large sample properties of generalized method of moments estimators,” *Econometrica* 50, 1029-1054.

Hansen, L P, J C Heaton, and N Li (2008), “Consumption strikes back? Measuring long‐run risk,” *Journal of Political Economy* 116, 260-302.

Hansen, L P and R Jagannathan (1997), “Assessing specification errors in stochastic discount factor models,” *Journal of Finance* 52(2), 557-590.

Hansen, L P and T J Sargent (2001), “Robust control and model uncertainty,” *The American Economic Review* 91(2), 60-66.

Hansen, L P and K J Singleton (1982), “Generalized instrumental variable estimation of nonlinear rational expectations models,” *Econometrica* 50(5), 1269-1286.

Lintner, J (1965), “The valuation of risk assets and the selection of risky investments in stock portfolios and capital budgets,” *Review of Economics and Statistics* 47, 13-37.

Sharpe, W (1964) “Capital asset prices: A theory of market equilibrium under conditions of risk,” *Journal of Finance* 19, 425-442.

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

Shiller, R J (1981b), “The use of volatility measures in assessing market efficiency,” *Journal of Finance* 36(2), 291-304.

Shiller, R J (2000), *Irrational Exuberance*, Princeton University Press.