Understanding Risk Aversion in Financial Markets

At the economics meetings here in San Diego this weekend, I learned about some very interesting new research on one of the core questions in finance and macroeconomics that had long puzzled me.

We know that some assets on average offer you a higher return than others. For example, over time you’ll make more money investing in stocks compared to bonds. This clearly is a consequence of the fact that stocks are riskier than bonds, for which stocks compensate investors by offering a higher average return. We also know that this compensation for risk changes over time in dramatic ways that are related to business cycles and credit booms and busts.

But understanding exactly what’s behind this has proven elusive. One idea is that an asset’s risk compensation depends on the covariance between its return and aggregate consumption. Something that pays off big when times are good is not as attractive (and therefore must offer a higher average return) compared to an asset that pays big when you really need the money. Although this is a compelling formulation from the perspective of many standard macroeconomic models, it has proven very difficult to reconcile with the observed data.

Another popular approach, known as the capital asset pricing model, suggests that what matters is an asset’s comovement with the overall market. According to CAPM, an asset whose biggest payoffs come when the market is doing well would be less attractive than others unless it offers a higher average return. Again there are elegant theoretical motivations for why such a relation should hold, and abundant evidence that something more is going on in the data.

Researchers Tobias Adrian of the Federal Reserve Bank of New York, Erkko Etula of the Federal Reserve Bank of New York (now at Goldman Sachs), and Tyler Muir of Northwestern University have a very interesting paper that will soon be appearing in the Journal of Finance that offers another perspective on what ultimately drives the market price of risk. They argue that the key economic agents whose arbitrage ensures that risk is priced consistently across assets are broker-dealers. Rather than try to explain risk-compensation in terms of the marginal value of a dollar to a representative consumer or investor in the economy, the authors suggest that we should look at the marginal value of a dollar to broker-dealers as a group. The motivation for looking at broker-dealers is that they are market makers across various asset classes, trade actively, and constantly monitor the evolution of economic activity. Broker-dealers are perhaps the closest entity to act as rational, forward looking and continuously well informed economic agents. In contrast, rational inattention or behavioral biases on the part of households might partially explain the failure of consumption-based models or CAPM.

The leverage of broker-dealers varies substantially over time. When leverage is high, it is easy for them to use their assets to meet margin requirements. That means that an asset that pays off big in times of high leverage is less useful to broker-dealers (and so must offer a higher expected return in compensation) compared to an asset that does better in times of lower leverage.

The graph below plots the series for broker-dealer leverage that Adrian, Etula, and Muir suggest we look at. If we thought of assets minus liabilities as the net equity of broker-dealers, leverage could be defined as the ratio of assets to net equity. This is not particularly a business cycle indicator– leverage actually increased during the recessions of 1970 and 1982 and during the first half of the recessions of 2001 and 2007-2009. Instead, abrupt drops in leverage were observed to follow specific financial events noted by the authors, such as the stock market crash of October 1987, the peso crisis in December 1994, the failure of Long Term Capital Management in the fall of 1998, the terrorist attacks in September of 2001, and the failure of Lehman in September of 2008.


Natural log of ratio of (1) total assets of broker-dealers to (2) total broker-dealer assets minus total broker-dealer liabilities, quarterly, 1968:Q1 to 2012:Q3, from Flow of Funds, Table L127, Federal Reserve. Shaded areas denote NBER recession dates.

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The authors then demonstrate that two-quarter changes in this leverage measure are remarkably effective in explaining the prices of various financial assets. The scatter diagram below summarizes the average returns on a variety of different asset groups, with assets higher on the vertical axis providing higher average returns over the last half century. The horizontal axis gives the predicted average return for that asset group based on its comovement with shocks to broker-dealer leverage. For example, if you look at stocks that have been doing poorer than others recently (the Mom 1 or Mom 2 group), their performance over the next 3 months is probably going to depend on events that are unrelated to those that will drive changes in broker-dealer leverage over those same 3 months. For this reason, these stocks are far to the left of other assets on the graph and according to the authors’ model are predicted to have a lower expected return than other groups. The actual average return (position on the vertical axis) for Mom 1 or Mom 2 indeed turned out to be quite low over this sample period. Portfolios constructed from short-maturity Treasuries also have little comovement with leverage which gives them lower expected returns according to the model, and such assets are also observed historically to offer lower realized returns. On the other hand, the prices of stocks with low market capitalization but high book-to-market ratios (such as S1B5 and S2B5) turn out to move strongly with leverage. A portfolio constructed from such stocks appears on the far right of the scatter diagram, and the model successfully predicts the high average return observed for these stocks.


Vertical axis: average realized mean excess returns over 1968:Q1-2009:Q4 for 25 different equity portfolios constructed on the basis of size and book-to-market, 10 equity portfolios sorted by momentum, and 6 Treasury bond portfolios sorted by maturity. Horizontal axis: predicted excess return based on the portfolio’s covariance with the 2-quarter shock to broker-dealer leverage. Source: Adrian, Etula and Muir (2012).

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The authors find that the price of risk implied by this leverage factor is remarkably consistent across different portfolios with low cross-sectional pricing errors. The long-sought “stochastic discount factor” underlying modern finance theory may finally have been given a name and a face.

This piece is cross-posted from Econbrowser with permission.

3 Responses to "Understanding Risk Aversion in Financial Markets"

  1. Michael Stern   January 15, 2013 at 11:10 am

    Nice post, thanks. A question about their data — this looks to be based on the Fed's flow of funds data, so quarterly with about a two month delay. Is that right? If so, does it have any predictive value, or is it merely explanatory in hindsight. Is there some way to get perspective on market maker leverage without the lag?

  2. Per Kurowski   January 17, 2013 at 6:07 pm

    If all bank crises are caused by excessive lending to some of “The Infallible”, why need banks to hold more capital when lending to “The Risky”?

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