Option-Implied Risk Aversion Estimates

THE JOURNAL OF FINANCE • VOL. LIX, NO. 1 • FEBRUARY 2004

Option-Implied Risk Aversion Estimates

ROBERT R. BLISS and NIKOLAOS PANIGIRTZOGLOU∗ ABSTRACT

Using a utility function to adjust the risk-neutral PDF embedded in cross sections of options, we obtain measures of the risk aversion implied in option prices. Using FTSE 100 and S&P 500 options, and both power and exponential-utility functions, we estimate the representative agent’s relative risk aversion (RRA) at different horizons. The estimated coefficients of RRA are all reasonable. The RRA estimates are remarkably consistent across utility functions and across markets for given horizons. The degree of RRA declines broadly with the forecast horizon and is lower during periods of high market volatility.

ESTIMATING THE REPRESENTATIVE AGENT’S or the market’s degree of risk aversion from securities prices has a long history. However, it is only recently that scholars have begun using options data to do so. Options provide a particularly promising context for studying risk preferences. Stocks are infinitely lived and so inferences must be drawn from the discounted stream of cash f lows over an indefinite horizon. Usually this involves additional assumptions as to how those cash f lows evolve (e.g., constant growth of dividends). Since only one value, the discounted present value of all cash f lows, is known, no inferences are possible about variations in preferences over different horizons. Options on the other hand have a fixed expiry date at which payoffs are realized.1 Furthermore, options contracts exist for different investment horizons. Options thus permit studying preferences over specific horizons and simultaneously over multiple horizons. Futures contracts also share this fixed-horizon characteristic. Options

∗ Bliss is with the Federal Reserve Bank of Chicago and Panigirtzoglou is with the Bank of

England. We are particularly grateful for helpful discussions with Lars Hansen; for comments by...