Wednesday, April 30, 2008

Options and The Volatility Risk Premium

Classical mean-variance portfolio theory assumes that investors are risk-averse. Here's a paper that examines the "volatility risk" premium using options data, titled "The Price of Market Voilatility Risk", by Jefferson Duarte and Christopher Jones:
We analyze the volatility risk premium by applying a modified two-pass Fama-MacBeth procedure to the returns of a large cross section of the returns of options on individual equities. Our results provide strong evidence of a volatility risk premium that is increasing in the level of overall market volatility. This risk premium provides compensation for risk stemming both from the characteristics of the option contract and the riskiness of the underlying equity. We also show with a large scale Monte Carlo simulation that measurement error in option prices and violations of arbitrage bounds induce highly economically significant biases in the mean returns of options. In fact, our simulation results demonstrate that biases can be up to several percentage points per day. These large biases can lead researchers to faulty conclusions with respect to both the magnitude of the volatility risk premium and the sign of expected option returns.
Read the whole thing here.

While their paper does a good job of showing how option returns in academic studies can be biased by bid-ask spread, they also give some nice results on just how big the "volatility premium" may be (they're not the first to find this, but I like their results nonetheless).

The following table from the paper, shows mean returns on S&P 500 index options at various maturities (Short, Medium, Long) and degrees of of moneyness (In The Money, At The Money, Out of The Money). The figures are in basis points/day and are adjusted for bid-ask spread biases. What I found most striking were the results for short positions on short-term deep out-of-the-money puts (4% return per day) and deep OTM calls (3-9% per day).

Now THAT's definitely a table suitable for use in class.

HT: CXO Advisory Group

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