To test multifactor pricing models, the authors use S&P 500 Index put and call option portfolios. They reduce the skewness and variance of monthly portfolio returns to approximate a near-normal distribution to which they can then apply linear factor models. They find that just four crisis-related factors, among the many they consider, can sufficiently explain index option returns.
The authors use S&P 500 Index put and call option portfolios to test multifactor pricing models. By adjusting portfolio weights to maintain target betas, maturity, and “moneyness,” they reduce the skewness and variance of monthly portfolio returns so that the returns resemble a normal distribution. The authors are then able to apply linear factor models to the data.
Based on their use of leverage-adjusted returns of S&P 500 options, the authors disagree with the predictions of the Black–Scholes–Merton model. They also find that out-of-the-money puts are very sensitive to market conditions.
How Is This Research Useful to Practitioners?
This research is useful to practitioners because it identifies crisis-related factors that explain the behavior of option returns with more accuracy than the one-factor CAPM, reducing the root mean square error by around 50%. Two key factors that the authors identify are “jump,” which captures jumps in the price of the market index, and “jump volatility,” which captures jumps in the market volatility. Either of these factors, in conjunction with the market, captures major financial crises, and both are highly negatively correlated (at –74%).
Two additional factors that explain option returns are identified, although they are slightly less effective at reducing the root mean square error: the volatility (the change in the implied volatility of at-the-money index call option portfolios) and a liquidity factor.
This research also provides a methodology for normalizing option price returns. The authors offer a publicly available panel of deleveraged monthly returns of options, split by moneyness, maturity, and type, which might provide further opportunities for testing linear pricing models.
How Did the Authors Conduct This Research?
The authors begin by constructing a cross section of portfolios of options with varying levels of moneyness and different maturities. Their universe includes 54 portfolios (27 calls and 27 puts) using S&P 500 European options, with nine different target moneyness ratios and three different maturities (30, 60, and 90 days). The data are closing prices from April 1986 to January 2012. They are sourced from Berkeley Options Database and the OptionMetrics database. These portfolios are then deleveraged to produce a target market beta of 1.
The option prices are sifted with a variety of filters to ensure that only those options with reliable price quotes are included in the final analysis. These data consist of 173,125 observations from the Berkeley Options Database and 824,397 observations from the OptionMetrics database (which accounted for 49% of the call data).
Outliers (options with portfolio weights below 1%) are removed, and the weights are then adjusted to sum to 1. The authors use the one-day arithmetic return for the options, with the bid–ask midpoint. With these data, the authors conduct daily rebalancing to produce monthly option portfolio returns with distributions that are close to normal. They use these data to estimate factor betas.
To reduce the impact of errors in their variables, the authors report bootstrapped standard errors by regressing the average returns of the portfolios on their betas, with the added restriction that the intercept (an estimate for alpha or excess return) is equal to zero. This process increases the power of their test and reduces the likelihood of spurious results. They then draw 10,000 simulations to calculate bootstrapped standard errors.
With standard CAPM estimations, call options are overpriced. But each of the four factors used by the authors is able to improve these results, providing an effective method of more accurately pricing call returns. The authors also test three-factor models and find that these models—in particular, a three-factor model with volatility jump, liquidity, and the market—explain option returns better than the two-factor model does.
The authors use a number of different econometric techniques. As they admit, this procedure contains a few different stages, each of which could introduce errors into the different variables being estimated.
They argue that with their methodology, they have removed the impact of skewness and kurtosis to provide data on option price returns that are close to being normally distributed so that they can test linear factor models. It is unclear whether the “normalization” process itself changes the properties of the data so much that it reduces the impact of noise and actually removes key characteristics of the underlying option investments.