# Options Information: Can It Lead to a Better Stock Portfolio?

## Winner of the 2014 AIMA Canada Research Award.

BY Peter Christoffersen and Xuhui (Nick) Pan | June 11, 2014

It has long been recognized that options provide excellent forecasts of the future volatility of the underlying asset. Academic researchers have furthermore found evidence that option-implied volatility estimates from index options can help predict future returns on the market.

Recently, academics have begun to investigate if option prices contain information that is useful for equity portfolio allocation. They do and we therefore provide an overview of this literature in our article. Three representative papers in the literature we survey are:

**Ang, Hodrick, Xing and Zhang (2006)** who spearheaded the literature by showing that a stock’s exposure to the option-implied stock market volatility, VIX, is an important determinant of its expected return.

**Conrad, Dittmar and Ghysels (2013)** who report significant spreads in stock returns when sorting on firm-specific option-implied skewness and kurtosis using individual equity options.

**Christoffersen and Pan (2014**) who in recent work find that stocks’ exposure to crude-oil option volatility provides important information for equity portfolio management.

The literature we survey has two important features. First, while various pieces of information from equity, index and commodity options are used, options are not actually traded in any of the strategies we present. This is important because option spreads tend to be wider than the spreads on stocks and futures contracts. Second, the focus is on cross-sectional equity market prediction as opposed to time-series prediction. The articles we survey show that stocks with exposure to certain option-implied characteristics tend to perform better than other stocks on average through time.

Conrad, Dittmar, and Ghysels (2013) compute model-free option-implied volatility, skewness and kurtosis each month during 1996 to 2005 for each of approximately 307 stocks using all the available options on each stock during the month. They show that the portfolio that buys the third of the stocks with the lowest volatility and sells short the third of the stocks with the highest volatility earns 56 bps per month, although this return is not statistically significant nor is its characteristic-adjusted counterpart. Sorting on option-implied skewness earns a large and significant return. The long-short spread return is 82 bps per month when going long stocks with small (that is large negative) skewness and short stocks with high skewness. The long-short spread using option-implied kurtosis is also large and significant at 72 bps. Stocks with large kurtosis on average outperform stocks with low kurtosis.

Ang, Hodrick, Xing and Zhang (2006) were to our knowledge the first to implement an option-implied risk factor in the academic literature. They used the daily change in the Chicago Board Options Exchange (CBOE) volatility index, VIX, as the market-wide option-implied risk factor. Each month, they regress daily excess returns from all stocks on NYSE/AMEX/NASDAQ on changes in the VIX beta for each stock. They use a rolling sample of 30 calendar days to estimate each beta. The following month’s average return on each quintile portfolio is then recorded through time. They find that an equity strategy that goes long stocks with the lowest (largest negative) beta with changes in the VIX and short stocks with the largest beta earn on average 104 bps per month with an alpha of 83 bps. Both return measures are significant as the t-statistics in the parentheses show. Stocks that have a large (positive) exposure to changes in the VIX may be a good hedge against shocks to economic uncertainty and they are therefore priced relatively rich and earn a low average return.

In Christoffersen and Pan (2014), we investigate if stocks’ exposure to uncertainty in option-implied oil price volatility determines their return on average. We estimate each stock’s beta with the so-called oil VIX each month using daily stock returns and daily changes in the oil VIX within the month. We then check if, on average, stocks’ exposure to the oil VIX is reflected in the cross-firm patterns in stock returns in the following month. Our results show that the average return on stocks in the quintile with the lowest oil VIX beta is 108 bps compared with 42 bps per month for stocks with the highest oil VIX beta. The spread of 66 bps per month is strongly significant. The alpha is 75 bps and it is not as strongly significant due to the added sampling error when estimating factor loadings. The returns and alphas both decrease in a monotone fashion across quintile portfolios as the oil VIX beta increases. Stocks with a high oil VIX beta do well when oil volatility increases. They are viewed by investors as being good hedges against economic uncertainty shocks and therefore trade at relatively high valuations and offer relatively low returns on average.

In our article we also highlight some interesting recent work applying option price information when implementing mean-variance portfolios as well as the CAPM.

While the Markowitz mean-variance formula is a cornerstone of modern portfolio theory, it is challenging to implement in practice. The expected return vector and the covariance matrix must both be estimated and will therefore contain estimation error. The nonlinearity of the Markowitz formula compounds the problems from the seemingly inevitable problems from estimation error. The academic literature depressingly finds that a simple equal-weighted portfolio often works as well as the theoretically-optimal Markowitz portfolio. Recently, DeMiguel, Plyakha, Uppal, Vilkov (2014), however, have shown show that all is not lost. One can increase the Sharpe ratio of a mean-variance portfolio of stocks when using option-implied volatility and skewness estimates.

The CAPM is a workhorse model used in many applications in both corporate finance and investment management. Unfortunately, its key parameter, beta, is difficult to estimate. Typically historical returns are used. In many cases, however, historical returns may not be representative of the stock’s risk going forward. This is the case for example for firms with recently reorganized balance sheets or operations, or for firms facing a new competitive environment caused, for example, by new market entrants. Fortunately, Chang, Christoffersen, Jacobs, and Vainberg (2012) show that the CAPM beta can be estimated from a single day of options if the stock has close to zero co-skewness and zero idiosyncratic skewness. In this case the option-implied beta can be computed from the relative slopes and levels of the Black-Scholes implied volatility curves for equity and index options. The ability to compute a beta from just a single day of option data renders it much less exposed to the challenges from structural breaks which plague traditional beta estimates based on long samples of historical returns.

Read the full paper here.