The Role of Options in Long Horizon Portfolio Choice

Abstract

The paper documents some theoretical results about the attractiveness of European style call and put options for long horizon CRRA investors. Investors are assumed to derive utility of life time consumption, rebalance discretely and allowed to take long positions in a log normal index and a riskless asset. Options are assumed to be priced according to the Black and Scholes (1973) and Merton (1973) formula using the correct underlying index volatility where the expiration dates coincide with the next rebalancing date. Risk aversion changes from 2 to 10 and moneyness changes from 0.85 to 1.15. Since there is discreet rebalancing and margin constraints options are not redundant. Index returns can be i.i.d. or predictable. Two key findings are; first, when there is no non-capital income, utility cost of not being able to add long call or put positions is generally small. Second, when there is non-capital income in the form of wage income calibrated reasonably to PSID data, the same cost for long call option positions can be substantial while that for long put option positions is close to zero. The paper also asks if the non-parametric empirical long call or put returns are attractive to the same agent, rather than the Black and Scholes (1973) and Merton (1973) returns. Long call or put positions are significantly less attractive with hardly any demand when risk aversion is 6 and for strike to spot ratios changing from 0.95 to 1.05. The result holds with or without wage income.