The Role of Options in Long Horizon Portfolio Choice
44 Pages Posted: 25 Mar 2008
Date Written: August 2007
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. 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 is substantial while that for long put option positions is close to none.
Keywords: life-cycle portfolio choice, stock options
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