On the Optimality of Portfolio Insurance

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Abstract
This paper examines the optimality of an insurance strategy in which an investor buys a risky asset and a put on that asset. The put's striking price serves as the insurance level. In complete markets, it is highly unlikely that an investor would utilize such a strategy. However, in some types of less complete markets, an investor may wish to purchase a put on the risky asset. Given only a risky asset, a put, and noncontinuous trading, an investor would purchase a put as a way of introducing a risk‐free asset into the portfolio. If, in addition, there is a risk‐free asset and the investor's utility function displays constant proportional risk‐aversion, then the investor would buy the risk‐free asset directly and not buy a put. In sum, only under the most incomplete markets would an investor find an insurance strategy optimal.

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