On the inefficiency of portfolio insurance and caveats to the mean/downside-risk framework

Portfolio insurance strategies based on options typically treat the investment in the risky asset, e.g., stock, as fixed. We show in a mean/downside-risk framework that such a strategy is inefficient. Using at the money put options, expected returns can be increased by more than 250 basis points without taking on more risk. Gains can become arbitrarily large when one uses options with extremely high strike prices. This is due to a serious caveat to the mean/downside-risk framework that is typically adopted in the literature by substituting downside-risk measures for standard risk measures such as the variance of returns. These pathologic results vanish when one maximizes an appropriately chosen HARA utility function. In this framework, fixing the holding of the risky asset in advance leads to efficiency losses that vary between 250 and 650 basis points depending on the degree of risk aversion.mean/downside-risk efficiency; option strategies; optimal portfolio choice; portfolio insurance; downside-risk.

Black Scholes for Portfolios of Options in Discrete Time: the Price is Right, the Hedge is wrong

Taking a portfolio perspective on option pricing and hedging, we show that within the standard Black-Scholes-Merton framework large portfolios of options can be hedged without risk in discrete time. The nature of the hedge portfolio in the limit of large portfolio size is substantially different from the standard continuous time delta-hedge. The underlying values of the options in our framework are driven by systematic and idiosyncratic risk factors. Instead of linearly (delta) hedging the total risk of each option separately, the correct hedge portfolio in discrete time eliminates linear (delta) as well as second (gamma) and higher order exposures to the systematic risk factor only. The idiosyncratic risk is not hedged, but diversified. Our result shows that preference free valuation of option portfolios using linear assets only is applicable in discrete time as well. The price paid for this result is that the number of securities in the portfolio has to grow indefinitely. This ties the literature on option pricing and hedging closer together with the APT literature in its focus on systematic risk factors. For portfolios of finite size, the optimal hedge strategy makes a trade-off between hedging linear idiosyncratic and higher order systematic risk.Option Hedging; Discrete Time; Portfolio Approach; Preference Free Valuation; Hedging Errors; Arbitrage Pricing Theory