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1 May 1990 Financial Analysts Journal Volume 46, Issue 3

The Effects of Volatility Misestimation on Option-Replication Portfolio Insurance

  1. Richard J. Rendleman
  2. Thomas J. O'Brien

To insure a stock portfolio, one could purchase a put option with a striking price equal to some desired minimum value for the portfolio. Alternatively, one could replicate this stock-plus-put portfolio with a portfolio of stock and cash. The initial allocations to stock and cash will depend upon the parameters of an option valuation formula and will change as those parameters change. In particular, the construction of such synthetic, option-replicating portfolio insurance, hence its outcome, will depend critically on correct estimation of the volatility of the portfolio being insured.

Volatility misestimation will cause the price of the synthetic put to deviate from its expected price and will result in incorrect allocations between stock and cash. As a result, the outcome of a synthetic portfolio insurance strategy based on misestimated volatility will be unpredictable. A manager who underestimates volatility will typically end up buying less insurance than is necessary to ensure a given return, while a manager who overestimates volatility will buy more insurance than is necessary. Both outcomes can be costly in terms of missed floors and forgone gains.

Simulations of portfolio insurance performance over the period of the October 1987 market crash indicate that most insured portfolios would have fallen short of their promised values. In general, however, the lower the guaranteed floor of the insurance program (hence the lower its insurance), the worse its results.

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