A diversified portfolio’s value can be insured using options written on a corresponding index (e.g., the S&P 500). If we assume that the portfolio closely replicates the index, that its dividends match the index dividends, and that its beta equals 1, then by purchasing an appropriate number of put options, it becomes possible to insure the portfolio’s value against falling below a chosen lower bound.
Let’s take an example and assume we want to insure the portfolio’s value over a 3-month horizon:
Based on these figures, we can derive that 5 put options with a strike price of 900 index points are sufficient to insure the portfolio against a drop below the target protection level.
The calculations become slightly more complex when the portfolio’s beta differs from 1, because beta affects the portfolio’s expected return relative to the risk-free rate. For this reason, it becomes necessary to determine the appropriate strike price.
In such cases, we use the CAPM formula to establish the relationship between the portfolio’s expected future value and the strike price of the put option.
In our example, we obtain that when the index level becomes 960, the portfolio’s expected value equals the protection floor ($450,000):
Therefore, we need 5 put options with a 960 strike price. In the end, we arrive at the following structure:
Adapted from:
Options, Futures & Other Derivatives — John C. Hull