Derivatives

CHAPTER 29Portfolio Insurance

Aims

• To show how static stock+put insurance can achieve a lower bound for the value of a diversified stock portfolio, while maintaining most of the upside potential.
• To demonstrate how static stock+put insurance is equivalent to a replication portfolio of calls and T-bills. This is an example of put–call parity using stock index options.
• To analyse how day-to-day price changes of a ‘stock+put’ portfolio can be replicated using either a ‘stock+futures’ portfolio or a ‘stock+T-Bill’ portfolio. Replication portfolios are used because they are often less costly than directly using the ‘stock+put’ combination.

Portfolio insurance is a general term which refers to a strategy of hedging an equity portfolio to ensure that it does not fall below some prescribed minimum value, while also retaining most of the upside potential, should stock prices increase. We have already outlined the static hedging strategy of stock+put insurance which at maturity (of the put) ensures a lower bound equal to the strike price of the put. Upside potential is also maintained because if the stock price (at maturity of the put) is greater than the strike price, the put expires worthless but the investor benefits from high stock prices (less the put premium). However, in practice, stock+put insurance has a number of drawbacks, namely:

• the hedging horizon of pension funds and mutual fund managers may be long and stock index options then have to be rolled over and this may be costly. ...