On the thirtieth anniversary of Black Monday, the stock market crash of October 19th and 20th in 1987, there have been mentions of “portfolio insurance” having possibly exacerbated the crash.

Portfolio insurance, in principle, is exactly what you might expect it to be: if you own a stock, Stock A, you insure it with a put option on Stock A. Your position becomes equivalent to a call option on Stock A until the put option expires, with the price of this position being the premium of the put option when you bought it.

If you are managing a portfolio on behalf of clients, though, and you just need to insure the portfolio up to a certain date, after which, say, you hand over the portfolio, then to buy American put options to insure the portfolio would be unnecessary. European put options would suffice. So let’s suppose that we are only interested in European options.

In the article that I cite at the bottom (Abken, 1987), it seems that at the time, buying put options as insurance had a few issues. This is assuming that the portfolio we want to insure is a stock index: the S&P 500 index. The issues were:

- Exchange-traded index options only had matures up to nine months
- Exchange-traded index options had a limited number of strike prices
- It’s implied that only American options were available (which we would expect have a premium over European options).

Thus, instead of using put options to insure the portfolio, the portfolio and put options are replicated by holding some of the money in the portfolio and some of it in bonds, Treasury bills, that we assume to provide us with the risk-free rate.

Without worrying about the math, the Black-Scholes equation gives us a way to represent our stock index S and put options P as:

$$S + P = S \cdot N_1 + K \cdot DF \cdot N_2$$

d

Source:

Abken, Peter A. “An Introduction to Portfolio Insurance.” Economic Review, November/December 1987: 2-25.

Link to article. Archived.

*Related*