Articles

Options Before Quants
By David Blitzer

Page 2 of 3

As the old Dutch traders knew, options are analytically—and historically—similar to insurance. A put on a stock is one way to purchase insurance to limit downside risk. Writing a call can be thought of as insurance to the buyer of a call as well—insuring against the regret suffered if one doesn’t buy a stock and misses a big move. In either case, the writer is offering insurance and is paid a premium for accepting the risks while having no control of whether the option is exercised.

Options have changed and expanded since the 1600s. With the support of various quantitative models and theories, we now think we understand them better. Their coverage can also be broader today than a single stock or a single risk. Through options on indexes, one can insure, or accept risk on, a portfolio of stocks. Further, to the extent that a particular portfolio is similar to a widely recognized index, one can insure, or add risk to, one’s own personal portfolio through the use of options.

Many investors looking back at the last few years of financial turmoil would like to insure their entire portfolio, maybe their total net worth, against all risks. Until the S&P 500 lost 50 percent twice in the last decade, we all thought that was a once-in-a-lifetime event. Until the financial crisis began in 2007, we were completely convinced the Great Depression was history, rather than a current worry. One might add other risks: rioting over debt and taxes as seen in Greece, or natural disasters that clobber the economy such as the March 2011 earthquake and tsunami in Japan. If the premiums were reasonable, many of us would consider insuring our net worth. The rising interest in tail-risk hedging suggests a bull market in such insurance.

But the truth is, in one sense, we are all being paid that premium to accept many of the unknown, and unquantifiable, risks. There is a long-debated puzzle about the equity risk premium (ERP)—the extra return one expects from holding a risky stock instead of a Treasury bill—why does it seem as large as 3 to 5 percent or more? Research by Robert Barro⁴ argues that the ERP is compensation for accepting a small risk of a truly catastrophic event. An example might be a war that would close markets for several years and devastate an economy. Barro estimates the probability of such catastrophic events and then links this to an individual’s utility function to show that the degree of risk aversion is reasonable. Through the market, the ERP is compensating investors for risks they are facing through their investors. The ERP means that each investor writes a put option on his entire investment holdings and then sells it to himself. He accepts the risks and receives the premiums. The market sets the premium. Writing and buying this put is mandatory if an investor participates in the market. Those other options—from the Dutch East India Company to an option on the S&P 500 Index—are voluntary, not mandatory.