## Wednesday, February 6, 2013

### Call Options on Hedge Funds: Double Markups and Detrimental Mispricing

By Eddie O'Neal, PhD

A recently settled FINRA Arbitration case was brought by an investor who was sold a $2M call option on a basket of hedge funds by a large investment bank. The case was notable for two reasons. First, the investment bank charged a 25 percent markup on the fair value of the option. This large amount was charged even though the investment bank -- call it Investment Bank 1 -- simultaneously laid off all of its risk by buying an equivalent call option from another investment bank -- call it Investment Bank 2. Even more interesting is that the markup that Investment Bank 2 charged Investment Bank 1 was also passed along to the investor. Of course, it would have certainly been much cheaper for the investor to buy the option directly from Investment Bank 2, thereby avoiding the markup of Investment Bank 1. But Investment Bank 1 did not advise the customer to do that, choosing instead to charge the additional markup in what turned out to be a risk-less transaction for the bank. The second interesting aspect of the case is how the option was priced. All of the marketing materials given to the client stated that the option would be priced on the clients account statements according to the Black-Scholes model. The target volatility of the underlying hedge fund basket was 6%. Numerous documents showed that indeed the underlying hedge fund basket had 6% volatility. However, when the option was sold to the investor, it was priced as though the volatility was 15%. Higher volatility on the underlying asset leads to higher option prices. The use of 15% rather than 6% in the Black-Scholes model caused the price paid by the investor to be 37% higher than the fair value calculated with 6% volatility. After the option was sold at the artificially inflated price, internal documents show that the volatility Investment Bank 1 used to price the option declined monotonically from 15% to 6% over the ensuing two and a half years. This decline in the volatility caused a reduction in the value of the option regardless of the performance of the underlying basket of hedge funds. At the end of the day, the investor paid$2M for an option that had a value of approximately $1.1M. The$900,000 overpayment by the investor was a combination of option mispricing by the investment banks and two large markups.