## Ed Thorp – A Perspective on Quantitative Finance: Models for Beating the Market

Ed Thorp developed and perfected many of the techniques for successful card counting, he also ran Newport Partners a hedge fund which outperformed even Buffett’s Partnership.

Thorp focused on applying the Kelly Optimization Formula (also used by many investors, Pabrai, etc) criterion to backjack and (later) financial markets. You can read more about his accomplishments in the book Fortunes Formula

**Background (Via Wikipedia)**

Dr. Edward Oakley Thorp is an American mathematics professor, author, hedge fund manager, and blackjack player. He is widely known as the author of the 1962 book

Beat the Dealer, which was the first book to prove mathematically that blackjack could be beaten by card counting. The technique eliminated the advantage of the house, which had an estimated maximum of approximately 5% (when following strategies with the smallest possibility of winning, either mimicking the dealer or never busting), and instead gave the player an advantage of approximately 1% He is also regarded as the co-inventor of the first wearable computer along with Claude Shannon.^{}

**Introduction (Via Ed Thorp)**

This is a perspective on quantitative finance from my point of view, a 45-year effort to build mathematical models for “beating markets”, by which I mean achieving risk-adjusted excess returns. I’d like to illustrate with models I’ve developed, starting with a relatively simple example, the widely played casino game of blackjack or twenty-one. What does blackjack have to do with finance? A lot more than I first thought, as we’ll see.

**Excerpt (Via Ed Thorp)**

My next illustration is the evolution over more than two decades of a model for convertible bonds. Simplistically, a convertible bond pays a coupon like a regular bond but also may be exchanged at the option of the holder for a specified number of shares of the “underlying” common stock. It began with joint work during 1965 and 1966 with economist Sheen Kassouf on developing models for common stock purchase warrants. Using these models, we then treated convertible bonds as having two parts, the first being an ordinary bond with all terms identical except for the conversion privilege. We called the implied market value of this ordinary bond the “investment value of the convertible”. Then the value of the conversion privilege was represented by the theoretical value of the attached “latent” warrants, whose exercise price was the expected investment value of the bond at the (future) time of conversion.