Thursday, March 10, 2011

Black-Scholes - Will they have to give back their Nobel Prize someday?

I've been delinquent in writing posts, mostly because I'm lazy. As a 2nd year MBA with a job offer in hand, my life is not that much different from an unemployed beach bum, much to my wife's chagrin.

Fischer Black, Myron Scholes, and Robert Merton are economists who developed a formula, now known as Black-Scholes, to value European style options.  A European style option gives you the right to buy or sell (known as exercising) a financial instrument at a fixed point in the future for a fixed price. Normally you must pay an upfront fee for this right, and Black-Scholes is what is used to calculate that fee. To keep this at a level which is understandable to the lay person, Black-Scholes uses the past prices of the asset, amount of time for which the option is available, and current borrowing rates to establish the price of the option. Black-Scholes makes a number of assumptions about each of these variables and a few others, and has been widely adopted by the finance community as the preferred method for valuing options. Scholes and Merton won a Nobel Prize for their work in 1997, Black was unfortunately dead and therefore ineligible for the honor.

Both Scholes and Merton were part of an infamous hedge fund called Long-Term Capital Management, or LTCM. For those of you who are curious about a disaster that nearly became a prominent part of American history, you should read this book that details the story. I find it riveting, though you may find it a good way to fall asleep after a busy or stressful day. On a side note, many of the characters in the book came back to haunt us in this most recent financial crisis. The short story of LTCM is that they used many of the concepts that Black-Scholes developed, primarily the role of historical pricing in estimating future prices. LTCM failed miserably in 1998 when the Russian and East Asian financial crises occurred.

When I first heard about Black-Scholes as undergraduate economics major at West Point I considered it to be a intellectual gimmick. The difficulty is that Nobel Prize winners are likely to ask for your better idea when you point out that theirs is rubbish. Modern finance has spun this idea of using historical assets prices (or more accurately, volatility in those asset prices) to predict future prices into a frightening swirl of bullshit. While it may or may not be accurate in the very short term, in any period longer than a few weeks or months the validity of the model becomes questionable. A company's future profits are dependent on a myriad of factors, not least of which are the overall economy, individual market served, and company's operations. None of these factors are stagnant, rather they constantly evolve such that it is extraordinarily unlikely that the same set of variables which existed in the spring of 2011 may ever again exist. If these variables are not static, it becomes very difficult (I would say impossible) to use them in predicting future prices or volatility.

The recent financial crisis has put a bulls-eye on the back of adherents to this theory. It also raised very serious concerns about modern portfolio theory and the efficient market hypothesis which are the fundamental reasons that most Americans use something called index funds to invest for retirement. I don't believe that markets are efficient in the short or medium term or that index funds represent the best way to invest for retirement. That, however, does not translate to recommending that disinterested investors abandon their index funds. For most individuals, identifying market pricing failures is a task too difficult or boring to engage in and an index fund is the best option.

I've written this long-winded explanation as a lead-in to some interesting comments made by Warren Buffet. In his most recent letter to shareholders he made the following statement, "Both Charlie and I believe that Black-Scholes produces wildly inappropriate values when applied to long-dated options...More tangibly, we put our money where our mouth was by entering into our equity put contracts. By doing so, we implicitly asserted that the Black-Scholes calculations used by our counterparties or their customers were faulty." (paragraph 6, page 20, here).

I find the second part of the statement particularly amusing. Scholes and Merton received about $1 million and the undying love of their fellow academia's for their formula. Buffet is betting billions of dollars that they are full of it, and he's winning.

I've decided over the past year that my future investments will include a number of LEAPS. They are certainly risky, in most instances you must invest $1000s in each option and run the risk of the investment becoming worthless. You must be willing to lose on the vast majority of these bets, but one winner can make your year. I also love the risk, it's not unlike doubling down at the blackjack table if your two card total is 11. It doesn't matter what

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