Finance

Black-Scholes     Recommended Books

We were wondering how George W. Bush could win with the Dow dropping, economic indicators falling, the dollar sinking and the bond market signaling an economic slump. The polls show the two candidates neck and neck; Bush could not afford more slippage. He needed a rally. And here it is...at least for now.

Our guess is that a good rally will push the neocon candidate over the top. Our guess is also that if the election were held a week or two later, nothing could save Bush. Each passing day brings more evidence that the chief executive has no idea what he is doing.

Each day, the U.S. government goes $1.3 billion further into debt. Our friend Gregor points out that in just three years, the new debt will come to more than the value of every ounce of gold ever pulled out of the earth since mining began more than 3,000 years ago.  Daily Reckoning 11/28/04

To Fischer Black, Myron Scholes and Robert Merton, price changes in financial markets were random. No one could predict any particular change, but over a long period of time, they assumed that the distribution of all such prices would mirror the pattern of random events like coin flips. The Black-Scholes formula explicitly states, " We will assume ideal conditions in the market for the stock and price of the option.. the stock price follows a random walk in continuous time". 

Black-Scholes:  makes a key assumption that the volatility of a security is a constant. Merton assumed that the volatility was so constant that prices would trade in continuous time, in other words without any jumps.  Continuous time is merely an ideal state. 

Eugene Fama, Scholes thesis advisor had written his thesis on the price movements of the DJIA stocks and discovered: for every stock there were many more days of extreme price movements than would occur in a normal distribution.  In his words,  if the population of price changes is strictly normal, on the average for any stock...an observation more than five standard deviations from the mean should be observed about once every 7,000 years. In fact such observations seem to occur about once every three to four years."

"The evangelical Merton showed disdain for the very possibility that investors could be anything but calculating automatons, and he blithely ignored the times when their emotions ran riot. Thus he took credit for the contribution that his theories made to "the portfolio-insurance products of 1980's" as if he were blind to the fact that ,when real people tried those products, portfolio insurance failed miserably"¹

An efficient market is one less volatile. It has no black Mondays. 

"The efficient market hypothesis is the most remarkable error in the history of economic theory"  Lawrence Summers, former US Secretary Treasury

1.    When Genius Failed, Roger Lowenstein, page 74.

Recommended Books

When Genius Failed, Roger Lowenstein

Against the Gods, The History of Probability, Peter Bernstein

Technical Analysis of Financial Markets: A Comprehensive Guide to Trading Methods and Applications, John J Murphy

Why Stock Markets Crash: Critical Events in Complex Financial Systems. Didier Sornette.