A BAD DAY on WALL STREET – BLACK MONDAY

A BAD DAY on WALL STREET – BLACK MONDAY

On a typical day the overall value of stocks traded on the U.S. stock market can rise or fall by 1% or even more. This is a lot, but nothing compared to what happened on Monday, October 19, 1987. On “Black Monday,” the Dow Jones Industrial Average (an average of 30 large industrial stocks) fell by 25.6%! From January 1, 1980, to October 16, 1987, the standard deviation of daily percentage price changes on Dow Jones was 1.16%, so the drop of 25.6% was a negative return of 25.6/1.16=22 standard deviation. The enormity of this drop can be seen in the figure below.

 

If the daily percentage price changes are normally distributed, then the probability of a drop of at least 22 standard deviation is Pr(Z less than or equal to -22). We can calculate this with help of computer, this probability is 1.4*10^-107, that is, 0.000....000014, where there are total of 106 zeros.

So, how small is 1.4*10^-107? Consider the following which are larger than this number:

·        The world population is about 6 billion, so the probability of winning a random lottery among all the living people by you is one in 6 billion i.e. 2*10^-10

·        The universe is believed to have existed for 15 billion years, or about 5*10^17 seconds, so the probability of choosing a particular second at random from all the seconds since the beginning of time is 2*10^-18.

·        There are approximately 10^43 molecules of gas in the first kilometre above the earth’s surface. The probability of choosing one at a random is 10^43.

Although Wall Street did have a bad day, the fact that is happened at all suggests that its probability was more than 1.4*10^-107. In fact, stock price percentage changes have a distribution with the heavier tails than the normal distribution; in the other words, there are more days with large positive or negative changes than the normal distribution would suggest. For this reason, finance professional use econometric models in which the variance of the percentage change in stock prices can evolve over time, so some periods have higher volatility than other. These models with changing variances are more consistent with the very bad – and very good – day we actually see on Wall Street.