The NYT vs. Math

A recent New York Times article makes a big deal about the one-week falloff of the Dow. Robert Ferguson, a newbie blogger, shows that it’s really no big deal (warning: math ahead):

Roughly, the DJI has a mean weekly return of about zero. Its annual standard deviation of return is about 15%, more or less. Assuming weekly returns are independent as an approximation, a 15% annual volatility corresponds to a 2.08% weekly volatility. A weekly return of -3.2% is only 1.54 standard deviations from the mean.
Assuming normality, the probability of a result 1.54 standard deviations below the mean or worse is 6.2%. This sounds pretty low, but Mr. Sommer did not pick this week at random. He scoured recent history for the worst week and found that it was the worst since about a year ago.
The real question is how likely is at least one weekly decline of at 3.2% or worse in a year.
Roughly this size negative return or worse should occur about three times a year (0.062*52=3.2). In fact, the probability that it would occur at least one week a year is about (1-(1-0.062)^52)=0.964, or about 96.4%.
Something that is expected to happen at least once a year with probability 96.4% is not unusual.

Posted by on June 12th, 2006 at 9:48 pm


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