Mulla Nasreddin, Gaussian Distribution and Capital Asset Pricing Model
Mulla Nasreddin, a 13th century legend lived somewhere between Turkey and Afghanistan (both countries included). I am sure he must have been a kid and a young man in his time but he is remembered as an old man, old and outrageously wise. One evening he was seen looking for some lost article under a street lamp. A passerby inquired what was the Mulla looking for. “My ring”, came the reply . “Now, where exactly did you lose it” the stranger persisted. “Oh, yonder on the commons while grazing my donkey”Mulla replied. The stranger laughed and wondered aloud why the hell was the Mulla looking for the ring on the street then. The Mulla answered, with unshakable patience, "it is too dark on the commons to see anything, on the street there are lamp posts".
Mulla surely knew a thing or two. In 1962, Mandelbrot had demonstrated that asset returns are not normally distributed. Still, our risk models built in nineties (now I guess conclusively proved obsolete but still very much in use) were based on normal distribution of asset returns. Why? Because calculations are a lot simpler with this assumption.
Empirical evidence for CAPM is at best mixed. There are other models that, reportedly, better mimic the returns from risky assets. Still ninety-nine percent (or more) of finance graduates pass out from their schools without trying out any model other than CAPM. Why? Oh, it is so easy (for instructors).
|
