Chapter 2: FAQs 203
(asymmetry). Whether this matters or not depends on
several factors:
- Are you holding stock for speculation or are you
hedging derivatives? - Are the returns independent and identically
distributed (i.i.d.), albeit non normally? - Is the variance of the distribution finite?
- Can you hedge with other options?
Most basic theory concerning asset allocation, such
asModern Portfolio Theory, assumes that returns are
normally distributed. This allows a great deal of analyti-
cal progress to be made since adding random numbers
from normal distributions gives you another normal
distribution. But speculating in stocks, without hedg-
ing, exposes you to asset direction; you buy the stock
since you expect it to rise. Assuming that this stock
isn’t your only investment then your main concern is
for the expected stock price in the future, and not so
much its distribution. On the other hand, if you are
hedging options then you largely eliminate exposure to
asset direction. That’s as long as you aren’t hedging too
infrequently.
If you are hedging derivatives then your exposure is
to the range of returns, not the direction. That means
you are exposed to variance, if the asset moves are
small, or to the sizes and probabilities of discontinuous
jumps. Asset models can be divided roughly speaking
into those for which the variance of returns is finite,
and those for which it is not.
If the variance is finite then it doesn’t matter too much
whether or not the returns are normal. No, more impor-
tant is whether they are i.i.d. The ‘independent’ part is
also not that important since if there is any relation-
ship between returns from one period to the next it