Normal distribution & portfolio theory

Paul Tergat

does anyone know why when constructing a portfolio its assumed that the return of the assets follow a normal distribution?

Cheers in advance

Pherekydes

Probably due to a combination of the Central limit theorem and the law of large numbers:

The Central Limit Theorem states that if the sum of the variables has a finite variance, then it will be approximately normally distributed (i.e., following a Gaussian distribution).

The law of large numbers (LLN) is a theorem in probability that describes the long-term stability of a random variable. Given a sample of independent and identically distributed random variables with a finite population mean and variance, the average of these observations will eventually approach and stay close to the population mean [which is what a normal distribution does].

Paul Tergat

Cheers

hivizman

There's a discussion of "mean-variance analysis" in the context of portfolio theory at http://www.stanford.edu/~wfsharpe/mia/rr/mia_rr1.htm - this discussion is by William Sharpe, who was one of the developers of the Capital Asset Pricing Model, so it should be definitive.

More recently, the use of the normal distribution as the distribution of security returns has been questioned - the normal distribution is symmetrical, but in practice most security returns are bounded below at -1 (the most you can lose is the whole investment, but limited liability means that you can't normally lose more than the whole investment), while conceivably there is no upper bound to security returns. Using the normal distribution is a case of trading off descriptive accuracy in favour of more straightforward maths - alternatives such as assuming that security returns are lognormally distributed are more complex to analyse.