Note---Naive Diversification and Portfolio Risk---A Note

A number of authors have used the portfolio standard deviation to model the risk reduction advantages of naive diversification. Other authors have pointed out that when risk is modelled by the portfolio's variance the modelling process becomes much simpler and is computationally more efficient. In this note we derive an exact parametric relationship between portfolio standard deviation and size and thus highlight the dangers of using the standard deviation in conjunction with O.L.S. regression techniques to model the risk reduction advantages of naive diversification. It is then shown that past empirical studies which have used this methodology are deficient.