Fat Tails and the Effect on Optimal Asset Allocations

Abstract

In investment management problems one often uses scenarios to determine optimal strategies and to quantify the uncertainty associated with these strategies. Such scenarios are mostly based on the assumption of normality for variables like asset returns, inflation rates and interest rates. Financial economic time series often display leptokurtic behaviour, implying that the assumption of normality may be inappropriate. In this chapter we use a simple asset allocation problem with one shortfall constraint in order to uncover the main consequences of non-normal distributions on optimal asset allocations. It is found that the probability of shortfall plays a crucial role in determining the effect of fat tails on optimal asset allocations. Depending on this probability, the presence of fat tails may lead to either more aggressive or more prudent asset mixes. We also examine the effect of misspecification of the degree of leptokurtosis. Using distributions with an incorrect tail behaviour may lead to portfolios with a minimum return that is up to 418 basis points below the minimum return imposed in the model. In value-at-risk calculations, this implies that the true value-at-risk may deviate by more than 4 per cent (as a fraction of the invested notional) from what an incorrectly specified model suggests.