Changing Correlation and Portfolio Diversification Failure in the Presence of Large Market Losses

We consider Sharpe’s one factor model of asset returns and its extension to K factors in order to explain theoretically why diversification can fail. This model can be used to explain nonlinear dependence amongst the assets in a portfolio. The result is intimately related to the tail distribution of the driving factor, the market. We study these properties for general classes of distribution functions. We find asymptotic conditions on the tails of the distribution which determine whether diversification will succeed or fail in the presence of a market fall. Turning to exact analysis, we characterise the only distribution having constant correlation when the market falls, namely the exponential distribution.