Pieter Klaassen

Extreme returns, downside risk, and optimal asset allocation

The issue of asset allocation is important to every investor, but because of common, yet questionable, assumptions, these allocations may be significantly biased. Perhaps the most common investor assumption is normality or lognormality of asset returns. Evidence indicates, however, that return distributions often have fat tails (i.e., are leptokurtic). If so, how far from optimality are these “optimal” allocations?

Tail Behavior of Credit Loss Distributions for General Latent Factor Models

Using a limiting approach to portfolio credit risk, we obtain analytic expressions for the tail behavior of credit losses. To capture the co‐movements in defaults over time, we assume that defaults are triggered by a general, possibly non‐linear, factor model involving both systematic and idiosyncratic risk factors. The model encompasses default mechanisms in popular models of portfolio credit risk, such as CreditMetrics and CreditRisk+. We show how the tail characteristics of portfolio credit losses depend directly upon the factor models functional form and the tail properties of the models risk factors. In many cases the credit loss distribution has a polynomial (rather than exponential) tail. This feature is robust to changes in tail characteristics of the underlying risk factors. Finally, we show that the interaction between portfolio quality and credit loss tail behavior is strikingly different between the CreditMetrics and CreditRisk+ approach to modeling portfolio credit risk. Correspondence to: alucas@econ.vu.nl, pieter.klaassen@nl.abnamro.com, spreij@wins.uva.nl, or s.straetmans@berfin.unimaas.nl.

Fat Tails and the Effect on Optimal Asset Allocations

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.