Abstract
We analyze the systematic errors coming from two approximations in use in financial modelling: that the portfolio logreturn is the weighted average of the asset logreturns, and that the logreturn is equal to the simple return. Usually, the errors inherent in the approximations are taken to be small and so they are simply ignored. We estimate the errors using Monte Carlo simulations with different distributional assumptions on single asset logreturns. We analyze the impacts of the errors in the context of portfolio choice. The approximations are found to significantly underestimate portfolio logarithmic returns, leading investors to systematically select riskier portfolios than actually desired. On a portfolio with a target logreturn of 10% the true mean exceeds the approximated mean by up to 1%, while the error on volatility is about 2.7%. Furthermore, we show that not only does diversification reduce risk, it also increases the portfolio logreturn mean and skewness, whatever assumptions you make on single asset distributions.
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