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Risk decomposition, estimation error, and naïve diversification

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How to achieve adequate diversification is important in portfolio construction. Efficient markets should not reward an investor for taking on risk that can be diversified away. Hence, when minimizing risk exposure, investors need to measure what part of total portfolio risk is systematic and what part can be diversified away. I examine several methods for decomposing total portfolio risk into systematic and diversifiable components and then carry out simulations to compare cross-sectional distributions of estimated and true risk as number of stocks increases in portfolios constructed using naïve diversification. Ordinary least squares estimators of diversifiable risk are relatively robust, and their cross-sectional distributions closely track the cross-sectional distributions of the corresponding true diversifiable risk. Other proposed estimators of diversifiable risk as well as all estimators of systematic risk have cross-sectional dispersion much greater than the corresponding true risk although, with one exception, bias is small. Results are relatively robust to the choice of method for generating market returns and to the underlying asset pricing model but not to random security betas. The simulation analysis also shows that risk and magnitude of shocks due to diversifiable risk are not negligible, even for 300-stock portfolios.