The Impact of Risk Mismatch on Personal Portfolio Performance

Within the Modern Portfolio Theory framework, personal portfolio choice is driven by the investor’s risk aversion. In practice, this criterion is usually replaced by a target volatility level, potentially leading to similar allocation choices. Reconciling these two approaches leads to the design of a performance measure that explicitly allows us to isolate a penalty for the mismatch between the actual and targeted portfolio risks. This penalty is particularly strong for defensive investors and when the market risk premium is high. We also show that the target volatility criterion leads to inadequate portfolio choices when market conditions change or when the investor is confronted with a well-performing active portfolio. We extend this approach with a second dimension that represents the investor’s attitude towards asymmetry (skewness) risk. The resulting performance measurement framework involves a penalty for risk unsuitability that can be substantially aggravated, especially for investors who simultaneously exhibit a strong aversion to volatility and skewness risks.