Risk-adjusted expected return for selection decisions

The results of genetic evaluation are predictions of breeding values for the selection candidates, and these involve uncertainty with regard to future returns from the use of those selected individuals. This uncertainty is due to differential variability in BLUP of breeding values and can be translated into risk: High fluctuations mean greater risk, which is not taken into account by just looking at expected return. In this research, the methodology of value at risk (VaR) and expected shortfall is introduced for animal breeding decisions as a means to adjust the expected return for the cost of uncertainty in prediction of breeding values. This methodology has recently received a great deal of attention from financial institutions. Given a specified probability alpha, VaR is the alpha-quantile of the distribution of economic returns. The conditional value at risk (CVaR), or expected shortfall, is the expectation of the economic returns, which are less or equal to the VaR. By subtracting the CVaR from the predicted aggregate genotype (mu(R)), a risk-adjusted expected return (RAER) measure was obtained. The measures mu(R), VaR, and RAER were calculated for a data set with progeny of 161 Polled Hereford bulls belonging to a beef cattle company. The Pearson and Spearman correlations between mu(R) and RAER were 0.89 (P < 0.001) and 0.90 (P < 0.001), respectively. Even though the latter correlation was high, some bulls ranked differently for mu(R) compared with RAER. The Pearson correlation between mu(R) and VaR was low (0.124) and nonsignificant (P > 0.05), whereas the correlation between VaR and RAER was -0.31 (P < 0.0001). The results indicate the need to take into account the adjustment for risk in expected return in order to alleviate the effects of possible losses when overrated animals are selected.