We implement the human capital CAPM (HCAPM) using the income growth of high income households, rather than aggregate income growth, to proxy the return to human capital (HCRT). We find that identifying the HCRT with the income growth of affluent households, those who are most likely to hold stocks, substantially improves the performance of the HCAPM. Specifically, the pricing errors, R-square's, average returns on factor mimicking portfolios, and performance relative to other macro-finance models uniformly improve as the HCRT is identified with the income growth of successively more affluent households.

This paper reviews a variety of backtests that examine the adequacy of Value-at-Risk (VaR) measures. These backtesting procedures are reviewed from both a statistical and risk management perspective. The properties of unconditional coverage and independence are defined and their relation to backtesting procedures is discussed. Backtests are then classified by whether they examine the unconditional coverage property, independence property, or both properties of a VaR measure. Backtests that examine the accuracy of a VaR model at several quantiles, rather than a single quantile, are also outlined and discussed. The statistical power properties of these tests are examined in a simulation experiment. Finally, backtests that are specified in terms of a pre-specified loss function are reviewed and their use in VaR validation is discussed.