In this paper, we examine the effect of implicit seller reserves on the estimation of value-at-risk based on historical asset sales data. We direct our examination toward how and whether fine art might prove an appropriate form of loan collateral for banks and other financial institutions. Using a data set of French Impressionist paintings brought to auction from 1985 to 2001, we control for the effect of works that are bought in-house to construct a distribution of potential sale values that corrects for sample selection bias. It turns out that the downside risk surrounding deviations of auction prices from expert presale estimates depends critically on how buy-ins are incorporated. If downside risk is assessed solely on historical experience with successful auction sales, the data appear to support loan-to-value ratios between 50% and a 100% larger than loan-to-value ratios that countenance the existence of seller reserves. The auction process, however, is quantifiable and can reveal the necessary risk information required for loan consideration.

This paper tests the hypothesis that the expected return premium on the market portfolio is always non-negative. A violation of this lower bound restriction provides evidence against a broad class of risk-based equilibrium models in favor of bubble behavior. Our tests utilize information variables, identified in prior literature, that predict time variation in market return premia. We employ out-of-sample forecasts and bootstraps generated with parameters that are consistent with non-negativity but closest to the estimated parameters. We find statistically reliable evidence against non-negativity for the excess return on the value-weighted market index. The most negative out-of-sample prediction was −2.01% in September 1973.