Gallant, Hansen, and Tauchen (1990) show how to use conditioning information optimally to construct a sharper unconditional variance bound (the GHT bound) on pricing kernels. The literature predominantly resorts to a simple but suboptimal procedure that scales returns with predictive instruments and computes standard bounds using the original and scaled returns. This article provides a formal bridge between the two approaches. We propose an optimally scaled bound that coincides with the GHT bound when the first and second conditional moments are known. When these moments are misspecified, our optimally scaled bound yields a valid lower bound for the standard deviation of pricing kernels, whereas the GHT bound does not. We illustrate the behavior of the bounds using a number of linear and nonlinear models for consumption growth and bond and stock returns. We also illustrate how the optimally scaled bound can be used as a diagnostic for the specification of the first two conditional moments of asset returns.

We derive the optimal investment policy of a risk-averse investor in a market where there is a textbook arbitrage opportunity, but where liabilities must be secured by collateral. We find that it is often optimal to underinvest in the arbitrage by taking a smaller position than collateral constraints allow. Even when the optimal policy is followed, the arbitrage portfolio typically experiences losses before the final convergence date. In fact, its initial performance may be indistinguishable from that of a conventional portfolio with a poor track record. These results have important implications for the role of arbitrageurs in financial markets.

Gallant, Hansen, and Tauchen (1990) show how to use conditioning information optimally to construct a sharper unconditional variance bound (the GHT bound) on pricing kernels. The literature predominantly resorts to a simple but suboptimal procedure that scales returns with predictive instruments and computes standard bounds using the original and scaled returns. This article provides a formal bridge between the two approaches. We propose an optimally scaled bound that coincides with the GHT bound when the first and second conditional moments are known. When these moments are misspecified, our optimally scaled bound yields a valid lower bound for the standard deviation of pricing kernels, whereas the GHT bound does not. We illustrate the behavior of the bounds using a number of linear and nonlinear models for consumption growth and bond and stock returns. We also illustrate how the optimally scaled bound can be used as a diagnostic for the specification of the first two conditional moments of asset returns. Copyright 2004, Oxford University Press.

We derive the optimal investment policy of a risk-averse investor in a market where there is a textbook arbitrage opportunity, but where liabilities must be secured by collateral. We find that it is often optimal to underinvest in the arbitrage by taking a smaller position than collateral constraints allow. Even when the optimal policy is followed, the arbitrage portfolio typically experiences losses before the final convergence date. In fact, its initial performance may be indistinguishable from that of a conventional portfolio with a poor track record. These results have important implications for the role of arbitrageurs in financial markets.

ABSTRACT While many studies document that the market risk premium is predictable and that betas are not constant, the dividend discount model ignores time‐varying risk premiums and betas. We develop a model to consistently value cashflows with changing risk‐free rates, predictable risk premiums, and conditional betas in the context of a conditional CAPM. Practical valuation is accomplished with an analytic term structure of discount rates, with different discount rates applied to expected cashflows at different horizons. Using constant discount rates can produce large misvaluations, which, in portfolio data, are mostly driven at short horizons by market risk premiums and at long horizons by time variation in risk‐free rates and factor loadings.