IN his Economics and Information Theory, Theil (1967) developed a theorem which states that under certain conditions the covariance between the variation in the demand for two goods, holding constant prices and income, would measure the substitutability of the two goods (more precisely, will measure their Slutsky-Hicks substitution effect up to a negative scaler) (chapter 7). This theorem and the framework behind it have subsequently been used in further studies of commodity preferences and substitution (Barten (1968), Phlips (1971), and Phlips and Rouzier (1972)). If the covariance measure of substitution could be usefully applied to asset substitution, it could prove to be a valuable supplement to the more traditional measure of asset substitution, i.e., the estimation of relations between asset demand and asset yields. Theoretically, the measure can be applied to time-series or crosssection data. The measure might have a wider applicability to cross-section data than the traditional asset demand-yield measure since the latter can only be applied to assets with regional markets (e.g., deposits). Moreover, to some extent, it can be expected that errors or biases that might arise in the covariance measure would be independent of those incurred in using the traditional measure of asset substitutability. This paper will attempt to apply the covariance measure to estimating asset substitution among households. Part I considers the theoretical underpinnings of the covariance measure and its theoretical relation to the asset demandasset yield measure of substitutability. In part II an empirical formulation of the covariance measure is developed and applied to cross-section asset data for households and the results analyzed. The results are then compared to two earlier, and more limited, asset studies which used essentially a covariance type measure to assess substitutability. The results are also compared to those of household studies which have used the traditional method for estimating substitution among assets. Findings and suggestions for further study are summed up in the conclusion.

ABSTRACT This paper studies the information value of immediate disclosure of the FOMC policy directive. The value of disclosure is measured by its ability to reduce investors' expected uncertainty about futures interest rates where uncertainty is defined as the conditional variance of forecast errors. Analytical relationships between new information and the conditional variance of forecast errors are developed and the relation of the “uncertainty‐reducing” value of information to its social value, as defined in recent literature, is indicated. In the empirical work, forward interest rates are treated as reflecting market expectations conditioned on existing information. The empirical tests indicate that information in the undisclosed, prevailing policy directives (1974–79) were able to make only a very marginal improvement in the predictive accuracy of forecasts relying only on the forward rates. Thus, the hypothesis that immediate disclosure has a significant information value to market participants is not supported.

ABSTRACT In recent years, the trading accounts at large commercial banks have grown substantially and become progressively more diverse and complex. We provide descriptive statistics on the trading revenues from such activities and on the associated Value‐at‐Risk (VaR) forecasts internally estimated by banks. For a sample of large bank holding companies, we evaluate the performance of banks trading risk models by examining the statistical accuracy of the VaR forecasts. Although a substantial literature has examined the statistical and economic meaning of Value‐at‐Risk models, this article is the first to provide a detailed analysis of the performance of models actually in use.

We study the performance and behavior of Value at Risk measures used by a number of large U.S. banks before, during and after the financial crisis. Alternative benchmark VaR measures, including GARCH-based measures, are estimated directly from the banks’ trading revenues to explain the bank VaR performance results. While overly conservative in both the pre-crisis and post-crisis periods, bank VaR exceedances were excessive and clustered in the crisis period. This contrasted with mostly unbiased benchmark HS and GARCH VaRs in the pre-crisis and post-crisis periods, and vastly superior GARCH-based VaR performance in the crisis period with lower exceedance rates and no exceedance clustering. Our results document the bank VaRs very slow adjustment to changing market conditions and their systematic bias in all studied periods. Our results indicate that bank VaRs could be improved by the use of models with time-varying volatility, and built on banks’ knowledge of their current positions.