This paper provides a simple proof of a recent theorem presented by Haim Reisman (1992) concerning the use of proxies for the factors in the return-generating process of the arbitrage pricing theory. In the single-factor case, the theorem asserts that any variable correlated with the factor can serve as the benchmark in an approximate arbitrage pricing theory expected return relation. The significance of this result is considered and a new direction for empirical work on "arbitrage pricing" is outlined.

This paper provides a simple proof of a recent theorem presented by In the single-factor case, the theorem asserts that any variable correlated with the factor can serve as the benchmark in an approximate APT expected return relation. The significance of this result is considered and a new direction for empirical work on "arbitrage pricing" is outlined.

This paper provides a simple proof of a recent theorem presented by Reisman (1992) , concerning the use of proxies for the factors in the return‐generating process of the arbitrage pricing theory (APT). In the single‐factor case, the theorem asserts that any variable correlated with the factor can serve as the benchmark in an approximate APT expected return relation. The significance of this result is considered and a new direction for empirical work on “arbitrage pricing” is outlined.

Evidence is presented that indicates that the standard estimator of the covariance matrix of daily returns provides a distorted view of the true covariance‐factor structure. An alternative estimator, based on a model of the price‐adjustment delay process, reveals roughly twice as much covariation in individual security returns. The number of factors identified also appears to increase when this estimator is employed. Since the linear space spanned by the estimated factor‐loading vectors is quite sensitive to the estimator used, it is important that the consistent estimator be considered in the usual two‐stage empirical investigations of the APT.

A lower bound on the distribution function of the likelihood ratio test of portfolio efficiency is derived. An empirical application demonstrates that the bound may sometimes be used to infer rejection of the null hypothesis without appeal to asymptotic statistical approximations. A procedure for incorporating partial information about the zero‐beta intercept, in the multivariate framework, is also developed and applied.

This paper extends Kandel's [3] analysis of the testability of the mean‐variance efficiency of a market index when the return on some component of the index is not perfectly observable. In addition to information about the mean and variance of the missing asset, considered by Kandel, we explore the usefulness of information about the beta of the missing asset on the observed sub‐portfolio in an economy with a riskless asset. The results are somewhat more supportive of the notion that mean‐variance efficiency is testable on a subset of the assets.