There is a false, but widely-held belief about orthogonal (“zero-beta”) portfolios: for a given market index, all zero-beta portfolios have the same expected return and the minimal-variance, zero-beta portfolio is unique. This is true only when the index is mean/variance efficient. Every nonefficient index possesses zero-beta portfolios at all levels of expected return. For a given index, minimal-variance zero-beta portfolios corresponding to different expected returns lie along an “orthogonal frontier” in the mean/variance space. The frontier has some unusual properties which turn out to be relevant for empirical work on asset pricing. It is functionally related to deviations about the “securities market line.”

The Sharpe model of capital asset pricing under conditions of risk has received wide theoretical acclaim and empirical support. This paper presents an econometric study of the model with the following objectives: (a) to show the effect of measuring the model's independent variables incorrectly; (b) to derive and use a new procedure for empirically testing the adequacy of the model as it is currently formulated.

The mean return computational method has a substantial effect on the estimated small firm premium. The buy-and-hold method, which best mimics actual investment experience, produces an estimated small-firm premium only one-half as large as the arithmetic and re-balanced methods which are often used in empirical studies. Similar biases can be expected in mean returns when securities are classified by any variable related to trading volume.

Mayers and Rice do not resolve the basic problem in portfolio performance evaluation with the securities market line, the ambiguity introduced by being obliged to choose a market index. Other performance evaluation techniques exist and possess some superior qualities. The Mayers-Rice discussion of my critique of the capital asset pricing model (CAPM) fails to recognize the CAPM's unusual testing implications and ignores the existence of alternative asset pricing theories. Residual analysis should give approximately correct estimates of the abnormal returns caused by specific events if it is conducted with the market model.

Testing the two-parameter asset pricing theory is difficult (and currently infeasible). Due to a mathematical equivalence between the individual return/‘beta’ linearity relation and the market portfolio's mean-variance efficiency, any valid test presupposes complete knowledge of the true market portfolio's composition. This implies, inter alia, that every individual asset must be included in a correct test. Errors of inference inducible by incomplete tests are discussed and some ambiguities in published tests are explained.

Sometimes it pays to exercise an American-type call option prematurely, just prior to a cash emission by the underlying security. Such an option can be expressed as a combination of three European-type options whose valuation formulae are known.

Rational expectations must not be expected to change. Hence, a rational expectation about a future random quantity follows a pure martingale until the uncertainty is resolved. This implies that the expectation itself could be non-stationary and, in fact, is non-stationary if the increments are iid. Most asset prices are functions of expectations about future quantities, so asset prices also could be non-stationary. This has consequences for tests based on prices rather than on returns.

Stock Price Indices are compared across countries in an attempt to explain why they exhibit such disparate behavior. Three separate explanatory influences are empirically documented. First, part of the behavior can be attributed to a technical aspect of index construction; some indices are more diversified than others. Second, each country's industrial structure plays a major role in explaining stock price behavior. Third, for the majority of countries, a portion of national equity index behavior can be ascribed to exchange rate behavior. Exchange rates explain a significant portion of common currency denominated national index returns, although the amount explained by exchange rates is less than the amount explained by industrial structure for most countries.