Knowledge that Transforms

Using option and stock transaction data for the period 1978–1979, three issues were investigated: first, the conformance of observed prices to various boundary conditions; second, the evolution of the market over time, as the volume of trading and the number of listed options increased; and third, to test the efficiency of the market. It was found that violations did occur. Using a trading rule based on the signal of observed violations, the results suggest that even after transaction costs the market was inefficient over the sample period.

For the risk-averse investor, consideration of estimation risk is important in selecting an expected-utility-maximizing portfolio. It has previously been shown that the composition of the tangency portfolio is unaffected by the recognition of estimation risk if the Full Covariance Model is used. Alternatively, if the Market Model is used, the composition of the tangency portfolio has been shown to be affected by the recognition of estimation risk. However, as is demonstrated in this paper, the effect will generally not be as substantive as previously believed and in many situations can be safely ignored.

We show that the set of expected return vectors, for which an observed portfolio is mean variance (MV) efficient, is a two-parameter family. We identify ten ways to specify the time series behavior of the two parameters; the result highlights a number of inconsistencies involved in MV modelling. For each of the cases, it permits the inference of the time series of expected return vectors, as well as all the other Capital Asset Pricing Model (CAPM) variables, compatible with a known covariance matrix and the observed time series of market value weights. The empirical work shows that there are substantial case-to-case differences in the time series of mean vectors and many of them are quite different from the constant mean vector envisioned in tests of the CAPM.

Robert Shiller, An Unbiased Reexamination of Stock Market Volatility: Discussion, The Journal of Finance, Vol. 40, No. 3, Papers and Proceedings of the Forty-Third Annual Meeting American Finance Association, Dallas, Texas, December 28-30, 1984 (Jul., 1985), pp. 688-689

This paper characterizes conditions under which asset returns and consumption are consistent with risk-averse preferences. It is shown that risk aversion is equivalent to “zero arbitrage” on a transformation of the payoff space. The implicit state prices which are dual to this no-arbitrage condition can be interpreted as prices of “pure consumption hedges.” This zero-arbitrage restriction implies the usual restrictions associated with nonsatiation. The analysis holds in both complete and incomplete market settings.

In an arbitrage-free economy, there will always exist a set of linear operators which map future contingent dividends of securities into their current prices. It happens that such operators will also form an “evolution semigroup” as a consequence of intertemporal analysis of the no-arbitrage restriction. This paper summarizes some of the major implications of the semigroup properties, but avoids almost all of the technical discussion which underlies them. Instead, several practical examples are presented. Some well-known continuous-time results are replicated by this alternative method, and certain new developments are explored.

This paper provides some new insights about approximate factor structures, as defined by Chamberlain and Rothschild [2], and their implications for empirical tests. First, we show that any economy that satisfies an approximate factor structure can be transformed, in a manner that does not alter the characteristics of investor portfolios, into an economy that satisfies an exact factor structure, as defined by Ross [9]. Second, we show that principal components analysis represents just one of many methods of forming groups of well-diversified portfolios with no idiosyncratic risk in large samples. Correct factor loadings will be obtained by regressing security returns on any group of these portfolios. Our interpretations of the Chamberlain and Rothschild results also provide additional insights into the testability of the Arbitrage Pricing Theory. We show that securities cannot be repackaged to hide factors in the manner suggested by Shanken [10] without the variance of some of the repackaged securities approaching infinity in large economies.