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Discussion

Published online by Cambridge University Press:  19 October 2009

Dale D. McFarlane
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Extract

The number of empirical studies aimed at examination of the relationship between risk and return to securities portfolios has increased dramatically over the last five years. There are basically two features of Nancy Jacob's paper, “The Measurement of Systematic Risk for Securities and Portfolios: Some Empirical Results,” that I feel contribute significantly to this area of study. First, the empirical analysis is based on an axiomatic system of characterizing the securities investment decision; this departs substantially from the assumptions underlying the more familiar mean-variance approach. A comparison of the conclusions reached while empirically investigating different axiomatic systems of investor behavior may play an important role in the validation of positive models of capital markets. The second contribution stems from the depth of the study as it relates to the effects of changes in the observation interval, the horizon time, and the portfolio selection procedures. Determining the appropriate horizon time and observation interval is always a major problem, when working with historical price and dividend data. The author's grouping of data into one-, five-, and ten-year horizon periods - along with varying the observation interval over monthly, quarterly, and annual data - illuminates many of the problems associated with empirical studies using a fixed holding period and observation interval.

Type
Discussants
Information
Journal of Financial and Quantitative Analysis , Volume 6 , Issue 2 , March 1971 , pp. 855 - 860
Copyright
Copyright © School of Business Administration, University of Washington 1971

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References

1 As is pointed out in the paper, a more exhaustive coverage of the derivation of the market similarity measure from a state preference framework can be found in Jacob, Nancy, “The Measurement of Market Similarity for Securities Under Uncertainty,” Journal of Business, Vol. 43, No. 3 (July 1970), pp. 328–340.CrossRefGoogle Scholar

2 In a footnote we find

Let T = 1; VM, o = the value of the “market” or population of common stocks at time zero; VM, t = the value of holding the market portfolio at the end of a single time period; VP, o = the value of a selected portfolio at time zero; and VP, t = the value of holding the selected portfolio at the end of the period.

Then,

and then

3 While I have not taken the space to derive this form of the E(Up) function, the derivation follows directly from the recognition that (1) a1 must be equal distance from a0 and a2. if two portfolios with the same E(R) must have the same expected utility provided Δ P(G) = Δ P(L) and (2) utility functions are unique only up to linear transformation.