
INVESTMENT PERFORMANCE IN GENERAL, and the performance of professional money managers in particular, has been the subject of substantial examination. Treynor [14, 15], Sharpe [13] and Jensen [8, 9], among others, have made contributions in this area. Expanding upon their work, Fama [4] has proposed "finer breakdowns of performance" which identify not only the level of performance, but also the source. Such breakdowns may provide the information required to determine the relative abilities of managers to identify undervalued securities (selectivity) or to predict the direction of the market (timing).' This information is also essential to any comprehensive cost/benefit analysis of these management activities. In this paper we will be concerned with questions of performance relating to timing. Our purpose is to identify in detail not only the return attributable to timing but also a previously unspecified "cost". We will do this under behavioral assumptions compatible with both single period, and multiperiod, models of portfolio performance and representative of the manager/investor decision making process. In Sectior II we present our model of analysis and quantify a "cost", in terms of increased risk, which timing decisions incur. We analyse the nature of this cost under simplifying assumptions in Section III. When we consider the Sharpe [13] one parameter performance measure, these assumptions also permit us to discuss the "quality" of the timing decisions which is necessary to compensate for its cost. This section concludes with a discussion of the potential application of the findings and indicates the role which simulations can play. In Section IV we consider the empirical implications of this analysis for the Jensen and Treynor measures of portfolio performance. Jensen's original work [8] contains a mathematical error and a conceptual problem. The significance of the former is nullified by resolution of the latter: for portfolios managed with respect to timing the expected value of the least-squares estimate of /8 is an upward, not, as Jensen suggested, downward biased estimate of the expected value of periodic systematic risk, but the systematic risk of such portfolios is not E(,8/). We will argue that the expected value of the least-squares estimate of /B is an unbiased estimate of systematic risk. Therefore neither Jensen's nor Treynor's
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