thetheoryofactiveportfoliomanagement(编辑修改稿)

thetheoryofactiveportfoliomanagement(编辑修改稿)内容摘要：

s based on analysts39。 forecasts with no restriction on portfolio weights, the standard deviation of tracking error is % (see Table ), more than any reallife manager who is evaluated against a benchmark would be willing to bear. However, with weight of on the active portfolio, the benchmark risk falls to % (Table ).Finally, suppose a manager wishes to restrict benchmark risk to the same level as it was using the original forecasts, that is, to %. Equations and instruct us to invest WA = .43 in the active portfolio. We obtain the results in Table . This portfolio is moderate, yet superior in performance: (1) its standard deviation is only slightly higher than that of the passive portfolio, %。 (2) its beta is .98。 (3) the standard deviation of tracking error that we specified is extremely low, %。 (4) given that we have only six securities, the largest position of 12% (in Target) is quite low and would be lower still if more securities were covered。 yet (5) the Sharpe ratio is a whopping , and the M−square is an impressive %. Thus, by controlling benchmark risk we can avoid the flaws of the unconstrained portfolio and still maintain superior performance. p. 933Table The optimal risky portfolio with the analysts39。 new forecasts (benchmark risk constrained to %)1Fischer Black and Robert Litterman, “Global Portfolio Optimization,” Financial Analysts Journal, September/October 1992. Originally published by Goldman Sachs Company, 169。 1991. The TreynorBlack Model and Forecast PrecisionSuppose the risky portfolio of your 401(k) retirement fund is currently in an Samp。 P 500 index fund, and you are pondering whether you should take some extra risk and allocate some funds to Target39。 s stock, the highperforming discounter. You know that, absent research analysis, you should assume the alpha of any stock is zero. Hence, the mean of your prior distribution Probability distribution for a variable before adjusting for empirical evidence on its likely value. of Target39。 s alpha is zero. Downloading return data for Target and the Samp。 P 500 reveals a residual standard deviation of %. Given this volatility, the prior mean of zero, and an assumption of normality, you now have the entire prior distribution of Target39。 s alpha.One can make a decision using a prior distribution, or refine that distribution by expending effort to obtain additional data. In jargon, this effort is called the experiment. The experiment as a standalone venture would yield a probability distribution of possible outes. The optimal statistical procedure is to bine one39。 s prior distribution for alpha with the information derived from the experiment to form a posterior distribution Probability distribution for a variable after adjustment for empirical evidence on its likely value. that reflects both. This posterior distribution is then used for decision making.A “tight” prior, that is, a distribution with a small standard deviation, implies a high degree of confidence in the likely range of possible alpha values even before looking at the data. In this case, the experiment may not be sufficiently convincing to affect your beliefs, meaning that the posterior will be little changed from the In the context of the present discussion, an active forecast of alpha and its precision provides the experiment that may induce you to update your prior beliefs about its value. The role of the portfolio manager is to form a posterior distribution of alpha that serves portfolio construction.p. 934Adjusting Forecasts for the Precision of AlphaImagine it is June 1, 2006, and you have just downloaded from Yahoo! Finance the analysts39。 forecasts we used in the previous section, implying that Target39。 s alpha is %. Should you conclude that the optimal position in Target, before adjusting for beta, is α/σ2(e) = .281/.1982 = (717%)? Naturally, before mitting to such an extreme position, any reasonable manager would first ask: “How accurate is this forecast?” and “How should I adjust my position to take account of forecast imprecision?”Treynor and Black3 asked this question and supplied an answer. The logic of the answer is quite straightforward。 you must quantify the uncertainty about this forecast, just as you would the risk of the underlying asset or portfolio. A Web surfer may not have a way to assess the precision of a downloaded forecast, but the employer of the analyst who issued the forecast does. How? By examining the forecasting record The historical record of the forecasting errors of a security analyst. of previous forecasts issued by the same forecaster. Suppose that a security analyst provides the portfolio manager with forecasts of alpha at regular intervals, say, the beginning of each month. The investor portfolio is updated using the forecast and held until the update of next month39。 s forecast. At the end of each month, T, the realized abnormal return of Target39。 s stock is the sum of alpha plus a residual: where beta is estimated from Target39。 s security characteristic line (SCL) using data for periods prior to T,The 1month, forwardlooking forecast αf(T) issued by the analyst at the beginning of month T is aimed at the abnormal return, u(T), in Equation . In order to decide on how to use the forecast for month T, the portfolio manager uses the analyst39。 s forecasting record. The analyst39。 s record is the paired time series of all past forecasts, αf(t), and realizations, u(t). To assess forecast accuracy, that is, the relationship between forecast and realized alphas, the manager uses this record to estimate the regression: Our goal is to adjust alpha forecasts to properly account for their imprecision. We will form an adjusted alpha Forecasts for alpha that are modulated to account for statistical imprecision in the analyst39。 s estimate. forecast α(T) for the ing month by using the original forecasts αf(T) and applying the estimates from the regression Equation , that is, 16。