Bodie−Kane−Marcus: Essentials of Investments, Fifth Edition VI. Active Investment Management 20. Performance Evaluation and Active Portfolio Management © The McGraw−Hill Companies, 2003 where E(r M ) Ϫ r f is the risk premium on M, and ␴ M is the standard deviation of M. To make a rational allocation of funds requires an estimate of ␴ M and E(r M ), so even a passive investor needs to do some forecasting. Forecasting E(r M ) and ␴ M is complicated further because security classes are affected by different environment factors. Long-term bond returns, for example, are driven largely by changes in the term structure of interest rates, while returns on equity depend also on changes in the broader economic environment, including macroeconomic factors besides interest rates. Once you begin considering how economic conditions influence separate sorts of investments, you might as well use a sophisticated asset allocation program to determine the proper mix for the portfolio. It is easy to see how investors get lured away from a purely passive strategy. Even the definition of a “pure” passive strategy is not very clear-cut, as simple strategies involving only the market index portfolio and risk-free assets now seem to call for market analysis. Our strict definition of a pure passive strategy is one that invests only in index funds and weights those funds by fixed proportions that do not change in response to market condi- tions: a portfolio strategy that always places 60% in a stock market index fund, 30% in a bond index fund, and 10% in a money market fund, regardless of expectations. Active management is attractive because the potential profit is enormous, even though competition among managers is bound to drive market prices to near-efficient levels. For prices to remain efficient to some degree, decent profits to diligent analysts must be the rule rather than the exception, although large profits may be difficult to earn. Absence of profits would drive people out of the investment management industry, resulting in prices moving away from informationally efficient levels. Objectives of Active Portfolios What does an investor expect from a professional portfolio manager, and how do these ex- pectations affect the manager’s response? If all clients were risk neutral (indifferent to risk), the answer would be straightforward: The investment manager should construct a portfolio with the highest possible expected rate of return, and the manager should then be judged by the realized average rate of return. When the client is risk averse, the answer is more difficult. Lacking standards to proceed by, the manager would have to consult with each client before making any portfolio decision in order to ascertain that the prospective reward (average return) matched the client’s attitude toward risk. Massive, continuous client input would be needed, and the economic value of professional management would be questionable. Fortunately, the theory of mean-variance efficiency allows us to separate the “product deci- sion,” which is how to construct a mean-variance efficient risky portfolio, from the “con- sumption decision,” which describes the investor’s allocation of funds between the efficient risky portfolio and the safe asset. You have learned already that construction of the optimal risky portfolio is purely a technical problem and that there is a single optimal risky portfolio appropriate for all investors. Investors differ only in how they apportion investment between that risky portfolio and the safe asset. The mean-variance theory also speaks to performance in offering a criterion for judging managers on their choice of risky portfolios. In Chapter 6, we established that the optimal risky portfolio is the one that maximizes the reward-to-variability ratio, that is, the expected excess return divided by the standard deviation. A manager who maximizes this ratio will sat- isfy all clients regardless of risk aversion. Clients can evaluate managers using statistical methods to draw inferences from realized rates of return about prospective, or ex ante, reward-to-variability ratios. The Sharpe measure, 20 Performance Evaluation and Active Portfolio Management 701 Bodie−Kane−Marcus: Essentials of Investments, Fifth Edition VI. Active Investment Management 20. Performance Evaluation and Active Portfolio Management © The McGraw−Hill Companies, 2003 or the equivalent M 2 , is now a widely accepted way to track performance of professionally managed portfolios: S P ϭ The most able manager will be the one who consistently obtains the highest Sharpe meas- ure, implying that the manager has real forecasting ability. A client’s judgment of a manager’s ability will affect the fraction of investment funds allocated to this manager; the client can in- vest the remainder with competing managers and in a safe fund. If managers’ Sharpe measures were reasonably constant over time, and clients could reli- ably estimate them, allocating funds to managers would be an easy decision. Actually, the use of the Sharpe measure as the prime measure of a manager’s ability re- quires some qualification. We know from the discussion of performance evaluation earlier in this chapter that the Sharpe ratio is the appropriate measure of performance only when the client’s entire wealth is managed by the professional investor. Moreover, clients may impose additional restrictions on portfolio choice that further complicate the performance evaluation problem. 20.4 MARKET TIMING Consider the results of three different investment strategies, as gleaned from Table 5.3: 1. Investor X, who put $1 in 30 day T-bills (or their predecessors) on January 1, 1926, and always rolled over all proceeds into 30-day T-bills, would have ended on December 31, 2001, 76 years later, with $16.98. 2. Investor Y, who put $1 in large stocks (the S&P 500 portfolio) on January 1, 1926, and reinvested all dividends in that portfolio, would have ended on December 31, 2001, with $1,987.01. 3. Suppose we define perfect market timing as the ability to tell with certainty at the beginning of each year whether stocks will outperform bills. Investor Z, the perfect timer, shifts all funds at the beginning of each year into either bills or stocks, whichever is going to do better. Beginning at the same date, how much would Investor Z have ended up with 76 years later? Answer: $115,233.89! 3. What are the annually compounded rates of return for the X, Y, and perfect-timing strategies over the period 1926–2001? These results have some lessons for us. The first has to do with the power of compounding. Its effect is particularly important as more and more of the funds under management represent pension savings. The horizons of pension investments may not be as long as 76 years, but they are measured in decades, making compounding a significant factor. The second is a huge difference between the end value of the all-safe asset strategy ($16.98) and of the all-equity strategy ($1,987.01). Why would anyone invest in safe assets given this historical record? If you have absorbed all the lessons of this book, you know the reason: risk. The averages of the annual rates of return and the standard deviations on the all- bills and all-equity strategies were Arithmetic Mean Standard Deviation Bills 3.85% 3.25% Equities 12.49 20.30 E(r P ) Ϫ r f ␴ P 702 Part SIX Active Investment Management market timing Asset allocation in which the investment in the market is increased if one forecasts that the market will outperform bills. Concept CHECK > Bodie−Kane−Marcus: Essentials of Investments, Fifth Edition VI. Active Investment Management 20. Performance Evaluation and Active Portfolio Management © The McGraw−Hill Companies, 2003 The significantly higher standard deviation of the rate of return on the equity portfolio is commensurate with its significantly higher average return. The higher average return reflects the risk premium. Is the return premium on the perfect-timing strategy a risk premium? Because the perfect timer never does worse than either bills or the market, the extra return cannot be compensa- tion for the possibility of poor returns; instead it is attributable to superior analysis. The value of superior information is reflected in the tremendous ending value of the portfolio. This value does not reflect compensation for risk. To see why, consider how you might choose between two hypothetical strategies. Strat- egy 1 offers a sure rate of return of 5%; strategy 2 offers an uncertain return that is given by 5% plus a random number that is zero with a probability of 0.5 and 5% with a probability of 0.5. The results for each strategy are Strategy 1 (%) Strategy 2 (%) Expected return 5 7.5 Standard deviation 0 2.5 Highest return 5 10 Lowest return 5 5 Clearly, strategy 2 dominates strategy 1, as its rate of return is at least equal to that of strat- egy 1 and sometimes greater. No matter how risk averse you are, you will always prefer strat- egy 2 to strategy 1, even though strategy 2 has a significant standard deviation. Compared to strategy 1, strategy 2 provides only good surprises, so the standard deviation in this case can- not be a measure of risk. You can look at these strategies as analogous to the case of the perfect timer compared with either an all-equity or all-bills strategy. In every period, the perfect timer obtains at least as good a return, in some cases better. Therefore, the timer’s standard deviation is a misleading measure of risk when you compare perfect timing to an all-equity or all-bills strategy. Valuing Market Timing as an Option Merton (1981) shows that the key to analyzing the pattern of returns of a perfect market timer is to compare the returns of a perfect foresight investor with those of another investor who holds a call option on the equity portfolio. Investing 100% in bills plus holding a call option on the equity portfolio will yield returns identical to those of the portfolio of the perfect timer who invests 100% in either the safe asset or the equity portfolio, whichever will yield the higher return. The perfect timer’s return is shown in Figure 20.5. The rate of return is bounded from below by the risk-free rate, r f . To see how the value of information can be treated as an option, suppose the market index currently is at S 0 and a call option on the index has exercise price of X ϭ S 0 (1 ϩ r f ). If the market outperforms bills over the coming period, S T will exceed X; it will be less than X other- wise. Now look at the payoff to a portfolio consisting of this option and S 0 dollars invested in bills. Payoff to Portfolio Outcome: S T Յ XS T Ͼ X Bills S 0 (1 ϩ r f ) S 0 (1 ϩ r f ) Option 0 S T Ϫ X Total S 0 (1 ϩ r f ) S T 20 Performance Evaluation and Active Portfolio Management 703 Bodie−Kane−Marcus: Essentials of Investments, Fifth Edition VI. Active Investment Management 20. Performance Evaluation and Active Portfolio Management © The McGraw−Hill Companies, 2003 The portfolio returns the risk-free rate when the market is bearish (that is, when the market return is less than the risk-free rate) and pays the market return when the market is bullish and beats bills. This represents perfect market timing. Consequently, the value of perfect timing ability is equivalent to the value of the call option, for a call enables the investor to earn the market return only when it exceeds r f . Valuation of the call option embedded in market timing is relatively straightforward using the Black-Scholes formula. Set S ϭ $1 (to find the value of the call per dollar invested in the market), use an exercise price of X ϭ (1 ϩ r f ) (the current risk-free rate is about 3%), and a volatility of ␴ϭ.203 (the historical volatility of the S&P 500). For a once-a-year timer, T ϭ 1 year. According to the Black-Scholes formula, the call option conveyed by market tim- ing ability is worth about 8.1% of assets, and this is the annual fee one could presumably charge for such services. More frequent timing would be worth more. If one could time the market on a monthly basis, then T ϭ 1 ⁄12 and the value of perfect timing would be 2.3% per month. The Value of Imperfect Forecasting But managers are not perfect forecasters. While managers who are right most of the time presumably do very well, “right most of the time” does not mean merely the percentage of the time a manager is right. For example, a Tucson, Arizona, weather forecaster who always predicts “no rain” may be right 90% of the time, but this “stopped clock” strategy does not require any forecasting ability. Neither is the overall proportion of correct forecasts an appropriate measure of market forecasting ability. If the market is up two days out of three, and a forecaster always predicts a market advance, the two-thirds success rate is not a measure of forecasting ability. We need to examine the proportion of bull markets (r M Ͼ r f ) correctly forecast and the proportion of bear markets (r M Ͻ r f ) correctly forecast. If we call P 1 the proportion of the correct forecasts of bull markets and P 2 the proportion for bear markets, then P 1 ϩ P 2 Ϫ 1 is the correct measure of timing ability. For example, a forecaster who always guesses correctly will have P 1 ϭ P 2 ϭ 1 and will show ability of 1 (100%). An analyst who always bets on a bear market will mispredict all bull markets (P 1 ϭ 0), will correctly “predict” all bear markets (P 2 ϭ 1), and will end up with timing ability of P 1 ϩ P 2 Ϫ 1 ϭ 0. If C denotes the (call option) value of a perfect market timer, then (P 1 ϩ P 2 Ϫ 1)C measures the value of imperfect forecasting ability. 704 Part SIX Active Investment Management FIGURE 20.5 Rate of return of a perfect market time r f r f r M Rate of return Bodie−Kane−Marcus: Essentials of Investments, Fifth Edition VI. Active Investment Management 20. Performance Evaluation and Active Portfolio Management © The McGraw−Hill Companies, 2003 The incredible potential payoff to accurate timing versus the relative scarcity of billionaires should suggest to you that market timing is far from a trivial exercise and that very imperfect timing is the most that we can hope for. 4. What is the market timing score of someone who flips a fair coin to predict the market? Measurement of Market Timing Performance In its pure form, market timing involves shifting funds between a market index portfolio and a safe asset, such as T-bills or a money market fund, depending on whether the market as a whole is expected to outperform the safe asset. In practice, most managers do not shift fully between bills and the market. How might we measure partial shifts into the market when it is expected to perform well? To simplify, suppose the investor holds only the market index portfolio and T-bills. If the weight on the market were constant, say 0.6, then the portfolio beta would also be constant, and the portfolio characteristic line would plot as a straight line with a slope 0.6, as in Figure 20.6A. If, however, the investor could correctly time the market and shift funds into it in peri- ods when the market does well, the characteristic line would plot as in Figure 20.6B. The idea is that if the timer can predict bull and bear markets, more will be shifted into the market when the market is about to go up. The portfolio beta and the slope of the characteristic line will be higher when r M is higher, resulting in the curved line that appears in 20.6B. Treynor and Mazuy (1966) tested to see whether portfolio betas did in fact increase prior to market advances, but they found little evidence of timing ability. A similar test was imple- mented by Henriksson (1984). His examination of market timing ability for 116 funds in 20 Performance Evaluation and Active Portfolio Management 705 Concept CHECK < FIGURE 20.6 Characteristic lines A: No market timing, beta is constant B: Market timing, beta increases with expected market excess return Steadily increasing slope r P – r f r M – r f Slope = 0.6 r P – r f r M – r f A. No Market Timing, Beta Is Constant B. Market Timing, Beta Increases with Expected Market Excess Return Bodie−Kane−Marcus: Essentials of Investments, Fifth Edition VI. Active Investment Management 20. Performance Evaluation and Active Portfolio Management © The McGraw−Hill Companies, 2003 1968–1980 found that, on average, portfolio betas actually fell slightly during the market ad- vances, although in most cases the response of portfolio betas to the market was not statisti- cally significant. Eleven funds had statistically positive values of market timing, while eight had significantly negative values. Overall, 62% of the funds had negative point estimates of timing ability. In sum, empirical tests to date show little evidence of market timing ability. Perhaps this should be expected; given the tremendous values to be reaped by a successful market timer, it would be surprising to uncover clear-cut evidence of such skills in nearly efficient markets. 20.5 STYLE ANALYSIS Style analysis was introduced by Nobel laureate William Sharpe. 3 The popularity of the con- cept was aided by a well-known study 4 concluding that 91.5% of the variation in returns of 82 mutual funds could be explained by the funds’ asset allocation to bills, bonds, and stocks. Later studies that considered asset allocation across a broader range of asset classes found that as much as 97% of fund returns can be explained by asset allocation alone. Sharpe considered 12 asset class (style) portfolios. His idea was to regress fund returns on indexes representing a range of asset classes. The regression coefficient on each index would then measure the implicit allocation to that “style.” Because funds are barred from short posi- tions, the regression coefficients are constrained to be either zero or positive and to sum to 100%, so as to represent a complete asset allocation. The R-square of the regression would then measure the percentage of return variability attributed to the effects of security selection. To illustrate the approach, consider Sharpe’s study of the monthly returns on Fidelity’s Magellan Fund over the period January 1985 through December 1989, shown in Table 20.7. 706 Part SIX Active Investment Management TABLE 20.7 Sharpe’s style portfolios for the Magellan fund Regression Coefficient* Bills 0 Intermediate bonds 0 Long-term bonds 0 Corporate bonds 0 Mortgages 0 Value stocks 0 Growth stocks 47 Medium-cap stocks 31 Small stocks 18 Foreign stocks 0 European stocks 4 Japanese stocks 0 Total 100.00 R-squared 97.3 *Regressions are constrained to have nonnegative coefficients and to have coefficients that sum to 100%. Source: William F. Sharpe, “Asset Allocation: Management Style and Performance Evaluation,” Journal of Portfolio Management, Winter 1992, pp. 7–19. 3 William F. Sharpe, “Asset Allocation: Management Style and Performance Evaluation,” Journal of Portfolio Man- agement, Winter 1992, pp. 7–19. 4 Gary Brinson, Brian Singer, and Gilbert Beebower, “Determinants of Portfolio Performance,” Financial Analysts Journal, May/June 1991. Bodie−Kane−Marcus: Essentials of Investments, Fifth Edition VI. Active Investment Management 20. Performance Evaluation and Active Portfolio Management © The McGraw−Hill Companies, 2003 While there are 12 asset classes, each one represented by a stock index, the regression coefficients are positive for only 4 of them. We can conclude that the fund returns are well explained by only four style portfolios. Moreover, these three style portfolios alone explain 97.3% of returns. The proportion of return variability not explained by asset allocation can be attributed to security selection within asset classes. For Magellan, this was 100 Ϫ 97.3 ϭ 2.7%. To evalu- ate the average contribution of stock selection to fund performance we track the residuals from the regression, displayed in Figure 20.7. The figure plots the cumulative effect of these resid- uals; the steady upward trend confirms Magellan’s success at stock selection in this period. Notice that the plot in Figure 20.7 is far smoother than the plot in Figure 20.8, which shows Magellan’s performance compared to a standard benchmark, the S&P 500. This reflects the fact that the regression-weighted index portfolio tracks Magellan’s overall style much better than the S&P 500. The performance spread is much noisier using the S&P as the benchmark. Of course, Magellan’s consistently positive residual returns (reflected in the steadily increasing plot of cumulative return difference) is hardly common. Figure 20.9 shows the 20 Performance Evaluation and Active Portfolio Management 707 FIGURE 20.7 Fidelity Magellan Fund cumulative return difference: fund versus style benchmark Source: William F. Sharpe, “Asset Allocation: Management Style and Performance Evaluation,” Journal of Portfolio Management, Winter 1992, pp. 7–19. 1986 1987 1988 1989 1990 30 25 20 15 10 5 0 FIGURE 20.8 Fidelity Magellan Fund cumulative return difference: fund versus S&P 500 Source: William F. Sharpe, “Asset Allocation: Management Style and Performance Evaluation,” Journal of Portfolio Management, Winter 1992, pp. 7–19. 1986 1987 1988 1989 1990 12 10 8 6 4 2 0 Ϫ2 Bodie−Kane−Marcus: Essentials of Investments, Fifth Edition VI. Active Investment Management 20. Performance Evaluation and Active Portfolio Management © The McGraw−Hill Companies, 2003 frequency distribution of average residuals across 636 mutual funds. The distribution has the familiar bell shape with a slightly negative mean of Ϫ.074% per month. Style analysis has become very popular in the investment management industry and has spawned quite a few variations on Sharpe’s methodology. Many portfolio managers utilize websites that help investors identify their style and stock selection performance. 20.6 MORNINGSTAR’S RISK-ADJUSTED RATING The commercial success of Morningstar, Inc., the premier source of information on mutual funds, has made its Risk Adjusted Rating (RAR) among the most widely used performance measures. The Morningstar five-star rating is coveted by the managers of the thousands of funds covered by the service. Morningstar calculates a number of RAR performance measures that are similar, although not identical, to the standard mean-variance measures. The most distinct measure, the Morn- ingstar Star Rating, is based on comparison of each fund to a peer group. The peer group for each fund is selected on the basis of the fund’s investment universe (e.g., international, growth versus value, fixed-income, and so on) as well as portfolio characteristics such as average price-to-book value, price-earnings ratio, and market capitalization. Morningstar computes fund returns (adjusted for loads) as well as a risk measure based on fund performance in its worst years. The risk-adjusted performance is ranked across funds in a style group and stars are awarded based on the following table: Percentile Stars 0–10 1 10–32.5 2 32.5–67.5 3 67.5–90 4 90–100 5 708 Part SIX Active Investment Management FIGURE 20.9 Average tracking error, 636 mutual funds, 1985–1989 Source: William F. Sharpe, “Asset Allocation: Management Style and Performance Evaluation,” Journal of Portfolio Management, Winter 1992, pp. 7–19. Ϫ1.00 Ϫ0.50 0.00 0.50 1.00 90 80 70 60 50 40 30 20 10 0 Average tracking error (%/month) Bodie−Kane−Marcus: Essentials of Investments, Fifth Edition VI. Active Investment Management 20. Performance Evaluation and Active Portfolio Management © The McGraw−Hill Companies, 2003 The Morningstar RAR method produces results that are similar but not identical to that of the mean/variance-based Sharpe ratios. Figure 20.10 demonstrates the fit between ranking by RAR and by Sharpe ratios from the performance of 1,286 diversified equity funds over the pe- riod 1994–1996. Sharpe notes that this period is characterized by high returns that contribute to a good fit. 20.7 SECURITY SELECTION: THE TREYNOR-BLACK MODEL Overview of the Treynor-Black Model Security analysis is the other dimension of active investment besides timing the overall mar- ket and asset allocation. Suppose you are an analyst studying individual securities. Quite likely, you will turn up several securities that appear to be mispriced and offer positive alphas. But how do you exploit your analysis? Concentrating a portfolio on these securities entails a cost, namely, the firm-specific risk you could shed by more fully diversifying. As an active manager, you must strike a balance between aggressive exploitation of security mispricing and diversification considerations that dictate against concentrating a portfolio in a few stocks. Jack Treynor and Fischer Black (1973) developed a portfolio construction model for man- agers who use security analysis. It assumes security markets are nearly efficient. The essence of the model is this: 1. Security analysts in an active investment management organization can analyze in depth only a relatively small number of stocks out of the entire universe of securities. The securities not analyzed are assumed to be fairly priced. 2. For the purpose of efficient diversification, the market index portfolio is the baseline portfolio, which is treated as the passive portfolio. 3. The macro forecasting unit of the investment management firm provides forecasts of the expected rate of return and variance of the passive (market index) portfolio. 4. The objective of security analysis is to form an active portfolio of a necessarily limited number of securities. Perceived mispricing of the analyzed securities is what determines the composition of this active portfolio. 20 Performance Evaluation and Active Portfolio Management 709 FIGURE 20.10 Rankings based on Morningstar’s category RARs and excess return Sharpe ratios Source: William F. Sharpe, “Morningstar Performance Measures,” www.wsharpe.com. 0 0.2 0.4 0.6 0.8 1 1 0.8 0.6 0.4 0.2 0 Sharpe ratio percentile in category Category RAR percentile in category ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ ϩ 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Active Investment Management 20. Performance Evaluation and Active Portfolio Management © The McGraw−Hill Companies, 2003 5. Analysts follow several steps to make up the active portfolio and forecast its performance: a. Estimate the characteristic line of each analyzed security and obtain its beta and residual variance. From the beta and the macro forecast, E(r M ) Ϫ r f , determine the required rate of return of the security. b. Determine the expected return. Subtracting the required return yields the expected abnormal return (alpha) of the security. c. Use the estimates for the values of alpha, beta, and residual risk to determine the optimal weight of each security in the active portfolio. d. Estimate the alpha, beta, and residual variance for the active portfolio according to the weights of the securities in the portfolio. 6. The macroeconomic forecasts for the passive index portfolio and the composite forecast for the active portfolio are used to determine the optimal risky portfolio, which will be a combination of the passive and active portfolios. Although some sophisticated investment managers use the Treynor-Black model, it has not taken the industry by storm. This is unfortunate for several reasons: 1. Just as even imperfect market-timing ability has enormous value, security analysis of the sort Treynor and Black propose has similar potential value. Even with far-from-perfect security analysis, active management can add value. 2. The Treynor-Black model is easy to implement. Moreover, it is useful even relaxing some of its simplifying assumptions. 3. The model lends itself to use with decentralized decision making, which is essential to efficiency in complex organizations. Portfolio Construction Assuming all securities are fairly priced and using the index model as a guideline for the rate of return on securities, the rate of return on security i is given by r i ϭ r f ϩ␤ i (r M Ϫ r f ) ϩ e i (20.1) where e i is the zero mean, firm-specific (nonsystematic) component. Absent security analysis, Treynor and Black take Equation 20.1 to represent the rate of re- turn on all securities and assume the index portfolio (M) is efficient. For simplicity, they also assume the nonsystematic components of returns, e i , are independent across securities. Mar- ket timing is incorporated in the terms r M and ␴ M , representing index portfolio forecasts. The overall investment in the risky portfolio will be affected by the optimism or pessimism re- flected in these numbers. Assume a team of security analysts investigates a subset of the universe of available secu- rities, with the objective of forming an active portfolio. That portfolio will then be mixed with the index portfolio to improve diversification. For each security, k, that is researched, we write the rate of return as r k ϭ r f ϩ␤ k (r M Ϫ r f ) ϩ e k ϩ␣ k (20.2) where ␣ k represents the extra (abnormal) expected return attributable to the mispricing of the security. Thus, for each security analyzed, the research team estimates the parameters ␣ k , ␤ k , ␴ 2 (e k ) If all the ␣ k turn out to be zero, there would be no reason to depart from the passive strategy, and the index portfolio would remain the manager’s choice. But this is a remote 710 Part SIX Active Investment Management Treynor-Black model An optimizing model for portfolio managers who use security analysis in a nearly efficient market. [...]... equities This has come to be known as the home-country bias Despite a continuous increase in cross-border investing, home-country bias still dominates investor portfolios 21.2 RISK FACTORS IN INTERNATIONAL INVESTING Opportunities in international investments do not come free of risk or of the cost of specialized analysis The risk factors that are unique to international investments are exchange rate risk... funds in Table 21.9 indicates In addition to single-country funds, there are several open-end mutual funds with an international focus For example, Fidelity offers funds with investments concentrated overseas, generally in Europe, in the Pacific Basin, and in developing economies in an emerging opportunities fund Vanguard, consistent with its indexing philosophy, offers separate index funds for Europe,... and country-specific risk, discussed in the next two sections Exchange Rate Risk It is best to begin with a simple example 21.1 EXAMPLE Exchange Rate Risk Consider an investment in risk-free British government bills paying 10% annual interest in British pounds While these U.K bills would be the risk-free asset to a British investor, this is not the case for a U .S investor Suppose, for example, the current... The worst case scenario is in some cases sufficient to move a Bodie−Kane−Marcus: Essentials of Investments, Fifth Edition VI Active Investment Management © The McGraw−Hill Companies, 2003 21 International Investing 733 21 International Investing TA B L E 21.6 Current risk ratings and composite risk forecasts Current Ratings Country Composite Ratings Political Risk, Sept 2001 Financial Risk, Sept 2001... market timing, 702 Sharpe measure, 686 Treynor-Black model, 710 Treynor measure, 686 Questions 1–3 appeared in past CFA examinations 1 A plan sponsor with a portfolio manager who invests in small-capitalization, high-growth stocks should have the plan sponsor s performance measured against which one of the following? a S& P 500 index b Wilshire 5000 index c Dow Jones Industrial Average d Russell 2000 index... dollar investments in the United States grow faster than pound investments in the United Kingdom, each dollar is worth progressively fewer pounds as time passes Such an effect will exactly offset the advantage of the higher U .S interest rate interest rate parity relationship, or covered interest arbitrage relationship The spot-futures exchange rate relationship that precludes arbitrage opportunities Bodie−Kane−Marcus:... well equipped to properly assess the risk involved in international investing 21.3 INTERNATIONAL INVESTING: RISK, RETURN, AND BENEFITS FROM DIVERSIFICATION U .S investors have several avenues through which they can invest internationally The most obvious method, which is available in practice primarily to larger institutional investors, is to purchase securities directly in the capital markets of other... countries However, even small investors now can take advantage of several investment vehicles with an international focus Shares of several foreign firms are traded in U .S markets in the form of American depository receipts, or ADRs A U .S financial institution such as a bank will purchase shares of a foreign firm in that firm s country, then issue claims to those shares in the United States Each ADR is then... contracts We also introduce political and country-specific risk that must be considered in the overall risk assessment of international investments We then examine correlation across country portfolios with and without hedging foreign exchange risk Based on these insights, we assess the efficacy of investing globally in the context of equilibrium in international capital markets Finally, we show how performance... SUMMARY • The appropriate performance measure depends on the investment context The Sharpe measure is most appropriate when the portfolio represents the entire investment fund The Treynor measure or Jensen measure is appropriate when the portfolio is to be mixed with several other assets, allowing for diversification of firm-specific risk outside of each portfolio • The shifting mean and variance of . allocation alone. Sharpe considered 12 asset class (style) portfolios. His idea was to regress fund returns on indexes representing a range of asset classes. The regression coefficient on each index would then. model, 710 Treynor measure, 686 PROBLEM SETS Questions 1–3 appeared in past CFA examinations. 1. A plan sponsor with a portfolio manager who invests in small-capitalization, high-growth stocks should. first has to do with the power of compounding. Its effect is particularly important as more and more of the funds under management represent pension savings. The horizons of pension investments may