Performance Evaluation and Active Portfolio Management

CHAPTER 18 18.1 RISK-ADJUSTED RETURNS Performance Evaluation and Active Portfolio Management Introduction Complicated subject Theoretically correct measures are difficult to construct Different statistics or measures are appropriate for different types of investment decisions or portfolios Many industry and academic measures are different The nature of active managements leads to measurement problems Factors That Lead to Abnormal Performance Market timing Superior selection – Sectors or industries – Individual companies Abnormal Performance What is abnormal Abnormal performance is measured: – Comparison groups – Market adjusted – Market model / index model adjusted – Reward to risk measures such as the Sharpe Measure: E (rp-rf) / σp Comparison Groups Simplest method Most popular Compare returns to other funds with similar investment objectives 20-1 Figure 18.1 Universe Comparison Periods Ending December 31, 2008 Risk Adjusted Performance: Sharpe 1) Sharpe Index rp - rf σp rp = Average return on the portfolio rf = Average risk free rate σ p = Standard deviation of portfolio return Risk Adjusted Performance: Treynor 2) Treynor Measure rp - rf ßp rp = Average return on the portfolio rf = Average risk free rate ßp = Weighted average β for portfolio Risk Adjusted Performance: Jensen 3) Jensen’ Jensen’s Measure α p = rp - [ rf + ßp ( rm - rf) ] αp = Alpha for the portfolio rp = Average return on the portfolio ßp = Weighted average Beta rf = Average risk free rate rm = Avg. return on market index port. M2 Measure Developed by Modigliani and Modigliani Equates the volatility of the managed portfolio with the market by creating a hypothetical portfolio made up of TT-bills and the managed portfolio If the risk is lower than the market, leverage is used and the hypothetical portfolio is compared to the market M2 Measure: Example Return Stan. Dev Managed Portfolio 35% Market T-bill 30% 0% 42% 28% Hypothetical Portfolio: Same Risk as Market 6% 30/42 = .714 in P (1-.714) or .286 in T-bills (.714) (.35) + (.286) (.06) = 26.7% Since this return is less than the market, the managed portfolio underperformed 20-2 Figure 18.2 The M2 of Portfolio P T2 (Treynor Square) Measure Used to convert the Treynor Measure into percentage return basis Makes it easier to interpret and compare Equates the beta of the managed portfolio with the market’ market’s beta of 1 by creating a hypothetical portfolio made up of TT-bills and the managed portfolio If the beta is lower than one, leverage is used and the hypothetical portfolio is compared to the market T2 Example Risk Prem. (r-rf) Beta Alpha Treynor Measure Port. P. 13.00% 0.80 5.00% 16.25 Figure 18.3 Treynor Square Measure Market 10.00% 1.0 0.00% 10.00 Weight to match Market w = βM/βP = 1.0 / 0.8 Adjusted Return RP* = w (RP) = 16.25% T2P = RP* - RM = 16.25% - 10% = 6.25% Which Measure is Appropriate It depends on investment assumptions 1) If the portfolio represents the entire investment for an individual, Sharpe Index compared to the Sharpe Index for the market. 2) If many alternatives are possible, use the Jensen α or the Treynor measure The Treynor measure is more complete because it adjusts for risk Limitations Assumptions underlying measures limit their usefulness When the portfolio is being actively managed, basic stability requirements are not met Practitioners often use benchmark portfolio comparisons to measure performance 20-3 Figure 18.4 Portfolio Returns 18.2 STYLE ANALYSIS Style Analysis Introduced by Bill Sharpe Explaining percentage returns by allocation to style Style Analysis has become popular with the industry Figure 18.5 Fidelity Magellan Fund Difference: Fund versus Style Benchmark Figure 18.6 Fidelity Magellan Fund Difference: Fund versus S&P 500 18.3 MORNINGSTAR’S RISK-ADJUSTED RATING 20-4 Morningstar Premier source of information on mutual funds Risk Adjusted Rating (RAR) among most widely used performance measures Morning Star’s Risk Adjusted Rating Similar to mean Standard Deviation rankings Companies are put into peer groups Stars are assigned Figure 18.7 Average Tracking Error of 636 Mutual Funds, 1985 - 1989 Figure 18.8 Rankings Based on Morningstar’s RARs and Excess Return Sharpe Ratios – 1-lowest – 5-highest Highly correlated to Sharpe measures Performance Attribution 18.4 PERFORMANCE ATTRIBUTION PROCEDURES Decomposing overall performance into components Components are related to specific elements of performance Example components – Broad Allocation – Industry – Security Choice – Up and Down Markets 20-5 Process of Attributing Performance to Components Set up a ‘Benchmark’ Benchmark’ or ‘Bogey’ Bogey’ portfolio – Use indexes for each component – Use target weight structure Table 18.5 Performance Attribution Process of Attributing Performance to Components Calculate the return on the ‘Bogey’ Bogey’ and on the managed portfolio Explain the difference in return based on component weights or selection Summarize the performance differences into appropriate categories Table 18.6 Sector Allocation Within the Equity Market Table 18.7 Portfolio Attribution Summary 18.5 THE LURE OF ACTIVE MANAGEMENT 20-6 Lure of Active Management Are markets totally efficient? – Some managers outperform the market for extended periods – While the abnormal performance may not be too large, it is too large to be attributed solely to noise – Evidence of anomalies such as the turn of the year exist 18. MARKET TIMING The evidence suggests that there is some role for active management Market Timing Adjust the portfolio for movements in the market Shift between stocks and money market instruments or bonds With perfect ability to forecast behaves like an option Little evidence of market timing ability With Imperfect Ability to Forecast Long horizon to judge the ability Judge proportions of correct calls Bull markets and bear market calls Figure 18.9 Rate of Return of a Perfect Market Timer Market Timing & Performance Measurement Adjusting portfolio for up and down movements in the market – Low Market Return - low ßeta – High Market Return - high ßeta 20-7 Figure 18.10 Characteristic Lines 18.7 SECURITY SELECTION: THE TREYNOR-BLACK MODEL Superior Selection Ability Treynor-Black Model Concentrate funds in undervalued stocks or undervalued sectors or industries Balance funds in an active portfolio and in a passive portfolio Active selection will mean some nonsystematic risk Security analysts can analyze in depth only a small number of stocks Market index portfolio is the baseline portfolio Macro forecasting unit provides forecasts of expected rate of return Treynor-Black Model: Characteristics Treynor-Black Model: Characteristics Objective of security analysis is to form an active portfolio – Estimate the SCL – Determine the expected return – Use estimates for alpha, beta, and residual risk to determine optimal weight of each security Macroeconomic forecasts for passive index portfolio and composite forecast for the active portfolio are used to determine the optimal risky portfolio Analysis performed using the model can add value The model is easy to implement Lends itself to use with decentralized decision making 20-8 Portfolio Construction Rate of return on security i, where ei is the firm specific component ri = rf + βi (rm − rf ) + ei Portfolio Construction Subset of available securities are researched and that portfolio will be mixed with the index portfolio to improve diversification For each security k, where α represents abnormal expected return rk = rf + βk (rM − rf ) + ek + α k Estimating Parameters For each security analyzed, the following parameters would be estimated: α k , β k , σ 2 (ek ) Active portfolio would have the following parameters: α A , β A , σ 2 (eA ) Total variance would be: β A2σ M2 + σ 2 (eA ) Sharpe Measurement Appraisal Ratio αA α ( eA ) = Alpha for the active portfolio αA σ (e )= Nonsystematic risk A Sharpe Measurement Sharpe measurement of the risky portfolio is:  S 2 ( M ) + α A2  2 S ( P) =   2  α (e A )  1 Position in active portfolio relative to the market portfolio depends on the ratio of the active portfolio’ portfolio’s abnormal return relative to its weakness: appraisal ratio Summary Points: Treynor-Black Model Sharpe Measure will increase with added ability to pick stocks Slope of CAL>CML (rp-rf)/σ )/σp > (rm-rf)/σ )/σp P is the portfolio that combines the passively managed portfolio with the actively managed portfolio The combined efficient frontier has a higher return for the same level of risk 20-9 Figure 18.11 The Optimization Process with Active and Passive Portfolios 20-10