Evaluation of Portfolio Performance Chapter 25

Composite Portfolio Performance Measures Portfolio evaluation before 1960 Portfolio evaluation before 1960 rate of return within risk classes rate of return within risk classes Peer group comparisons Peer group comparisons no explicit adjustment for risk no explicit adjustment for risk difficult to form comparable peer group difficult to form comparable peer group Treynor portfolio performance measure Treynor portfolio performance measure market risk market risk individual security risk individual security risk introduced characteristic line introduced characteristic line

Treynor Portfolio Performance Measure Treynor recognized two components of risk Treynor recognized two components of risk Risk from general market fluctuations Risk from general market fluctuations Risk from unique fluctuations in the securities in the portfolio Risk from unique fluctuations in the securities in the portfolio His measure of risk-adjusted performance focuses on the portfolio’s undiversifiable risk: market or systematic risk His measure of risk-adjusted performance focuses on the portfolio’s undiversifiable risk: market or systematic risk

Treynor Portfolio Performance Measure The numerator is the risk premium The numerator is the risk premium The denominator is a measure of risk The denominator is a measure of risk The expression is the risk premium return per unit of risk The expression is the risk premium return per unit of risk Risk averse investors prefer to maximize this value Risk averse investors prefer to maximize this value This assumes a completely diversified portfolio leaving systematic risk as the relevant risk This assumes a completely diversified portfolio leaving systematic risk as the relevant risk

Composite Portfolio Performance Measures Portfolio evaluation before 1960 Portfolio evaluation before 1960 rate of return within risk classes rate of return within risk classes Peer group comparisons Peer group comparisons no explicit adjustment for risk no explicit adjustment for risk difficult to form comparable peer group difficult to form comparable peer group Treynor portfolio performance measure Treynor portfolio performance measure market risk market risk individual security risk individual security risk introduced characteristic line introduced characteristic line

Sharpe Portfolio Performance Measure Risk premium earned per unit of risk Risk premium earned per unit of risk

Treynor versus Sharpe Measure Sharpe uses standard deviation of returns as the measure of risk Sharpe uses standard deviation of returns as the measure of risk Treynor measure uses beta (systematic risk) Treynor measure uses beta (systematic risk) Sharpe therefore evaluates the portfolio manager on the basis of both rate of return performance and diversification Sharpe therefore evaluates the portfolio manager on the basis of both rate of return performance and diversification The methods agree on rankings of completely diversified portfolios The methods agree on rankings of completely diversified portfolios

Jensen Portfolio Performance Measure Also based on CAPM Also based on CAPM Expected return on any security or portfolio is Expected return on any security or portfolio is Where: E(R j ) = the expected return on security RFR = the one-period risk-free interest rate  j = the systematic risk for security or portfolio j E(R m ) = the expected return on the market portfolio of risky assets

Jensen’s Measure alpha value indicates whether portfolio manager is superior or inferior in market timing and/or security selection alpha value indicates whether portfolio manager is superior or inferior in market timing and/or security selection portfolio manager with no forecasting ability but no clearly inferior performance either will have alpha insignificantly different from zero portfolio manager with no forecasting ability but no clearly inferior performance either will have alpha insignificantly different from zero alpha measures how much of rate of return on portfolio is directly attributable to manager’s ability to derive above-average returns adjusted for risk alpha measures how much of rate of return on portfolio is directly attributable to manager’s ability to derive above-average returns adjusted for risk

M 2 Measure Developed by Modigliani and Modigliani Developed by Modigliani and Modigliani Equates the volatility of the managed portfolio with the market by creating a hypothetical portfolio made up of T-bills and the managed portfolio Equates the volatility of the managed portfolio with the market by creating a hypothetical portfolio made up of T-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 If the risk is lower than the market, leverage is used and the hypothetical portfolio is compared to the market

M 2 Measure: Example Managed Portfolio: return = 35%standard deviation = 42% Market Portfolio: return = 28%standard deviation = 30% T-bill return = 6% Hypothetical Portfolio: 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

Performance Attribution Analysis Allocation effect Allocation effect Selection effect Selection effect

Measuring Market Timing Skills Tactical asset allocation (TAA) Tactical asset allocation (TAA) Attribution analysis is inappropriate Attribution analysis is inappropriate indexes make selection effect not relevant indexes make selection effect not relevant multiple changes to asset class weightings during an investment period multiple changes to asset class weightings during an investment period Regression-based measurement Regression-based measurement

Factors That Affect Use of Performance Measures Market portfolio difficult to approximate Market portfolio difficult to approximate Benchmark error Benchmark error can affect slope of SML can affect slope of SML can affect calculation of Beta can affect calculation of Beta greater concern with global investing greater concern with global investing problem is one of measurement problem is one of measurement Sharpe measure not as dependent on market portfolio Sharpe measure not as dependent on market portfolio

Benchmark Portfolios Performance evaluation standard Performance evaluation standard Usually a passive index or portfolio Usually a passive index or portfolio May need benchmark for entire portfolio and separate benchmarks for segments to evaluate individual managers May need benchmark for entire portfolio and separate benchmarks for segments to evaluate individual managers

Characteristics of Benchmarks Unambiguous Unambiguous Investable Investable Measurable Measurable Appropriate Appropriate Reflective of current investment opinions Reflective of current investment opinions Specified in advance Specified in advance

Performance Presentation Standards AIMR PPS have the following goals: AIMR PPS have the following goals: achieve greater uniformity and comparability among performance presentation achieve greater uniformity and comparability among performance presentation improve the service offered to investment management clients improve the service offered to investment management clients enhance the professionalism of the industry enhance the professionalism of the industry bolster the notion of self-regulation bolster the notion of self-regulation

Performance Presentation Standards Total return must be used Total return must be used Time-weighted rates of return must be used Time-weighted rates of return must be used Portfolios valued quarterly and periodic returns geometrically linked Portfolios valued quarterly and periodic returns geometrically linked Composite return performance (if presented) must contain all actual fee-paying accounts Composite return performance (if presented) must contain all actual fee-paying accounts Performance calculated after trading expenses Performance calculated after trading expenses Taxes must be recognized when incurred Taxes must be recognized when incurred Annual returns for all years must be presented Annual returns for all years must be presented Disclosure requirements Disclosure requirements

CFA III A number of different management “styles” are utilized by investment managers. Performance evaluation, however, is not standardized either within or across management styles. One development aimed at mitigating this problem is the emergence of the “benchmark portfolio” concept. Against this background, comment on the role of benchmark portfolios in evaluating a manager’s investment performance and contrast the suitability of benchmark portfolios for this purpose with that of the “median manager” approach often employed. Include 4 elements of comparison in your discussion.