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Performance Evaluation and Active Portfolio Management

2. Performance Evaluation. We want to know whether a particular portfolio performance is abnormally highWhat is abnormal?Market adjusted, or market model adjustedReward to risk measures such as the Sharpe ratioComplicated issueMany kinds of different benchmarks and measuresDifferent measures may lead to different implications on performance evaluation.

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Performance Evaluation and Active Portfolio Management

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    1. Chapter 20 Performance Evaluation and Active Portfolio Management

    2. 2 Performance Evaluation We want to know whether a particular portfolio performance is abnormally high What is abnormal? Market adjusted, or market model adjusted Reward to risk measures such as the Sharpe ratio Complicated issue Many kinds of different benchmarks and measures Different measures may lead to different implications on performance evaluation

    3. 3 Two ways of performance evaluation 1) Relative performance measures Compare with other benchmark with similar risk characteristics (Ex) high-yield bond portfolio growth stock portfolio 2) Risk-adjustment based on MV or CAPM Sharpe measure Treynor measure Jensen measure

    4. 4 Sharpe Measure 1) Sharpe measure =

    5. 5 Treynor Measure 2) Treynor Measure =

    6. 6 Jensen’s Alpha

    7. 7 M2 Measure Attempt to resolve the difficulty in the interpretation of the Sharpe measure by translating it into a percentage term Developed by Modigliani and Modigliani (Modigliani-squared) Equates the volatility of the managed portfolio with the market by creating a hypothetical complete portfolio, rp*, made up of T-bills and the managed portfolio: M2 = rp* – rm where rp* is the return on the hypothetical portfolio If the risk is lower than the market, leverage is used and the hypothetical portfolio is compared to the market

    8. 8 M2 Measure: Example

    9. 9 T2 Measure Similar to the M2 measure, it converts the Treynor measure into percentage return basis Makes it easier to interpret and compare Equates the beta of the managed portfolio with the market’s beta of 1 by creating a hypothetical portfolio made up of T-bills and the managed portfolio T2 = Rp* – Rm where Rp* is the excess return on the hypothetical portfolio If the beta is lower than one, leverage is used and the hypothetical portfolio is compared to the market

    10. 10 T2 Example

    11. 11 Which Measure is Appropriate? It depends on investment assumptions 1) If the portfolio represents the entire investment of an individual, then total volatility matters Thus, Sharpe measure is appropriate, which can be compared to that of the market 2) If a portfolio is just one of a whole portfolio, then systematic risk matters Thus, use the Treynor or the Jensen a measure

    12. 12 Limitations of the model-based performance measures Assumptions underlying measures limit their usefulness Parameter stability When the portfolio is being actively managed, this stability requirement is not met Practitioners often use benchmark portfolio comparisons to measure performance

    13. 13 Performance Attribution Decomposing overall performance into components that are related to specific elements of performance Asset allocation decision Market timing Up and Down Markets Security selection decision Sectors or industries Individual companies

    14. 14 Decomposition of Performance Attribution Assume two broad asset markets, (1) stocks & (2) bonds. Want to compare a managed portfolio return (rp) with a benchmark portfolio return (rm) rp – rm = (wp1rp1 + wp2rp2) – (wm1rm1 + wm2rm2) = (wp1 – wm1)rm1 + (wp2– wm2)rm2 ? asset alloc. + wp1(rp1 – rm1) + wp2 (rp2 – rm2) ? sec. selec. Difference in weights leads to asset allocation bets, and difference in returns within asset classes leads to security selection bets

    15. 15 Asset allocation vs. Selection (1) (2) (3) (4) (5)=(3)×(4) Portfolio Benchmark Excess Index contribution to Market weight weight weight return performance Stocks 0.7 0.6 0.1 5.81% 0.581% Bonds 0.07 0.3 -0.23 1.45% -0.3335% Cash 0.23 0.1 0.13 0.48% 0.0624% Contribution of asset allocation 0.3099% (1) (2) (3) (4) (5)=(3)×(4) Portfolio Benchmark Excess Portfolio contribution to Market return return return weight performance Stocks 7.28 5.81 1.47 0.7 1.03% Bonds 1.89 1.45 0.44 0.07 0.03% Contribution of selection within markets 1.06%

    16. 16 Lure of Active Management Are markets really efficient? Some managers outperform the market for extended periods, and investors are willing to pay for expensive analysis The abnormal performance may not be too large, but it is too large to be attributed solely to noise Markets are “nearly efficient” Evidence of anomalies exists Turn of the year effect, small firm effect, momentum effect ? The evidence suggests that there is some role for active management

    17. 17 Market Timing What is market timing? Adjust the portfolio weights according to a forecast of the market movements for next period (EX) Shift between stocks, bond, and money market instruments Results: higher returns, lower risk (downside is eliminated) With perfect ability to forecast, the portfolio return behaves like an option The value of perfect market timing ability is equivalent to the value of a call option

    18. 18 Rate of Return for a Perfect Market Timer

    19. 19 How to judge timing ability? Need long horizon to judge the ability Judge proportions of correct calls Bull markets and bear market calls See if managers adjust portfolios for up and down movements in the market Low Market Return ? low ßeta High Market Return ? high ßeta

    20. 20 Example of Market Timing

    21. 21 Style Analysis Introduced by Bill Sharpe Explain percentage returns attributable to style investment Size effect Value vs. growth Momentum Style Analysis has become popular with the industry

    22. 22 Morning Star’s Risk Adjusted Rating Similar to mean Standard Deviation rankings Companies are put into peer groups Stars are assigned 1-lowest 5-highest Highly correlated to Sharpe measures

    23. 23 Active portfolio management Concentrate funds in undervalued stocks, sectors, or industries Active selection procedure results in taking some unsystematic risk Balanced funds in an active portfolio and in a passive portfolio Some portion based on passive strategy, and the rest based on active strategy (Ex) Treynor/Black model

    24. 24 Treynor-Black Model Model used to combine actively managed stocks with a passively managed portfolio Optimal combination of active and passive portfolios can be determined, based on a reward-to-risk measure that is similar to the the Sharpe Measure Assumptions Analysts have a limited ability to find a select number of undervalued securities Portfolio managers can estimate the expected return and risk for the actively-managed portfolio as well as the broad market portfolio (passively managed)

    25. 25 Reward-to-Variability Measure

    26. 26 Appraisal Ratio

    27. 27

    28. 28 Summary: Treynor-Black Model Sharpe ratio can be increased by active management with added ability to pick stocks Slope of new CAL > CML (rp-rf)/sp > (rm-rf)/sp 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

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