portfolio performance evaluation

Irwin/McGraw-Hill

24-24-11 The McGraw-Hill Companies, Inc., 1999

INVESTMENTSFourth Edition

Bodie Kane Marcus

Portfolio PerformancePortfolio PerformanceEvaluationEvaluation

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Bodie Kane Marcus

Recent Mutual Fund DataRecent Mutual Fund Data

Mutual Funds in Morningstar Database: 17,212 # of funds that have existed over 10 yrs: 2,073

In 10 yrs, 16.69% beat SP500 in avg return and 71% in Sharpe Ratio

10.6% beat the Value-Weighted NYSE index in avg return and 56.73% in Sharpe Ratio. Composite

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Mutual FundsMutual Funds

22% beat the SP 500 in any 5 of the past years.

13.2% beat the Value-Weighted NYSE index in any 5 of the past 10 years

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Hedge Funds?Hedge Funds?

Hedge Funds in TASS database: 1512 93 have existed over 10 years 41% and 31% beat the respective indices in

avg return 75% and 69% beat the indices in Sharpe

ratio 51% and 41% beat the indices in 5 or more

of the past 10 years.

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Bodie Kane Marcus% of Pensi on Asset s i n I ndi ces

75%70%

93%

70%

55%

- 5%

15%

35%

55%

75%

95%

Cal per s ( $155. 3 bi l l i on)

NY Common Ret i r ement ( $146 bi l l i on)

NY Teacher s' Ret i r ement ( $88 bi l l i on)

Penn Ret i r ement Syst em ( $28 bi l l i on)

Wi sconsi n Ret i r ement Syst em ( $67 bi l l i on)

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What is abnormal?Abnormal performance is measured relative to:

Benchmark portfolio Market adjusted Market model / index model adjusted Reward to risk measures such as the Sharpe

Measure:E (rp-rf) / p

Abnormal or Exceptional PerformanceAbnormal or Exceptional Performance

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Market timing

Superior selection- Sectors or industries

- Individual stocks

Factors That Lead to Abnormal Factors That Lead to Abnormal PerformancePerformance

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1) Sharpe Index

rp - rf

p

rp = Average return on the portfolio

rf = Average risk free rate

p= Standard deviation of portfolio

return

Risk Adjusted Performance: SharpeRisk Adjusted Performance: Sharpe

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MM2 2 MeasureMeasure

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

If the risk is lower than the market, leverage is used and the hypothetical portfolio is compared to the market

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MM2 2 Measure: ExampleMeasure: 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

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2) Treynor Measure rp - rf

ßp

rp = Average return on the portfolio

rf = Average risk free rate

ßp = Weighted average for portfolio

Risk Adjusted Performance: Risk Adjusted Performance: TreynorTreynor

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Risk Adjusted Performance: JensenRisk Adjusted Performance: Jensen

Jensen’s alpha

= rp - [ rf + ßp ( rm - rf) ]p

p= Alpha for the portfolio

rp = Average return on the portfolioßp = Weighted average Betarf = Average risk free raterm = Avg. return on market index port.

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Appraisal RatioAppraisal Ratio

Appraisal Ratio = p / (ep)

Appraisal Ratio divides the alpha of the portfolio by the nonsystematic risk

Nonsystematic risk could, in theory, be eliminated by diversification

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It depends on investment assumptions

1) If the portfolio represents the entire investment for an individual, the Sharpe ratio should be compared to the Sharpe ratio for the market.

2) If many alternatives are possible, use the Jensen or the Treynor measure

The Treynor measure is more complete because it adjusts for systematic risk

Which Measure is Appropriate?Which Measure is Appropriate?

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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

LimitationsLimitations

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Decomposing overall performance into components

Components are related to specific elements of performance

Example components- Broad Allocation- Industries- Up and Down Markets

Performance AttributionPerformance Attribution

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Set up a ‘Benchmark’ or ‘Bogey’ portfolio

Use indexes for each component

Use target weight structure

Process of Attributing Performance Process of Attributing Performance to Componentsto Components

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Calculate the return on the ‘Bogey’ and on the managed portfolio

Explain the difference in return based on component weights

Summarize the performance differences into appropriate categories

Process of Attributing Performance Process of Attributing Performance to Componentsto Components

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Two major problems- Need many observations even when portfolio mean

and variance are constant

- Active management leads to shifts in parameters making measurement more difficult

To measure well- You need a lot of short intervals

- For each period you need to specify the makeup of the portfolio

Complications to Measuring Complications to Measuring PerformancePerformance

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Adjusting portfolio for up and down movements in the market

In Low Market: adopt low ßeta strategy

In a High Return Market: load on ßeta!

Managing funds against benchmark: Managing funds against benchmark: Market Timing ExampleMarket Timing Example

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Example of Market TimingExample of Market Timing

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rp - rf

rm - rf

Steadily Increasing the Beta

portfolio performance evaluation

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