Chapter 18

Portfolio Performance Evaluation

Types of management revisited• Passive management

1. Capital allocation between cash and the risky portfolio

2. Asset allocation within the risky portfolio.– How passive the management actually is varies

• “Set it and forget it”• Change allocations in 1 or 2 according to perceptions

of risk to keep current with portfolio goals.• Active management

– Forecasting future rates of return on either/both asset classes and individual securities

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Performance evaluation• Purpose:

– Are the returns worth the risk and the fees?

• Measures– Average return by itself is an insufficient measure. Why?

• Average return may not = expected return• Risk return relationship• Major component of returns is the market

performance– Need a measure of abnormal (excess) performance

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Abnormal Performance

How is abnormal performance measured?

Comparisons to peer groups

Rank fund performance within a given category

Benchmark portfolio such as an index – choose the right index is important

USE reward to risk measures such as the alpha, Sharpe Measure (or variations)

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Factors That Lead to Abnormal Performance

• Successful across asset allocations (the most important step)

• Superior allocation within each asset class– Sectors or industries

• Overweight better performing sectors, underweight poorer performers

• Individual security selection• Pick the right stocks, those with performance

better than expected

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Risk Adjusted Performance: Jensen

3) Jensen’s Alpha Measure

MPPP Rβ-Rα

market the on return excess AverageR

beta Portfolioβ

portfolio the on return excess verageAR

alpha Portfolioα

M

P

P

P

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Measuring Risk Adjusted Performance: Sharpe Ratios

• 1) Historical Sharpe Ratios

p

fp

σ

rrRatios Sharpe

deviation standard Portfolioσ

rate free risk Averager

portfolio the on return Averager

p

f

p

Use:

When choosing among competing portfolios that will not be mixed.

In practice:

Used when one manager handles the (entire) portfolio.

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Risk Adjusted Performance: Treynor

• 2) Historical Treynor Ratios

p

fp rrRatios Treynor

beta Portfolio

rate free risk Averager

portfolio the on return Averager

p

f

p

Use:

Evaluate a portfolio when portfolio is a piece of a larger portfolio that has different managers.

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Summary of measures and usagePerformance Measure

Definition Application

Sharpe pR / sas the

When choosing among portfolios competingoptimal risky portfolio

Treynor Rp / bWhen ranking many portfolios that will be mixed to form the optimal risky portfolio

Information ratio pa / se

When evaluating a portfolio to be mixed with a position in the passive benchmarkportfolio

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Alpha Capture & Transport

• If an analyst finds an undervalued security and invests in it, market moves may wipe out any gains. – Can hedge out market risk via shorting stock index or

stock index futures to establish a market neutral position.

– Process is called alpha capture or alpha transport.– When short positions and leverage are allowed a

significant non-zero alpha is a sufficient condition for an improvement in the Sharpe and information ratio.

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Evaluation with a multi-index model

• Evidence indicates we should use a multi-index model such as the Fama-French model to establish the expected return:

• This allows an estimation of alpha:

ptPHMLtHMLSMBtSMBMtPPt eαrβrβRβR

PHMLtHMLSMBtSMBMtPPt αrβrβRβR

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Style Analysis

• Complex method of performance evaluation introduced by William Sharpe

• Recent studies of mutual fund performance show that > 90% of variation in returns can be explained by the funds’ allocations to bills, bonds and stocks.

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Morning Star’s Risk Adjusted Rating

• Companies are put into peer groups based on Morningstar style definitions

• Risk adjusted fund performance is ranked and then Stars are assigned according to the following table (5 stars is the highest rating)

• Star ratings are highly correlated to Sharpe measure rankings

Percentile Stars

0-10 1

10-32.5 2

32.5-67.5 3

67.5-90 4

90-100 5

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Problems with performance measures

• In a large universe of funds, some funds will have abnormal performance in every period just by chance.– Requires statistical work

• Volatility is quite high and creates large errors in estimation

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Performance Attribution• Decomposing overall performance into

components• Performance is determined by specific

portfolio choices, • Major performance determinants:

– Broad asset allocation among types of securities,

– Industry weighting in equity portfolio,– Security choice,– Timing of purchases and sales.

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Market Timing• Adjust the asset allocation 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

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Value of Market Timing

Invest $1 on December 1, 1926

*Perfect Timing: Every month 100% of the funds are placed in either stocks or cash based on which would have the higher return.

Strategy Value in 2008Geom Avg.

Return

Money Markets $20 3.71%

Stocks $1,626 9.44%

Perfect Timing* $36,699,302,473 34.54%

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