Porfolio Performance Evaluation

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Porfolio Performance Evaluation

• BKM Chapter 17

Covered All of it except Treynor-Black model
2
Agenda

• How to evaluate portfolio performance
• How well did the portfolio do?
• How do we adjust for risk, to compare different
  managers?
• Did managers do well because they pick stocks
  well, time the markets well, etc?
• How to put stocks or funds that outperform the
  market into your active portfolio

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Performance Evaluation Measures

• Sharpes measure
• The portfolios average excess return per unit of
  total risk
• Treynors measure
• The portfolios average excess return per unit of
  systematic risk
• Jensens measure
• The excess of the portfolios return over that
  predicted by the CAPM
• Appraisal Ratio
• Excess return (over that predicted by the CAPM)
  divided by the amount of non-systematic risk
  taken on

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Performance Evaluation Measures

• Sharpes measure
• Treynors measure
• Jensens measure
• Appraisal Ratio

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Risk Adjusted Performance Sharpe

• 1) Sharpe Ratio

?
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Sharpe Measure

• Recall that under the assumptions of the CAPM,
  the market has the highest Sharpe ratio of any
  basket of securities.

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Usage of the Sharpe Measure

• Makes sense to use it
• If you are a mean-variance investor, and you are
  considering different securities that will
  constitute your entire portfolio.
• Dont use it otherwise

A
rf
B
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Sharpe Ratio Failure

• Example You are a diversified investor holding
  the market.
• E(rM)12, E(rf) 6. smarket24
• Sharpe Ratio ¼
• A new IPO comes along with
• E(rIPO)26, sIPO200, correl(IPO,Market)0
• Sharpe Ratio 1/10
• Would you buy a few shares?

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Risk Adjusted Performance Alpha
3) Jensens Measure
?
Alpha for the portfolio
p
rp Average return on the portfolio ßp
Beta of the portfolio rf Average risk free
rate rm Avg. return on market index port.

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Risk Adjusted Performance Treynor

• 2) Treynor Measure

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Treynor Measure vs. Jensens Alpha
B
Security Market Line E(ri)rfBi(E(rM)-rf)
A
Portfolio B has a higher Alpha
rf
Systematic Risk (Beta)
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Treynor Measure vs. Jensens Alpha
B
Security Market Line E(ri)rfBi(E(rM)-rf)
A
rf
Systematic Risk (Beta)
13
Treynor Measure vs. Jensens Alpha
B
Security Market Line E(ri)rfBi(E(rM)-rf)
T2 of portfolio A
T2 of portfolio B
A

• To resolve the discrepancy
• Standardize the betas to 1.
• Then compare the alpha of that standardized
  portfolio
• Call that number T2.

rf
Beta1
Systematic Risk (Beta)
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M2 (Variant of Sharpe Ratio)

• Portfolio A appears to have a higher Sharpe ratio
• But how big is the difference (economically)?
• Again, standardize portfolios to have the same
  risk as the market
• M2 is like an easier-to-interpret version of the
  Sharpe ratio.

B
M2 of portfolio A
M2 of portfolio B
A
Market
rf
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Appraisal Ratio

• Suppose
• the CAPM holds
• you are diversified
• but then you find an opportunity with positive
  alpha
• Overweighting the security is good (because alpha
  gt0) but is bad (because it makes you
  undiversified).
• Appraisal ratio accounts for this trade-off

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Which Measure is Appropriate?

• It depends on investment assumptions
• 1) If the portfolio represents the entire
  investment, use the Sharpe Ratio (compared to the
  market) or M2.
• 2) If adding on to a diversified portfolio, use
  Jensens ?, Treynor measure, T2 or the appraisal
  ratio.
• They all answer the same question would it be
  useful to add this security to an otherwise
  diversified portfolio?

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Performance Attribution

• Suppose an investor or portfolio manager did well
• Positive alpha
• To what do we attribute this
• Picked the right stocks (e.g. Home Depot vs.
  Lowes)?
• Picked the right industries (e.g. overweight
  pharmaceuticals)?
• Market timing?

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Process of Attributing Performance to Components

• Example In one month,
• A managed portfolio returned 5.34
• Its peers got 3.97
• Peers were invested 60 stocks, 30 bonds, 10
  cash
• Portfolio was 70 stocks, 7 bonds, 23 cash
• The manager
• was just in the right asset classes?
• OR
• picked the right stocks within these sectors?

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Process of Attributing Performance to Components

• Set up a Benchmark or Bogey portfolio
• Use indexes for each component
• Calculate the return on the Bogey and on the
  managed portfolio
• Explain the difference in return based on
  component weights or selection

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Performance Attribution1. Excess Return
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Performance Attribution2. Asset Allocation
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Last Questions of the Semester

• Empirically, how good is a typical fund manager
  at stock-picking? Asset allocation?
• Is the breakdown .31 vs. 1.37 realistic?
• What effect does market timing (shifting in and
  out of asset classes) have on returns?

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Market Timing

• Adjust the portfolio for expected market return
• Shift between stocks and money market instruments
  or bonds
• Results higher returns, lower risk (downside is
  eliminated)
• With perfect ability to forecast behaves like an
  option

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Rate of Return of a Perfect Market Timer
rf
Value of perfect timing value of a call option
on the SP
rM
rf
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Example of Market Timing
(If timing ability is good but not perfect)
rp - rf




















rm - rf



Beta increases in the Markets return
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Effect of Market Timing

• This strategy poses a difficulty
• for our performance
• evaluation measures
• Risk is changing constantly.
• To my knowledge this problem has not been
  satisfactorily solved.

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How do real-world managers do?

• Empirically, performance is almost entirely
  explained by asset allocation.
• On average, managers do not stock-pick well
  enough to cover their transaction costs

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How do real-world managers do?

• They do even worse after fees
• especially true for high-fee managers.

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Lesson I take away

• Market appears to be semi-strong efficient
  regarding stock-picking, but not regarding mutual
  fund picking
• Another (possible) inefficiency regards long-run
  divergences from fair value for an index or
  possibly asset classes.