Performance Evaluation and Risk Management

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Performance Evaluation and Risk Management
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Performance Evaluation

• Can anyone consistently earn an excess return,
  thereby beating the market?
• Performance evaluation is a term for assessing
  how well a money manager achieves a balance
  between high returns and acceptable risks.

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Performance Evaluation Measures

• The raw return on a portfolio, RP, is simply the
  total percentage return on a portfolio.
• The raw return has no adjustment for risk.
• The raw return is not compared to any benchmark,
  or standard.
• Therefore, the usefulness of the raw return on a
  portfolio is limited.

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Performance Evaluation Measures

• The Sharpe Ratio
• The Sharpe ratio is a reward-to-risk ratio that
  focuses on total risk.
• It is computed as a portfolios risk premium
  divided by the standard deviation for the
  portfolios return.

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Performance Evaluation Measures

• The Sharpe Ratio
• Find the Sharpe ratio for the portfolio below
• The Media Portfolio has average return of 16,
  standard deviation of 20.
• The risk-free rate is 6

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Performance Evaluation Measures

• The Treynor Ratio
• The Treynor ratio is a reward-to-risk ratio that
  looks at systematic risk only.
• It is computed as a portfolios risk premium
  divided by the portfolios beta coefficient.

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Performance Evaluation Measures

• The Treynor Ratio
• Find the Treynor ratio for the Media Portfolio,
  assuming a beta of 0.8
• Average return is 16, risk free rate is 6

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Performance Evaluation Measures

• Jensens Alpha
• Jensens alpha is the excess return above or
  below the security market line. It can be
  interpreted as a measure of how much the
  portfolio beat the market.
• It is computed as the raw portfolio return less
  the expected portfolio return as predicted by the
  CAPM.

Actual return
Extra Return
CAPM Risk-Adjusted Predicted Return
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Performance Evaluation Measures

• Jensens Alpha
• Find Jensens alpha for the Media Portfolio
• Beta 0.8, risk-free rate is 6 and the market
  rate of return is 14

Extra Return
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Jensens Alpha
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Performance Attribution

• Which investment decisions resulted in superior
  or inferior performance?
• Managed portfolio vs. benchmark portfolio -
  Difference in performance is the sum of
  contributions based on portfolio construction
  decisions
• Three possible components are
• Asset allocation across equity, fixed-income and
  money mkts
• Sector choice within each market
• Security selection within each sector
• The benchmark is called the bogey

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Bogey Performance vs. Managed Portfolio
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Bogey Performance vs. Managed Portfolio

• The managed fund outperformed the bogey by 1.37
  or 137 basis points
• Now we must determine which of the managers
  decisions are responsible for the superior
  performance of the fund
• We will first examine the managers asset
  allocation decisions by comparing the portfolios
  composition
• Cash
• Fixed Income
• Equities

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Contribution of Asset Allocation to Performance
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Contribution of Asset Allocation to Performance

• The managers asset allocation decisions caused
  his portfolio to outperform the bogey
• The amount of superior returns attributed to
  asset allocation is 0.3099 or 30.99 basis points
• The managers fund outperformed the bogey by a
  total of 137 basis points
• The remainder of excess performance (137 30.99
  106 basis points) can be attributed to sector
  selection and security selection

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Contribution of Selection Within Markets
Given Given Solve Given Solve
NOTE Money market instruments are not included,
because they are treated as cash (involves NO
security selection)!
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Contribution of Sector Selection
Within the Equity portion of the portfolio, these
are the sectors the manager picked vs. the Bogey
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Contribution of Sector Selection

• The managers equity portion outperformed the
  bogey by 1.47 or 147 basis points
• The managers sector selection within the equity
  portion of the portfolio outperformed the bogey
  by 1.29 or 129 basis points
• The remaining difference (147 129 18 basis
  points) can be attributed to the managers
  security selection within each sector.

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Portfolio Attribution Summary

• Contribution
• 1.Asset allocation 31.0
• 2. Selection
• a. Equity
• Sector allocation 129
• Security allocation 18
• 147 x 0.70 102.9
• b. Fixed-income excess 44 x 0.07 3.1
• Total excess return 137.0 1.37

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Style Analysis

• 91.5 of the variation in returns of 82 mutual
  funds could be explained by the funds asset
  allocation to bills, bonds and stocks
• Brinson, Singer, Beebower
• Regress fund returns on indexes representing a
  range of asset classes (12)
• Examine regression coefficients for each
• Fidelitys Magellan Fund had 4 positive
  regression coefficients, therefore the fund
  returns are well explained by only four style
  portfolios
• Three style portfolios explain 97.3 of returns
• Magellan vs. SP 500 shows a much wider spread

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Sharpes Style Portfolio

• Bills 0
• Intermediate Bonds 0
• Long term bonds 0
• Corporate bonds 0
• Mortgages 0
• Value stocks 0
• Growth stocks 47
• Medium-cap stocks 31
• Small stocks 18
• Foreign stocks 0
• European stocks 4
• Japanese stocks 0
• R-squared 97.3

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Market Timing

• Consider three investors
• Investor 1 Put 1 in 30 day T-bills on January
  1, 1926, and rolled over all proceeds into 30-day
  T-bills.
• Investor 2 Put 1 in large stocks on the same
  date and reinvested all dividends into the same
  portfolio.
• Investor 3 Shifts all funds at the beginning of
  each year into either bills or stocks, whichever
  is going to do better.
• On December 31, 2001 who has the most money?

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Market Timing

• So, why dont we all just time the market?
• There are no perfect timers!
• Suppose the market is up two days out of three
  and Investor 1 always predicts a market advance.
  The investor is correct 2/3 of the time, is this
  a measure of their forecasting ability?
• No, we should examine the proportion of bull
  markets correctly forecast and the proportion of
  bear markets correctly forecast
• Empirical tests show little evidence of market
  timing ability

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Quick Quiz

• What does Jensens alpha measure?
• What does performance attribution tell us about
  asset allocation and security selection?
• Which strategy is better active or passive?