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Performance Evaluation and Risk Management

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The managed fund outperformed the bogey by 1.37% or 137 basis points ... The manager's asset allocation decisions caused his portfolio to outperform the bogey ... – PowerPoint PPT presentation

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Title: Performance Evaluation and Risk Management


1
Performance Evaluation and Risk Management
13
2
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.

3
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.

4
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.

5
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

6
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.

7
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

8
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
9
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
10
Jensens Alpha
11
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

12
Bogey Performance vs. Managed Portfolio
13
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

14
Contribution of Asset Allocation to Performance
15
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

16
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)!
17
Contribution of Sector Selection
Within the Equity portion of the portfolio, these
are the sectors the manager picked vs. the Bogey
18
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.

19
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

20
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

21
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

22
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?

23
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

24
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?
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