Portfolio Performance Measures

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Portfolio Performance Measures

• What do we require of portfolio managers?
• 1. Earn an average (or fair) return for the
  level of risk in the portfolio
• 2. Ability to manage risk
• 3. Eliminate unnecessary risks

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Portfolio Performance Measurement

• Benchmarking
• Gives us a reference point for comparison
• Comparison of return and risk

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Portfolio Performance Measurement

• Choosing a benchmark
• The most important consideration for portfolio
  performance measurement is benchmark choice. All
  portfolio evaluation is dependent on benchmark
  choice
• 1. Make sure the benchmark is unambiguous
• 2. Make sure the benchmark is an investable
  index
• 3. Make sure the benchmark has a measurable
  value

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Portfolio Performance Measurement

• Choosing a benchmark
• 4. Make sure that the benchmark is appropriate
  for the style of portfolio that you are
  evaluating
• 5. Make sure the benchmark is specified in
  advance
• 6. Make sure the benchmark reflects current
  knowledge and opinion
• 7. Dont change indices. Be consistent across
  portfolios

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Portfolio Performance Measures

• Treynors measure

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Portfolio Performance Measures

• Treynors measure
• Treynors measure basically gives us a measure of
  return per unit of market risk (or systematic
  risk) that our investment earns
• Strictly speaking, the larger the Treynor measure
  the better. However, we would like to have some
  benchmark with which to compare our individual
  Treynor measures.

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Portfolio Performance Measures

• Tryenors measure
• Benchmark comparison

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Portfolio Performance Measures

• Treynors measure
• If Ti gt Tm, the portfolio would plot above the
  security market line, indicating superior
  performance by the portfolio manager.
• If Ti lt Tm, the portfolio would plot below the
  security market line, indicating poor performance
  by the portfolio manager.

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Portfolio Performance Measures

• Sharpe performance measure

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Portfolio Performance Measures

• Sharpe performance measure
• Thus, the Sharpe measure gives us a measure of
  return per unit of total risk. Again, the higher
  the Sharpe measure, the better the performance.
  We can also compare individual Sharpe measures to
  a benchmark

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Portfolio Performance Measures

• Sharpe performance measure
• Instead of plotting deviations from the security
  market line, like the Treynor measure, we are
  plotting deviations from the market determine
  price of risk as defined by the capital market
  line (CML).

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Portfolio Performance Measures

• Sharpe measure
• If Si gt Sm, the asset earn more than the risk
  premium required by the capital market line,
  indicating superior performance by the portfolio
  manager.
• If Si lt Sm the asset earn less than the risk
  premium required by the capital market line,
  indicating poor performance by the portfolio
  manager.

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Portfolio Performance Measures

• Comparing the Treynor and Sharpe measures
• For a completely diversified portfolio of assets,
  the Sharpe and Treynor measures would be
  identical in what they are measuring
• Treynor measures performance relative to
  systematic risk
• Sharpe measure s performance relative to total
  risk

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Portfolio Performance Measures

• Comparing the Treynor and Sharpe measures
• Sharpe measure gives some indication of how good
  the portfolio manager is at diversifying away
  unsystematic risk
• A poorly diversified portfolio could have a high
  Treynor ranking

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Portfolio Performance Measures

• Jensens Alpha
• Jensens alpha is based on the ideas contained in
  the CAPM. It, like the Treynor measure, measures
  how well a portfolio manager does at dealing with
  systematic risk
• To calculate Jensens alpha we need to estimate
  the following regression model

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Portfolio Performance Measures

• Jensens Alpha
• ? measures the degree to which managers are
  earning significant returns after accounting for
  market risk, as measured by beta. If the manager
  is earning a fair return for the given
  portfolios systematic risk, then ? would be zero.

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Portfolio Performance Measures

• Jensens Alpha
• () ? indicates good performance
• (-) ? indicates poor performance
• Jensens alpha allows us to statistically test
  whether the return the manager earns is
  significantly more (or less) than what we would
  expect using the CAPM.
• Jensens alpha allows us to get a performance
  measure that incorporates information from more
  than one time period.

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Portfolio Performance Measures

• Jensens Alpha
• The validity of the Jensen performance measure is
  tied to the validity of the CAPM. Thus, some
  individuals will choose estimate Jensen's alpha
  performing the regression model without
  subtracting the risk-free rate. This gives us
  the alpha from the characteristic line. Its
  interpretation is the same as the interpretation
  of Jensen's alpha.

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Portfolio Performance Measures

• Fama and French (1993) three factor model alpha

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Portfolio Performance Measures

• Fama and French (1993) three factor model
• The alpha in this model can be interpreted in the
  same way as the Jensen's alpha. A positive
  Fama/French alpha would indicate performance
  better than expectations.
• Given that the Fama/French model predicts returns
  better than the CAPM, the Fama/French alpha
  should be a more precise measure of portfolio
  performance than the Jensen's alpha.

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Portfolio Performance Measures

• Famas performance measure
• Fama breaks performance by a portfolio manager
  into two categories selectivity and
  diversification. Famas measure incorporates
  measures for managing both systematic and
  unsystematic risk.

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Portfolio Performance Measures

• Famas performance measure
• Selectivity measures the ability of the
  portfolio manager to earn a return that is
  consistent with the portfolios market
  (systematic) risk. The selectivity measure is

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Portfolio Performance Measures

• Famas performance measure
• () selectivity indicates that the manager earned
  a higher return than the systematic risk of the
  portfolio would indicate. Basically, you are
  just comparing the return on the asset with the
  return earned by the CAPM.

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Portfolio Performance Measures

• Famas performance measure
• Diversification Diversification measures the
  extent to which the portfolio may not have been
  completely diversified. Diversification is
  measured as

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Portfolio Performance Measures

• Famas performance measure
• If the portfolio is completely diversified,
  contains no unsystematic risk, then
  diversification measure would be zero. A
  positive diversification measure indicates that
  the portfolio is not completely diversified it
  would contain unsystematic risk.
• If the diversification measure is positive, it
  represents the extra return that the portfolio
  should earn for not being completely diversified.

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Portfolio Performance Measures

• Famas performance measure
• Net selectivity selectivity - diversification
• Net selectivity measures how well the portfolio
  manager did at earning a fair return for the
  portfolios systematic risk and how well the
  portfolio manager did at diversifying away
  unsystematic risk.
• Positive net selectivity indicates the portfolio
  manager did a good job. Negative net selectivity
  indicates that the portfolio manager did a poor
  job.