Portfolio Performance Evaluation

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Portfolio Performance Evaluation

• 05/28/08

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Evaluation of Portfolio Performance

• What are the components of portfolio performance
  evaluation?
• What are the different methods of calculating
  portfolio return with and without intraperiod
  external cash flows?
• What are the four major composite equity
  portfolio performance measures?
• How can we use attribution analysis to identify
  what factors drives a portfolios overall
  performance?

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Components of Portfolio Performance Evaluation

• There are three components to evaluating a
  portfolio
• Performance measurement calculating the return
  that a portfolio achieved over a period of time.
• Performance appraisal - evaluating the overall
  performance of a portfolio. Composite performance
  measures allow us to do this.
• Performance attribution - determining what
  portion of this overall performance was driven by
  the managers skill to select securities.
  Attribution analysis allows us to do this.

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Performance Measurement

• Return measurement without intraperiod external
  cash flows
• No external cash flows
• External cash flows at beginning of period

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Performance Measurement

• Return measurement without intraperiod external
  cash flows
• External cash flows at end of period

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Performance Measurement

• Return measurement with intraperiod external cash
  flows
• Time-weighted rate of return (TWR)
• Reflects the compound rate of growth over the
  evaluation period of 1 initially invested in the
  account.
• The account needs to be valued (and returns
  calculated) every time an external cash flow
  occurs.
• Where N represents the number of external cash
  flows plus 1.

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Performance Measurement

• Return measurement with intraperiod external cash
  flows
• Money-weighted rate of return (MWR)
• Measures the compound growth rate in the value of
  all funds invested in the account over the
  evaluation period.
• This measure is similar to IRR and represents an
  average growth rate of all the money invested.
• Where m is the number of time units in the
  evaluation period, L(i) is the number of days
  between the beginning of the period and when the
  ith cash flow occurs.

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Performance Measurement

• Return measurement with intraperiod external cash
  flows
• TWR vs. MWR
• MWR is sensitive to the size and timing of
  external cash flows, TWR is not.
• If a manager has no control over cash flows, a
  measure that is not sensitive to the timing of
  these cash flows is more appropriate. In most
  cases, this applies to portfolio managers. TWR is
  widely accepted as the appropriate measure of
  account performance.
• If a manager has control over cash flows (such as
  private equity investment managers), MWR is a
  more useful measure.

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Performance Measurement

• Regardless of whether there are external cash
  flows or not, rates of return are reported on an
  annualized basis for comparison purposes.

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Performance Appraisal

• There is no universally accepted measure for
  evaluating portfolios.
• The following four composite performance measures
  are typically used to provide quantitative
  evidence of the performance of portfolios
• Treynor Ratio
• Sharpe Ratio
• Information Ratio
• Jensens alpha

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Performance Appraisal Treynor Ratio

• The Treynor Ratio is the risk-adjusted return of
  a portfolio versus the market and is based on the
  CAPM and Security Market Line (SML).
• where all the values are measured during the same
  time period.

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Performance Appraisal Treynor Ratio

• Portfolios that plot above the SML represent
  portfolios that perform better than the overall
  market.
• When comparing portfolios, higher ratios are
  better.
• The method assumes that the portfolios being
  evaluated are completed diversified.

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Performance Appraisal Sharpe Ratio

• The Sharpe Ratio provides a risk-adjusted
  performance measure where the risk measure
  evaluates total risk and not just systematic risk
  of the portfolio.
• where all the values are measured during the same
  time period.

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Performance Appraisal Sharpe Ratio

• The measure is based on the Capital Market Line
  (CML)
• Portfolios that plot above the CML represent
  portfolios that perform better than the overall
  market.
• When comparing portfolios, higher ratios are
  better.

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Performance Appraisal Treynor versus Sharpe

• Sharpe uses standard deviation of returns as the
  measure of risk
• Treynor measure uses beta (systematic risk)
• Sharpe therefore evaluates the portfolio manager
  on the basis of both rate of return performance
  and diversification
• The methods agree on rankings of completely
  diversified portfolios
• The methods produce relative not absolute
  rankings of performance

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Performance Appraisal Information Ratio

• The Information Ratio provides a risk-adjusted
  performance measure of a portfolio versus a
  benchmark.
• where Rb is the average return on the benchmark
  and sER is the standard deviation of the excess
  return. All the values are measured during the
  same time period.

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Performance Appraisal Information Ratio

• This ratio measures the reward earned by the
  account manager per incremental unit of risk
  created by deviating from the benchmarks
  holdings
• When comparing portfolios, higher ratios are
  better.

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Jensens alpha

• Jensens alpha is also based on the CAPM.
• A managers alpha measures by how much the
  managers achieved return was different from what
  was expected for the level of portfolio
  systematic risk taken.
• Where the error term is a random error term and
  has a mean of zero. The risk free rate needs to
  be determined for each of the intervals in the
  evaluation period.

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Jensens alpha

• We can calculate the alpha for a particular
  manager / portfolio by running the appropriate
  regression. The intercept in the regression
  represents the portfolios alpha.
• The advantages of using Jensens alpha are
• The measure is easier to interpret.
• Because it is estimated from a regression
  equation, it is possible to make statements about
  the statistical significance of the managers
  skill level
• The measure is flexible enough to allow for
  alternative models of risk and return such as the
  multifactor model

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Readings

• RB 25 (pgs. 1040 62),
• RM 6 (pgs. 717-31)