Portfolio Performance Evaluation 03/09/09

2 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 portfolio’s overall performance?

3 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 manager’s skill to select securities. Attribution analysis allows us to do this.

4 Performance Measurement Return measurement without intraperiod external cash flows: No external cash flows: External cash flows at beginning of period:

5 Performance Measurement Return measurement without intraperiod external cash flows: External cash flows at end of period:

6 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.

7 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.

8 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.

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

10 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 Jensen’s alpha

11 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.

12 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.

13 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.

14 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.

15 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

16 Performance Appraisal: Information Ratio The Information Ratio provides a risk-adjusted performance measure of a portfolio versus a benchmark. where R b is the average return on the benchmark and σ ER is the standard deviation of the excess return. All the values are measured during the same time period.

17 Performance Appraisal: Information Ratio This ratio measures the reward earned by the account manager per incremental unit of risk created by deviating from the benchmark’s holdings. When comparing portfolios, higher ratios are better. An information ratio above 0.5 would place the manager in the top quartile of all managers.

18 Jensen’s alpha Jensen’s alpha is also based on the CAPM. A manager’s alpha measures by how much the manager’s achieved return was different from what was expected for the level of portfolio systematic risk taken. The risk free rate needs to be determined for each of the intervals in the evaluation period.

19 Jensen’s alpha We can calculate the alpha for a particular manager / portfolio by running the appropriate regression. (X-variable is the market risk premium and Y-variable is the portfolio risk premium.) The intercept in the regression represents the portfolio’s alpha. The advantages of using Jensen’s 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 manager’s skill level The measure is flexible enough to allow for alternative models of risk and return such as the multifactor model:

20 Performance Attribution Analysis Attribution analysis concerns itself with the investment results of individual portfolios relative to designated benchmarks. A manager’s value-added can be expressed as: Where r p and r B represent the return on the portfolio and benchmark, respectively.

21 Performance Attribution Analysis The value-added return can be segmented into two categories: Allocation effect Selection effect

22 Performance Attribution Analysis Allocation effect: This effect assumes that within each sector/asset class the manager held the same securities as the benchmark and in the same proportions. The return measures the sector/asset-class weighting decisions of the manager. Where i represents the sectors/asset classes in which the manager is invested.

23 Performance Attribution Analysis Selection effect: This effect assumes that the manager weights each sector/asset class in the portfolio in the same proportion as the benchmark although within the sector the manager may hold securities in weights that are different from the benchmark. The return measures the security selection decisions of the manager. Where i represents the sectors/asset classes in which the manager is invested.

24 Performance Attribution Analysis Other considerations: This attribution analysis is a ‘buy and hold’ attribution. This disregards transactions during the evaluation period. There may be need of a reconciling item that captures the difference between the actual portfolio return (which includes transactions) and the attribution analysis buy and hold return.

25 Performance Attribution Analysis Other considerations: Since in this analysis returns are not risk- adjusted, it is possible for the portfolio to generate higher returns simply because the securities invested in are of higher risk than the benchmark securities. This has nothing to do with the manager’s skill.

26 Readings RB 25 (pgs , ), RM 6 (Sections 6.5 and 6.6, pgs )