复旦大学：《投资学讲义》（英文版） Chapter 11 Performance Evaluation

Performance evaluation Fan longzhen

Performance Evaluation Fan Longzhen

Discussion points How to measure returns? How to choose benchmark? How to adjust for risk? Performance attribution Active return and risk

Discussion Points • How to measure returns? • How to choose benchmark? • How to adjust for risk? • Performance attribution. • Active return and risk

Why evaluate performance? If you manage your own portfolio, then you may possibly want to make alternations to your investment procedures If someone else is managing your portfolio, you want to know if they are adding value If not, perhaps you may have them manage a smaller amount of your money (or even replace them), or add constraints to what they want can do

Why evaluate performance? • If you manage your own portfolio, then you may possibly want to make alternations to your investment procedures. • If someone else is managing your portfolio, you want to know if they are adding value. • If not, perhaps you may have them manage a smaller amount of your money (or even replace them), or add constraints to what they want can do

How to measure returns The portfolio value is affected by cash inflow and outflows How do we compute the portfolio return when portfolio size changes over time In the following case, the portfolio has an ending value of S135. 000. and then an additional $50000 cash investment was made to the portfolio on january 5. what is the portfolio return in january market value of portfolio on January 5 Investment asset 31-Dec Before After 31-Jan cash equivalents $5, 000 400054000 7000 B sonas 1000011000|1100060650 stocks 1200001227001227001300 total 135000137700187700197650

How to measure returns • The portfolio value is affected by cash inflow and outflows. How do we compute the portfolio return when portfolio size changes over time? • In the following case, the portfolio has an ending value of $135, 000, and then an additional $50000 cash investment was made to the portfolio on January 5. What is the portfolio return in January. asset 31-Dec Before After 31-Jan. cash equivalents $5,000 4000 54000 7000 Bonds 10000 11000 11000 60650 stocks 120000 122700 122700 130000 total 135000 137700 187700 197650 January 5 Investment market value of portfolio on

Time-weighted returns Compute the return for two periods dec 31-Jan 5 and jan 5-Jan 31) Return on dec 31-jan 5 ($1377013501350020% Return on jan 5-Jan 31 ($197650187708770053% Time-weighted returns (1+2%)(1+5.3%)-1=741

Time-weighted returns • Compute the return for two periods (Dec 31-Jan 5 and Jan 5-Jan 31) • Return on Dec 31-Jan 5: – ($137700-135000)/135000=2.0% • Return on Jan 5-Jan 31 – ($197650-187700)/$187700=5.3% • Time-weighted returns: – (1+2%)(1+5.3%)-1=7.41%

Dollar-weighted return · Dollar-weighted return Compute the internal rate of return that will equate the future value of the beginning value and cash inflows with the ending value 197650=135000+50000+31 Dollar-weighted return(r)=7.16%

Dollar-weighted return • Dollar-weighted return: – Compute the internal rate of return that will equate the future value of the beginning value and cash inflows with the ending value Dollar-weighted return( r) =7.16% 26/31 197650 =135000 ( 1 + r ) + 50000 ( 1 + r ) ⇒

Which return measure is better Dollar weighted return Affected by any cash investments or withdrawals to the portfolio during the period over which the return is calculated Measure the returns to the owner of the portfolio allowing the benefits or losses associated with cash distributions and withdrawals during the measurement period Time-weighted return Not affected by any cash investment or withdrawals to the portfolio during the period over which the return is calculated Measure returns on the securities held in a portfolio (or performance of the manager)

Which return measure is better • Dollar weighted return: – Affected by any cash investments or withdrawals to the portfolio during the period over which the return is calculated. – Measure the returns to the owner of the portfolio allowing the benefits or losses associated with cash distributions and withdrawals during the measurement period. • Time-weighted return – Not affected by any cash investment or withdrawals to the portfolio during the period over which the return is calculated. – Measure returns on the securities held in a portfolio (or performance of the manager)

How to choose benchmark? Purpose of benchmark Evaluate performance Provide value weightings Provide constraints to portfolio manager Benchmark portfolio sually a passive index or portfolio US Sometimes no appropriate single benchmark exists, so you build your own

How to choose Benchmark? • Purpose of benchmark – Evaluate performance – Provide value weightings – Provide constraints to portfolio manager • Benchmark portfolio – Usually a passive index or portfolio – Sometimes no appropriate single benchmark exists, so you build your own

Performance measure of your portfolio any abnormal returns Compare the return of the portfolio with a comparable market index and adjust for risk Measure of abnormal returns Jensens alpha Treynor's measure Sharpes measure Information ratio

Performance measure of your portfolio • Any abnormal returns – Compare the return of the portfolio with a comparable market index and adjust for risk. • Measure of abnormal returns – Jensen’s alpha – Treynor’s measure – Sharpe’s measure – Information ratio

Performance measure of your portfolio Fix a particular time interval for which you are interested in assessing the performance of your portfolio Find a market index as market portfolio Determine the portfolio beta B compute the average return of your portfolio(denoted Dy ar ) the average risk-free return ar le average benchmark return ar over the interval you are assessing the performance of your portfolio

Performance measure of your portfolio • Fix a particular time interval for which you are interested in assessing the performance of your portfolio; • Find a market index as market portfolio; • Determine the portfolio beta • compute the average return of your portfolio (denoted by ), the average risk-free return , the average benchmark return over the interval you are assessing the performance of your portfolio. β p p ar f ar arM