Evaluating Portfolio Performance

1. Evaluating Portfolio Performance Chapter 22

2. Evaluating Performance • A portfolio manager analyzes the investment opportunities and decides on what to invest in…then forms the portfolio • After some time, need way to measure how well the portfolio did and how good the manager’s decisions were • A measure of performance must take into account both the return earned and the level of the risk

3. Evaluating Performance Three common measures of performance: • Treynor Measure • Sharpe Measure • Jensen’s Measure (Jensen’s alpha) • Both Treynor and Sharpe are ratios of return/risk

4. Treynor Measure • Where: • is the average return on portfolio i per period over the evaluation horizon • is the average risk free rate per period over the evaluation horizon • βi is the beta of portfolio i over the evaluation horizon

5. Treynor Measure • Treynor Measure evaluates performance based upon the average excess return per unit of risk • The risk used is systematic risk, measured by beta

6. Sharpe Measure • Where σi is the standard deviation of returns for portfolio i over the evaluation horizon

7. Sharpe Measure • Sharpe Measure evaluates performance based upon the average excess return per unit of risk • The risk used is total risk, measured by standard deviation

8. Comparing Treynor and Sharpe • Both measure (excess return)/risk • Only difference is measure of risk used • If the portfolio being evaluated is the total portfolio of the investor, then Sharpe is appropriate  since the investor will be exposed to the total risk of the portfolio • This is most common situation, Sharpe is much more commonly used than Treynor

9. Comparing Treynor and Sharpe • If the portfolio is being evaluated to see if it should be made part of a larger, more diversified, portfolio, then Treynor may be appropriate  since only the systematic risk of the portfolio will matter if it is held within a larger portfolio

10. Jensen Measure • Also called Jensen’s alpha Jensen’s alpha = (return on portfolio) minus (what would be expected under CAPM) • Note that the Jensen Measure could easily be extended to use multi-factor models instead of CAPM

11. Jensen Measure • Jensen Measure can be calculated by estimating regression using data from each period over the evaluation horizon: • I is the Jensen Measure

12. Jensen Measure • Or, perhaps more intuitively: Where the beta is estimated over the evaluation horizon and the returns are the averages over the evaluation horizon.

13. Jensen Measure e.g. If you want to know if your portfolio manager is doing a good job, estimate the alpha over some time frame. If  = 2%, this means that the manager generated returns 2% higher than should be expected given how much risk he took on. He is doing a good job! If  < 0, then the manager is doing a bad job, getting even less than should be expected.

14. Measuring Returns • How to measure returns generated by an investment manager? • Two ways to measure returns: • Dollar Weighted Rate of Return • Time Weighted Rate of Return

15. Measuring Returns • Dollar weighted rate of return is the internal rate of return (IRR) of an investment • In investment management industry, time weighted rate of return is preferred • Rate does not depend on when investment is made (timing of cashflows) • Since different clients will invest at different times, need a measure that is independent of timing

16. To calculate time weighted return, calculate holding period return for each sub-period, then calculate geometric mean to get annualized average return: