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©2015, College for Financial Planning, all rights reserved. Session 9 Risk/Return Measurements – Sharpe, Treynor, Jensen (alpha), and Beta Reliability.

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Presentation on theme: "©2015, College for Financial Planning, all rights reserved. Session 9 Risk/Return Measurements – Sharpe, Treynor, Jensen (alpha), and Beta Reliability."— Presentation transcript:

1 ©2015, College for Financial Planning, all rights reserved. Session 9 Risk/Return Measurements – Sharpe, Treynor, Jensen (alpha), and Beta Reliability CERTIFIED FINANCIAL PLANNER CERTIFICATION PROFESSIONAL EDUCATION PROGRAM Investment Planning

2 Session Details Module4 Chapter(s)3 LOs4-6 Explain the characteristics, uses, and limitations of stock performance measurement indexes. 4-7 Calculate one or more stock performance measurement indexes for given portfolio returns and risk. 4-8 Specify relationships among various indicators of security returns. 9-2

3 Investment Risk/Return Relationships 9-3

4 Required Return (r) 9-4

5 Performance Measurement Alpha (Jensen Index) Treynor Index Sharpe Index 9-5

6 Alpha (Jensen) Alpha is widely used to measure the value added by an active portfolio manager. Since beta is used in the formula, make sure beta is reliable (R-squared of 70 or higher). 9-6

7 Composite Performance Measures The Jensen Index (Alpha) The alpha measures whether the actual return exceeds the return that should have been earned based on the CAPM. Alpha is an absolute measure of return. 9-7

8 Alpha (Jensen) ABC Fund has a return of 15% and a beta of 0.90. The risk-free rate is 5%, and the return of the market is 16%. Has ABC provided the level of return required for the amount of risk taken? 15 - [5 + (16 – 5).90] 15 - [5 + 9.90] 15 - [14.90] = +0.10 9-8

9 Treynor Index Treynor is a relative measure (use for comparison). o the higher the better Beta needs to be reliable. 9-9

10 The Composite Performance Measures The Treynor Index Treynor standardizes the return in excess of the risk-free return by the portfolio’s beta. 9-10

11 Treynor Calculation You have to choose between the following two funds; the current risk-free rate is 5%. Fund A: 18% return, beta of 1.3 Fund B: 14% return, beta of 0.85 Fund A Fund B 18 – 5 = 10 14 – 5 = 10.59 1.3 0.85 9-11

12 Composite Performance Measures Sharpe Sharpe standardizes the return in excess of the risk-free rate by the portfolio’s standard deviation. 9-12

13 Sharpe Index Can be used when beta is not reliable Calculation is similar to Treynor — Sharpe uses standard deviation in the denominator, Treynor uses beta Relative measure used for comparison, the higher the better 9-13

14 Practice Question You are choosing among the following funds. Which fund should you purchase? a. Apple Fund b. Lemon Fund c. Apricot Fund AppleLemonApricot Return13%11%14% Alpha+1.2+0.6-0.8% Treynor.89.56.67 Beta0.91.11.2 Sharpe.35.44.23 R-squared455832 9-14

15 Fund Discussion Name R- squared (R2)BenchmarkBetaAlpha Vanguard 500 Index100S&P 5001.00-0.12 Davis NY87S&P 5000.842.19 Venture A89Russell 1000 Value0.820.84 RiverSource93S&P 5000.98-0.16 Large Value A96Russell 1000 Value0.95-1.78 First Eagle45MSCI EAFE1.71-11.45 Gold A95AMEX Gold Miners0.793.89 Fidelity Real39S&P 5001.302.80 Estate98Wilshire REIT0.94-.51 Source: Morningstar Principia Pro, Sept 2007 9-15

16 Information Ratio New on the Board exam: Extension of the Sharpe ratio: The numerator is the return of the portfolio minus the return of the benchmark (instead of risk-free rate). The denominator is the standard deviation of the difference between the returns on the portfolio and the returns on the benchmark. This is also a relative measure. 9-16

17 Question 1 Which of the following are correct interpretations of the meaning of each of the portfolio performance measurements? I.The higher the Treynor index is, the better the relative portfolio performance. II.Jensen measures absolute return relative to the amount of risk taken, as measured by standard deviation. III.Jensen is an absolute, not relative, measure of return. IV.If a portfolio is not well diversified, the Sharpe index is more representative of the risk-adjusted performance. a.I and II only b.I and III only c.III and IV only d.I, III, and IV only e.II, III, and IV only 9-17

18 Question 2 You have been given the following information on the following two funds and the market. The risk-free rate is 4%. Which of the following statements are correct? I.Fund B outperformed the market as measured by the Sharpe ratio. II.Fund A has a better Treynor ratio than Fund B. III.Fund B has a better return than the market with 87% of the risk. IV.Fund A has an alpha of +3.20. a.I only b.I and II only c.II and III only d.II and IV only e.I, II, and IV only Fund AFund BMarket Realized Return16%11%12% Beta1.1.81.0 Standard Deviation201215 R-squared with market.87.81 9-18

19 Question 3 Your client has narrowed her choices down to three different mutual funds, and you have compiled the following data on the funds shown. Which fund should you select? a.Fund GG b.Fund RR c.Fund ZZ BetaR-squaredTreynorSharpe GG.8443.365.52 RR.5192.227.66 ZZ.6351.954.34 9-19

20 Question 4 Jake is considering two mutual funds for purchase. The Circus Fund has a beta of 1.2 and 3-year return of 8.5%. The Hindsight Fund has a beta of 0.9, and 3-year return of 8%. The current market risk premium is 5%, and the risk-free rate is 3%. Which fund should Jake purchase, and why? a.the Circus Fund, because it has a higher alpha b.the Hindsight Fund, because it has a higher alpha c.either fund, since each has the same alpha d.neither fund, since both have negative alphas 9-20

21 Question 5 The return of a market index has been 11% with a standard deviation of 18. A managed fund, Fund America, has a return of 14% with a standard deviation of 25. If the risk-free rate is 2%, which of the following actions would you take? a.Purchase Fund America since its Sharpe ratio is higher. b.Purchase Fund America since it has a higher return. c.Purchase the market index because its risk is lower. d.Purchase the market index because its risk/return relationship is better. 9-21

22 ©2015, College for Financial Planning, all rights reserved. Session 9 End of Slides CERTIFIED FINANCIAL PLANNER CERTIFICATION PROFESSIONAL EDUCATION PROGRAM Investment Planning


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