1. 1 Fin 2802, Spring 10 - Tang Chapter 5: Risk and Return Fina2802: Investments and Portfolio Analysis Spring, 2010 Dragon Tang Lecture 8 Risk and Return: Past and Prologue February 4, 2010 Readings: Chapter 5 Practice Problem Sets: 3,4,5,14,15-17

2. 2 Chapter 5: Risk and Return Fin 2802, Spring 10 - Tang

3. 3 Chapter 5: Risk and Return Risk and Return in Chinese Risk: 危机 Danger | Opportunity Return: 回报 Come back | Gratitude Fin 2802, Spring 08 - TangFin 2802, Spring 10 - Tang

4. 4 Chapter 5: Risk and Return Risk and Return Objectives: 1.Characterize the risk and return on stocks (risky) and bonds (risk-free). 2.Historical risk and return of various securities

5. 5 Fin 2802, Spring 10 - Tang Chapter 5: Risk and Return Return over One Period: Holding Period Return (HPR) HPR: Rate of return over a given investment period

6. 6 Fin 2802, Spring 10 - Tang Chapter 5: Risk and Return Rates of Return: Single Period Example Beginning Price = 100 Ending Price = 110 Dividend = 4 HPR = ( 110 - 100 + 4 )/ ( 100) = 14%

7. 7 Fin 2802, Spring 10 - Tang Real vs. Nominal Rates Notation: –R=nominal return –i =inflation rate –r =real return Exact relationship Approximate relationship Example R = 9%, i = 6%: what is r? Chapter 5: Risk and Return

8. 8 Fin 2802, Spring 10 - Tang Chapter 5: Risk and Return Quoting Conventions APR = annual percentage rate (periods in year) X (rate for period) EAR = effective annual rate ( 1+ rate for period) Periods per yr - 1 Example: monthly return of 1% APR = 1% X 12 = 12% EAR = (1.01) 12 - 1 = 12.68%

9. 9 Fin 2802, Spring 10 - Tang Chapter 5: Risk and Return Return over Multiple Periods Dollar-weighting: Internal Rate of Return (IRR) Time-weighting: –Arithmetic Average: r A = (r 1 +r 2 )/2 –Geometric Average: r G = [(1+r 1 )(1+r 2 )] 1/2 – 1 –r A  ? r G always t = 012 $X$Y$Z r1r1 r2r2 $X, $Y, $Z: Cash Flows; r 1, r 2 : one-period HPR

10. 10 Fin 2802, Spring 10 - Tang Chapter 5: Risk and Return Example 1 2 3 4 Assets(Beg.) 1.0 1.2 2.0.8 HPR.10.25 (.20).25 TA (Before Net Flows) 1.1 1.5 1.6 1.0 Net Flows 0.1 0.5 (0.8) 0.0 End Assets 1.2 2.0.8 1.0

11. 11 Fin 2802, Spring 10 - Tang Chapter 5: Risk and Return Returns Using Arithmetic and Geometric Averaging Arithmetic r a = (r 1 + r 2 + r 3 +... r n ) / n r a = (.10 +.25 -.20 +.25) / 4 =.10 or 10% Geometric r g = {[(1+r 1 ) (1+r 2 ).... (1+r n )]} 1/n - 1 r g = {[(1.1) (1.25) (.8) (1.25)]} 1/4 - 1 = (1.5150) 1/4 -1 =.0829 = 8.29%

12. 12 Fin 2802, Spring 10 - Tang Chapter 5: Risk and Return Dollar Weighted Average Example Net CFs0 1 2 3 4 $ (mil)-1.0 - 0.1 - 0.5 0.8 1.0 Solving for IRR 1.0 = -.1/(1+r) 1 + -.5/(1+r) 2 +.8/(1+r) 3 +1.0/(1+r) 4 r =.0417 or 4.17%

13. 13 Fin 2802, Spring 10 - Tang Chapter 5: Risk and Return Which One to Use? Dollar-weighted return(IRR): Use if focus is total amount of money at some terminal date (wealth) Time-weighted return: - Arithmetic Average:, ignore compounding - Geometric Average:, compounding over time. Use if there is no control over timing Used most by money management industry

14. 14 Fin 2802, Spring 10 - Tang Chapter 5: Risk and Return HPR - Expected Return

15. 15 Fin 2802, Spring 10 - Tang Normal distribution Chapter 5: Risk and Return

16. 16 Fin 2802, Spring 10 - Tang Chapter 5: Risk and Return HPR - Risk Measure Variance or standard deviation:

17. 17 Fin 2802, Spring 10 - Tang Why do we need the variance? Two variables with the same mean. What do we know about their dispersion? Chapter 5: Risk and Return

18. 18 Fin 2802, Spring 10 - Tang Chapter 5: Risk and Return Example Suppose your expectations regarding the stock market are as follows: State of the economyScenario(s)Probability(p(s))HPR Boom10.344% Normal Growth20.414% Recession30.3-16% Compute the mean and standard deviation of the HPR on stocks. E( r ) = 0.3*44% + 0.4*14%+0.3*(-16%)=14% Sigma^2=0.3*(44%-14%)^2+0.4*(14%-14%)^2 +0.3*(-16%-14%)^2=0.54 Sigma=0.7348=73.48%

19. 19 Fin 2802, Spring 08 - Tang Chapter 5: Risk and Return Historical Mean and Variance Data in the n-point time series are treated as realization of a particular scenario each with equal probability 1/n Fin 2802, Spring 10 - Tang Chapter 5: Risk and Return

20. 20 Fin 2802, Spring 08 - Tang Chapter 5: Risk and Return Annual Holding Period Returns Geom.Arith.Stan. SeriesMean%Mean%Dev.% World Stk9.4111.1718.38 US Lg Stk10.2312.2520.50 US Sm Stk11.8018.4338.11 Wor Bonds 5.34 6.13 9.14 LT Treas 5.10 5.64 8.19 T-Bills 3.71 3.79 3.18 Inflation 2.98 3.12 4.35 Historical Returns: 1926-2003 Fin 2802, Spring 10 - Tang Chapter 5: Risk and Return

21. 21 Fin 2802, Spring 10 - Tang r r NegativePositive Skewed Distribution: Large Negative Returns Possible Median Chapter 5: Risk and Return

22. 22 Fin 2802, Spring 10 - Tang r rNegativePositive Skewed Distribution: Large Positive Returns Possible Median Chapter 5: Risk and Return

23. 23 Table 5.5 Risk Measures for Non-Normal Distributions Fin 2802, Spring 10 - Tang Chapter 5: Risk and Return

24. 24 Fin 2802, Spring 10 - Tang Chapter 5: Risk and Return Summary  Definition of Returns: HPR, APR and AER.  Risk and expected return  Next: Asset Allocation