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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. Fina2802: Investments and Portfolio Analysis Spring, 2010 Dragon Tang. Risk: 危机 Danger | Opportunity Return: 回报 Come back | Gratitude. Risk and Return in Chinese.

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Fina2802: Investments and Portfolio Analysis Spring, 2010 Dragon Tang

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

  2. Chapter 5: Risk and Return

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

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

  5. Return over One Period: Holding Period Return (HPR) HPR: Rate of return over a given investment period Chapter 5: Risk and Return

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

  7. 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 Chapter 5: Risk and Return

  8. 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% Quoting Conventions Chapter 5: Risk and Return

  9. Dollar-weighting: Internal Rate of Return (IRR) Time-weighting: Arithmetic Average: rA = (r1+r2)/2 Geometric Average: rG = [(1+r1)(1+r2)]1/2 – 1 rA? rG always Return over Multiple Periods $X $Y $Z r1 r2 t = 0 1 2 $X, $Y, $Z: Cash Flows; r1, r2: one-period HPR Chapter 5: Risk and Return

  10. 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 Example Chapter 5: Risk and Return

  11. Arithmetic ra = (r1 + r2 + r3 + ... rn) / n ra = (.10 + .25 - .20 + .25) / 4 = .10 or 10% Geometric rg = {[(1+r1) (1+r2) .... (1+rn)]} 1/n - 1 rg = {[(1.1) (1.25) (.8) (1.25)]} 1/4 - 1 = (1.5150) 1/4 -1 = .0829 = 8.29% Returns Using Arithmetic and Geometric Averaging Chapter 5: Risk and Return

  12. Net CFs 0 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% Dollar Weighted Average Example Chapter 5: Risk and Return

  13. 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 Chapter 5: Risk and Return

  14. HPR - Expected Return Chapter 5: Risk and Return

  15. Normal distribution Chapter 5: Risk and Return Chapter 5: Risk and Return

  16. HPR - Risk Measure Variance or standard deviation: Chapter 5: Risk and Return

  17. Why do we need the variance? • Two variables with the same mean. • What do we know about their dispersion? Chapter 5: Risk and Return Chapter 5: Risk and Return

  18. Suppose your expectations regarding the stock market are as follows: State of the economy Scenario(s) Probability(p(s)) HPR Boom 1 0.3 44% Normal Growth 2 0.4 14% Recession 3 0.3 -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% Example Chapter 5: Risk and Return

  19. 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 Chapter 5: Risk and Return Chapter 5: Risk and Return Fin 2802, Spring 08 - Tang

  20. Annual Holding Period Returns Geom. Arith. Stan. Series Mean% Mean% Dev.% World Stk 9.41 11.17 18.38 US Lg Stk 10.23 12.25 20.50 US Sm Stk 11.80 18.43 38.11 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 Chapter 5: Risk and Return Chapter 5: Risk and Return Fin 2802, Spring 08 - Tang

  21. Skewed Distribution: Large Negative Returns Possible Median Negative Positive r Chapter 5: Risk and Return Chapter 5: Risk and Return

  22. Skewed Distribution: Large Positive Returns Possible Median Negative r Positive Chapter 5: Risk and Return Chapter 5: Risk and Return

  23. Table 5.5 Risk Measures for Non-Normal Distributions Chapter 5: Risk and Return

  24. Summary • Definition of Returns: HPR, APR and AER. • Risk and expected return • Next: Asset Allocation Chapter 5: Risk and Return

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