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Part 2-3 評價

Part 2-3 評價. 報酬與風險. Outlines. Statistical calculations of risk and return measures Risk Aversion Systematic and firm-specific risk Efficient diversification The Capital Asset Pricing Model Market Efficiency. Rates of Return: Single Period. HPR = Holding Period Return

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Part 2-3 評價

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  1. Part 2-3 評價 報酬與風險

  2. Outlines • Statistical calculations of risk and return measures • Risk Aversion • Systematic and firm-specific risk • Efficient diversification • The Capital Asset Pricing Model • Market Efficiency

  3. Rates of Return: Single Period • HPR = Holding Period Return • P0 = Beginning price • P1 = Ending price • D1 = Dividend during period one

  4. Rates of Return: Single Period Example Ending Price = 48 Beginning Price = 40 Dividend = 2 HPR = (48 - 40 + 2 )/ (40) = 25%

  5. Return for Holding Period – Zero Coupon Bonds • Zero-coupon bonds are bonds that are sold at a discount from par value. • Given the price, P (T ), of a Treasury bond with $100 par value and maturity of T years

  6. Example - Zero Coupon Bonds Rates of Return

  7. Formula for EARs and APRs • Effective annual rates, EARs • Annual percentage rates, APRs

  8. Table - Annual Percentage Rates (APR) and Effective Annual Rates (EAR)

  9. Continuous Compounding • Continuous compounding, CC • rCC is the annual percentage rate for the continuously compounded case • e is approximately 2.71828

  10. Characteristics of Probability Distributions • Mean • most likely value • Variance or standard deviation • Skewness

  11. Mean Scenario or Subjective Returns • Subjective returns • ps = probability of a state • rs = return if a state occurs

  12. Variance or Dispersion of Returns • Subjective or Scenario • Standard deviation = [variance]1/2 • ps = probability of a state • rs = return if a state occurs

  13. Deviations from Normality • Skewness • Kurtosis

  14. Figure - The Normal Distribution

  15. Figure - Normal and Skewed (mean = 6% SD = 17%)

  16. Figure - Normal and Fat Tails Distributions (mean = .1 SD =.2)

  17. Spreadsheet - Distribution of HPR on the Stock Index Fund

  18. Mean and Variance of Historical Returns • Arithmetic average or rates of return • Variance • Average return is arithmetic average

  19. Geometric Average Returns • Geometric Average Returns • TV = Terminal Value of the Investment • rG = geometric average rate of return

  20. Spreadsheet - Time Series of HPR for the S&P 500

  21. Example - Arithmetic Average and Geometric Average

  22. Measurement of Risk with Non-Normal Distributions • Value at Risk, VaR • Conditional Tail Expectation, CTE • Lower Partial Standard Deviation, LPSD

  23. Figure - Histograms of Rates of Return for 1926-2005

  24. Table - Risk Measures for Non-Normal Distributions

  25. Investor’s View of Risk • Risk Averse • Reject investment portfolios that are fair games or worse • Risk Neutral • Judge risky prospects solely by their expected rates of return • Risk Seeking • Engage in fair games and gamble

  26. Fair Games and Expected Utility • Assume a log utility function • A simple prospect

  27. Fair Games and Expected Utility (cont.)

  28. Diversification and Portfolio Risk • Sources of uncertainty • Come from conditions in the general economy • Market risk, systematic risk, nondiversifiable risk • Firm-specific influences • Unique risk, firm-specific risk, nonsystematic risk, diversifiable risk

  29. Diversification and Portfolio Risk Example

  30. Diversification and Portfolio Risk Example (cont.)

  31. Components of Risk • Market or systematic risk • Risk related to the macro economic factor or market index. • Unsystematic or firm specific risk • Risk not related to the macro factor or market index. • Total risk = Systematic + Unsystematic

  32. Figure - Portfolio Risk as a Function of the Number of Stocks in the Portfolio

  33. Figure - Portfolio Diversification

  34. Two-Security Portfolio: Return • Consider two mutual fund, a bond portfolio, denoted D, and a stock fund, E

  35. Two-Security Portfolio: Risk • The variance of the portfolio, is not a weighted average of the individual asset variances • The variance of the portfolio is a weighted sum of covariances

  36. Table - Computation of Portfolio Variance from the Covariance Matrix

  37. Covariance and Correlation Coefficient • The covariance can be computed from the correlation coefficient • Therefore

  38. Example - Descriptive Statistics for Two Mutual Funds

  39. Portfolio Risk and Return Example • Apply this analysis to the data as presented in the previous slide

  40. Table - Expected Return and Standard Deviation with Various Correlation Coefficients

  41. Figure - Portfolio Opportunity Set

  42. Figure - The Minimum-Variance Frontier of Risky Assets

  43. Figure - Capital Allocation Lines with Various Portfolios from the Efficient Set

  44. Capital Allocation and the Separation Property • A portfolio manager will offer the same risky portfolio, P, to all clients regardless of their degree of risk aversion • Separation property • Determination of the optimal risky portfolio • Allocation of the complete portfolio

  45. Capital Asset Pricing Model (CAPM) • It is the equilibrium model that underlies all modern financial theory. • Derived using principles of diversification with simplified assumptions. • Markowitz, Sharpe, Lintner and Mossin are researchers credited with its development.

  46. Figure - The Efficient Frontier and the Capital Market Line

  47. Slope and Market Risk Premium • Market risk premium • Market price of risk, Slope of the CML

  48. The Security Market Line • Expected return – beta relationship • The security’s risk premium is directly proportional to both the beta and the risk premium of the market portfolio • All securities must lie on the SML in market equilibrium

  49. Figure - The Security Market Line

  50. Sample Calculations for SML • Suppose that the market return is expected to be 14%, and the T-bill rate is 6% • Stock A has a beta of 1.2 • If one believed the stock would provide an expected return of 17%

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