Mary shows risk aversion because her certainty

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Unformatted text preview: ted value of the gamble. . 80 Certified Financial Controller CFC 40 Determining Portfolio Expected Return m RP = Σ ( Wj )( Rj ) J=1 RP is the expected return for the portfolio, Wj is the weight (investment proportion) for the for the jth asset in the portfolio, in the portfolio, Rj is the expected return of the jth asset, 81 m is the total number of assets in the portfolio. Certified Financial Controller CFC Determining Portfolio Standard Deviation σP = m m Σ Σ Wj Wk σ jk J=1 K=1 Wj is the weight (investment proportion) for the jth asset in the portfolio, portfolio, Wk is the weight (investment 82 proportion) for the kth asset in the portfolio, Certified Financial Controller CFC 41 What is Covariance? σ jk = σ j σ k r jk σj is the standard deviation of the jth asset in the portfolio, σk is the standard deviation of the kth the standard deviation of the asset in the portfolio, rjk is the correlation coefficient between the jth and kth assets in the portfolio. 83 Certified Financial Controller CFC Correlation Coefficient A standardized statistical measure standardized statistical measure of the linear relationship between two variables. Its range is from –1.0 (perfect negative correlation), through 0 (no correlation), to +1.0 (perfect positive correlation). 84 Certified Financial Controller CFC 42 Portfolio Portfolio Risk and Expected Return Example You are creating a portfolio of Stock D and Stock BW (from earlier). You are investing $2,000 in Stock BW and $3,000 in Stock D Remember that D. the expected return and standard deviation of Stock BW is 9% and 13.15% respectively. The 13.15% expected return and standard deviation of Stock D is is 8% and 10.65% respectively. The correlation 10 The correlation coefficient coefficient between BW and D is 0.75. 75 What is the expected return and standard deviation of the portfolio? 85 Certified Financial Controller CFC Determining Portfolio Expected Return WBW = $2,000/$5,000 = 0.4 WD = $3,000/$5,000 = 0.6 RP = (WBW)(RBW) + (WD)(RD) RP = (0.4)(9%) + (0.6)(8%) RP = (3.6%) + (4.8%) = 8.4% 86 Certified Financial Controller CFC 43 Determining Portfolio Standard Deviation Two-asset portfolio: portfolio Col 1 Col 2 Row 1 WBW WBW σBW,BW WBW WD σBW,D Row 2 WD WBW σD,BW BW WD WD σD,D This represents the variance – covariance matrix for the two-asset portfolio. 87 Certified Financial Controller CFC Determining Portfolio Standard Deviation Two-asset portfolio: portfolio Col 1 Col 2 Row 1 (0.4)(0.4)(0.0173) (0.4)(0.6)(0.0105) Row 2 (0.6)(0.4)(0.0105) (0.6)(0.6)(0.0113) This represents substitution into the variance – covariance matrix. 88 Certified Financial Controller CFC 44 Determining Portfolio Standard Deviation Two-asset portfolio: portfolio Col 1 Col 2 Row 1 (0.0028) (0.0025) Row 2 (0.0025) (0.0041) This represents the actual element values in the variance – covariance matrix. 89 Certified Financial Controller CFC Determining Portfolio Standard Deviation σP = 0.0028 + (2)(0.0025) + 0.0041 σP = SQRT(0.0119) σP = 0.1091 or 10.91% A weighted average of the individual standard deviations is INCORRECT. 90 Certified Financial Controller CFC 45 Determining Portfolio Standard Deviation The WRONG way to calculate is a WRONG way to calculate is weighted average like: σP = 0.4 (13.15%) + 0.6(10.65%) σP = 5.2...
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