ST-1a.) The average rate of return for each stock is calculated by simply averaging thereturns over the 5-year period. The average return for Stock A isAvg A =(-18% + 44%22% + 22% + 34%)/5= 12%The realized rate of return on a portfolio made up of Stock A and Stock B wouldbe calculated by finding the average rate of return in each year asA,t(% of Stock A) + B,t (% of Stock B)Then average these annual returns:Year20092010201120122013Portfolio ABs Return, AB-21%34-131545Avg AB =12b.) The standard deviation od returns is estimated as follows:T- 1For Stock A, the estimated is about 30%(-0.180.12) 2 + (0.440.12)2 + (-0.220.12)2 + (0.220.12)2 +(0.340.12)2A=A= 0.302655130%The standard deviations of returns for Stock B and for the portfolio are similarlydetermined, and they are as follows:Standard deviationStock A30%Stock B30%Portfolio AB29%c.) Because the risk reduction from diversification is small (AB falls only from 30% to29%), the most likely value of the correlation coefficient is 0.80. If the correlationcoefficient were -0.8, then the risk reduction would be much larger. In fact, thecorrelation between Stocks A and B is 0.8.d.) If more randomly selected stocks were added to a portfolio, p would decline tosomewhere in the vicinity of 20%. The value of p would remain constant only if thecorrelation coefficient were + 1.0, which is most unlikely. The value of p would decline tozero only if p = -1.0 for some pair of stocks or some pair of portfolios.ST-2a.) b = (0.60) (0.70) + (0.25) (0.90) + (0.1) (1.30) + (0.05) (1.50)= 0.42 + 0.225 + 0.13 + 0.075 = 0.85b.) rRF = 6%; RPM = 5%; b = 0.85rp = 6% +; (5%)(0.85)= 10.25%c.) bN = (0.5)(0.70) + (0.25)(0.90) + (0.1)(1.30) + (0.15)(1.50)= 0.35 + 0.225 + 0.13 + 0.225= 0.93r = 6% + (5%)(0.93)= 10.65%
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