Stock A and Stock B have the following historical returns: Year Stock A\'s Retur

Question

Stock A and Stock B have the following historical returns:
Year               Stock A's Returns, rA             Stock B's Returns, rB

2004                   (18.00%)                              (14.50%)          

2005                   33.00                                    21.80           

2006                   15.00                                    30.50        

2007                   (0.50)                                   (7.60)        

2008                   27.00                                   26.30           

a) Calaulate the average rate of return for each stock during the period 2004 through 2008.

b) Assume that someone held a portfolio consisting of 50% of Stock A and 50% of Stock B. What would the realized rate of return on the portfolio have been each year ? What would the average return on the portfolio have been during this period ?

c) Calculate the standard deviation of returns for each stock and for the portfolio.

d) Calculate the coefficient of variation for each stock and for the portfolio.

e) Assuming you are a risk-averse investor, would you prefer to hold Stock A, Stock B, or the portfolio ? why ?

Explanation / Answer

a.

Average rate of return of Stock A = [ (18) + 33 + 15 + (0.50) + 27 ]/5 = 11.3%

Average rate of return of Stock B = [(14.50) + 21.80 + 30.50 + (7.60) + 26.30 ]/5 = 11.3%

b.Average rate of return of portfolio =11.3%

c. Standard Deviation

Standard Deviation of stock A = 0.186

Standard Deviation of stock B = 0.186

Standard Deviation of Portfolio = 50% of s.d. of stock A + 50% of s.d. of stock B

Standard Deviation of Portfolio = .50 * 0.186 + .50 * 0.186 = 0.093 + 0.093 = .186 or 18.6 %

d.coefficient of variation of stock = 15.1%

coefficient of variation Of portfolio = 7.6%

Correlation of AB = Covariance AB/s.d. of A + s.d. of B = 4.38

e.I would prefer to hold portfolio with the same return as I would be getting in holding individual stock because my risk will be reduced as risk of portfolio could be less than the risk of individual securities.

year Stock A's Returns, rA                     Stock B's Returns, rB                    50% 0f stock A return 50% of stock B return Portfolio return in each year 2004 -18 -14.5 -9 -7.25 -16.25 2005 33 21.8 16.5 10.9 27.4 2006 15 30.5 7.5 15.25 22.75 2007 -0.5 -7.6 -0.25 -3.8 -4.05 2008 27 26.3 13.5 13.15 26.65 56.5 56.5 56.5 11.3 11.3 11.3

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