Question Realized rates of return Stocks A and B have the ...



Question Realized rates of return Stocks A and B have the following historical returns: Year Stock A''s Returns, rA Stock B''s Returns, rB

2001 (18.00%) (14.50%)

2002 33.00 21.80

2003 15.00 30.50

2004 (0.50) (7.60)

2005 27.00 26.30

a. Calculate the average rate of return for each stock during the period 2001 through 2005. b. Assume that someone held a portfolio consisting of 50 percent of Stock A and 50 percent of Stock B. What would the realized rate of return on the portfolio have been in 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?

a) The average rate of return for Stock A during the period 2001 through 2005 is given by

Average Return = ( -18 + 33.0 + 15.00 – 0.50 +27.00)/5 = 11.30%

The average rate of return for Stock b during the period 2001 through 2005 is given by

Average Return = ( -14.50 + 21.80 + 30.50 – 7.60 +26.30)/5 = 11.30%

b) Portfolio Return for 2001:

Portfolio Return = 0.5*(-18) + 0.5*(-14.50) = -16.25%

Portfolio Return for 2002:

Portfolio Return = 0.5*33+ 0.5*21.80= 27.40%

Portfolio Return for 2003:

Portfolio Return = 0.5*15 + 0.5*30.5 = 22.75%

Portfolio Return for 2004:

Portfolio Return = 0.5*(-0.5) + 0.5*(-7.6) = -4.05%

Portfolio Return for 2005:

Portfolio Return = 0.5*27+ 0.5*26.3 = 26.25%

The average return on the portfolio have been during this period is given by

Average Return = ( -16.25 + 27.40 + 22.75 – 4.05 +26.25)/5 = 11.30%

c) The standard deviation of returns for stock A is

[pic]= 20.79

The standard deviation of returns for stock B is

[pic]= 20.78

The standard deviation of returns for the portfolio is

[pic]= 20.13

d) The coefficient of variation for stock A is

CV = Standard Deviation / Average = 11.30/20.79 = 1.84

The coefficient of variation for stock B is

CV = Standard Deviation / Average = 11.30/20.78 = 1.84

The coefficient of variation for the portfolio is

CV = Standard Deviation / Average = 11.30/20.13 = 1.78

e) A risk-averse investor would choose the portfolio over either Stock A or Stock B alone, since the portfolio offers the same expected return but with less risk.

Please see the Excel File for calculation

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