REALIZED RATES OF RETURN Stocks A and B have the following historical a. Calcula
ID: 2778882 • Letter: R
Question
REALIZED RATES OF RETURN Stocks A and B have the following historical a. Calculate the average rate of return for each stock during the period 2009 through 2013. b. Assume that someone held a portfolio consisting of 50?0 of Stock A and 50% of Stock B. What would the realized rate of return on the portfolio have been each year? 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 arc a risk-averse investor, would you prefer to hold Stock A, Stock B, or the portfolio? Why?Explanation / Answer
Year
Ra
Rb
2009
-18%
-14.50%
2010
33%
21.80%
2011
15%
30.50%
2012
-0.50%
-7.60%
2013
27%
26.30%
Total
56.50%
56.50%
Average return (Stock A) = 56.50%/ 5
= 11.30%
Average return (Stock B) = 56.50%/ 5
= 11.30%
Realized return
Year
Ra
Rb
Realized return
2009
-18%
-14.50%
(18%-14.50%)/2=
-16.25%
2010
33%
21.80%
(33%21.80%)/2=
27.40%
2011
15%
30.50%
(15%30.50%)/2=
22.75%
2012
-0.50%
-7.60%
(0.50%-7.60%)/2=
-4.05%
2013
27%
26.30%
(27%26.30%)/2=
26.65%
Total
56.50%
Average realized return = total realized return/ no. of return periods
= 56.50%/5
=11.30%
Stock A
Variance = sum of (Ra-ARa)^2 / (n-1)
Year
Ra
D=Ra-ARa
D^2
2009
-18%
-29.300%
0.085849
2010
33%
21.700%
0.047089
2011
15%
3.700%
0.001369
2012
-0.50%
-11.800%
0.013924
2013
27%
15.700%
0.024649
Total
0.17288
Variance = 0.17288/(5-1)
=
Standard deviation = variance ^0.5
=
=20.79%
Stock B
Year
Ra
D=Rb-ARb
D^2
2009
-14.50%
-25.800%
0.066564
2010
21.80%
10.500%
0.011025
2011
30.50%
19.200%
0.036864
2012
-7.60%
-18.900%
0.035721
2013
26.30%
15.000%
0.0225
Total
0.172674
Variance = 0.172674/(5-1)
=
Standard deviation = variance ^0.5
=
=20.78%
Year
Ra
D=Rp-Arp
D^2
2009
-16.25%
-27.550%
0.07590025
2010
27.40%
16.100%
0.025921
2011
22.75%
11.450%
0.01311025
2012
-4.05%
-15.350%
0.02356225
2013
26.65%
15.350%
0.02356225
Total
0.162056
Variance = 0.162056/(5-1)
=
Standard deviation = variance ^0.5
=
=20.13%
Covariance = standard deviation/ average return
Covariance (stock A) = 20.79%/11.30% =1.8398
Covariance (stock B) = 20.78%/11.30% =1.8389
Covariance (stock A) = 20.13%/11.30% =1.7814
Year
Ra
Rb
2009
-18%
-14.50%
2010
33%
21.80%
2011
15%
30.50%
2012
-0.50%
-7.60%
2013
27%
26.30%
Total
56.50%
56.50%
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