1.Use the following table of states of the economy and stock returns to calculat
ID: 2776478 • Letter: 1
Question
1.Use the following table of states of the economy and stock returns to calculate the percentage standard deviation of a portfolio of a portfolio of 22 percent Roten and the rest in Bradley.
Security
if State
Returns
Occurs
Prob of State of Economy
Roten
Bradley
Bust
0.1
-9%
25%
Boom
?
37
5
2.Copy of
You have a $1,000 portfolio which is invested in stocks A and B plus a risk-free asset. $500 is invested in stock A. Stock A has a beta of 1.3 and stock B has a beta of 0.7. How much needs to be invested in stock B if you want a portfolio beta of 0.9?
Security
if State
Returns
Occurs
Prob of State of Economy
Roten
Bradley
Bust
0.1
-9%
25%
Boom
?
37
5
Explanation / Answer
1.Use the following table of states of the economy and stock returns to calculate the percentage standard deviation of a portfolio of a portfolio of 22 percent Roten and the rest in Bradley.
Security
if State
Returns
Occurs
Prob of State of Economy
Roten
Bradley
Bust
0.1
-9%
25%
Boom
?
37
5
Prob of State of Economy of Boom = (1-0.10) = 0.90
Expected Return of Roten = Prob of State of Economy of Bust * Return + Prob of State of Economy of Boom * Return
Expected Return of Roten = 0.10*-9% + 0.90*37%
Expected Return of Roten = 32.40%
Expected Return of Bradley = Prob of State of Economy of Bust * Return + Prob of State of Economy of Boom * Return
Expected Return of Bradley = 0.10*25% + 0.90*5%
Expected Return of Bradley = 7%
Variance of Roten = (-9-32.4)^2*0.1 + (37-32.4)^2*0.90
Variance of Roten = 190.44
Variance of Bradley = (25-7)^2*0.1 + (5-7)^2*0.90
Variance of Bradley = 36
CoVariance = 190.44^(1/2)*36^(1/2) = 82.80
Standard deviation of a portfolio =( Weight^2*Variance of Roten + Weight^2*Variance of Bradley + 2*weight of Roten*Weight of Bradley *Covariance)^(1/2)
Standard deviation of a portfolio = (22%^2 * 190.44 + 78%^2*36 + 2*22%*78%*82.80)^(1/2)
Standard deviation of a portfolio = 7.72%
Security
if State
Returns
Occurs
Prob of State of Economy
Roten
Bradley
Bust
0.1
-9%
25%
Boom
?
37
5
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