1.a) You want to create a portfolio equally as risky as the market, and you have
ID: 2634218 • Letter: 1
Question
1.a) You want to create a portfolio equally as risky as the market, and you have $500,000 to invest. Information about the possible investments is given below:
How much must you invest in Stock C?
1.b) Your portfolio has a beta of 0.9. The portfolio consists of 15 percent U.S. Treasury bills, 30 percent stock A, and 55 percent stock B. Stock A has a risk level equivalent to that of the overall market. What is the beta of stock B?
Asset Investment Beta Stock A $133,310 0.8 Stock B $141,185 1.36 Stock C -- 1.48 Risk-free asset -- --Explanation / Answer
We need a beta of 1 to create a portfolio equally as risky as the market
Weight
(Investment/50,000)
Beta
Weighted beta
Stock A
133,310
0.26662
0.8
0.213296
Stock B
141,185
0.28237
1.36
0.384023
Stock C
0
1.48
0
Risk free asset
0
0
0
Total
0
0.26662
0.597319
Investment in stock C should be such that sum of weighted beta =1
Let amount invested in stock c = x
Weight of investment in c = x/500,000
Weighted beta of c =x*1.48/500,000
Total weighted beta =0.213296+0.384023 +x*1.48/500,000 =1
Solving for x, x(Investment in stock c) = 136041
Investment in risk free asset =500,000-133,310-141,185-136041 = 89464
Weight
(Investment/500,000)
Beta
Weighted beta
Stock A
133,310
0.26662
0.8
0.213296
Stock B
141,185
0.28237
1.36
0.384023
Stock C
136,041
0.272081622
1.48
0.402681
Risk free asset
89464
0.178928
0
0
Total (Sum)
500,000
0.999999622
1
1.b
Weight
Beta
weighted beta
T-Bills(Risk free asset)
15%
0
0
Stock A
30%
1
0.3
Stock B
55%
x
Total
100%
0.9
The portfolio has a beta of 0.9.
Sum of weighted beta =0.9
So weighted beta of stock B =0.9-0.3-0 =0.6
Beta of stock B* weight =0.6
Beta of stock B*0.55 =0.6
Beta of stock B =1.091
Weight
(Investment/50,000)
Beta
Weighted beta
Stock A
133,310
0.26662
0.8
0.213296
Stock B
141,185
0.28237
1.36
0.384023
Stock C
0
1.48
0
Risk free asset
0
0
0
Total
0
0.26662
0.597319
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