You own a stock portfolio invested 25 percent in Stock Q, 20
percent in Stock R,...
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Finance
You own a stock portfolio invested 25 percent in Stock Q, 20percent in Stock R, 15 percent in Stock S, and 40 percent in StockT. The betas for these four stocks are .9, 1.4, 1.1 and 1.8,respectively. What is the portfolio beta?
You want to create a portfolio equally as risky as the market(i.e, a portfolio with beta equal to 1), and you have $1,000,000 toinvest. Given this information, fill in the rest of the followingtable:
Asset
Investment
Beta
Stock A
$200,000
.70
Stock B
$250,000
1.10
Stock C
1.60
Risk-free asset
Answer & Explanation
Solved by verified expert
4.0 Ratings (441 Votes)
1)
Portfolio
beta is the sum of weighted beta of portfolio.
Stock
Weight
Beta
a
b
a*b
Q
25%
0.9
0.2
R
20%
1.4
0.3
S
15%
1.1
0.2
T
40%
1.8
0.7
Portfolio beta
1.4
2)
Investment
Beta
Stock C
$
3,65,600
Risk-free asset
$
1,84,375
0
Working:
Risk free
asset has beta of 0.
Weight of
:
Stock A
$ 2,00,000
/
$ 10,00,000
=
0.20
Stock B
$ 2,50,000
/
$ 10,00,000
=
0.25
Suppose
weight of Risk free asset is "w".Portfolio beta is 1.So, weight of
Stock C is (1-0.20-0.25-w) or (0.55-w).
Now, as per
question,
Portfolio
beta
=
Sum of
weighted beta
1
=
(0.20*0.70)
+
(0.25*1.10)
+
((0.55-w)*1.60)
+
(w*0)
1
=
0.14
+
0.275
+
((0.55-w)*1.60)
+
0
1
=
0.415
+
((0.55-w)*1.60)
0.585
=
(0.55-w)*1.60
0.365625
=
0.55-w
w
=
0.1844
So, weight
of :
Risk free
asset
0.1844
Stock C
0.55-0.1844
=
0.3656
Stock A
0.2000
Stock B
0.2500
Total
1.0000
Investment
in :
Stock C
=
$ 10,00,000
*
0.3656
=
$ 3,65,600
Risk free
asset
=
$ 10,00,000
*
0.1844
=
$ 1,84,375
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