Answer: $543
Explanation:
The portfolio beta is a weighted average of the individual stock betas.
Portfolio beta = (Weight of stock A * Stock A beta) + (Weight of stock B * Stock B beta)
0.9 = (400/1,000 * 1.3) + (w * 0.70)
0.9 = 0.52 + 0.7w
0.7w = 0.9 - 0.52
0.7w = 0.38
w = 0.38/0.7
w = 0.543
The portfolio value is $1,000 so the dollars would be:
= 0.543 * 1,000
= $543
The amount of dollars that is needed to be invested in stock B if you want a portfolio beta of 0.90 is $543.
Let x represent the amount of dollars
Hence:
Beta Portfolio= .90 = ($400÷$1,000 ×1.3) + ($x ÷$1,000×.7) + [(($1,000-$400)–x) ÷$1,000 ×0]
Beta Portfolio= .90 = ($400÷$1,000 ×1.3) + ($x ÷$1,000×.7) + (($600–x) ÷$1,000 ×0)
.90 = .52 + .7x + 0
.7x=.90-.52
Divide both side by .7x
.7x = .38
x=.38/.7
x = $542.86
x= $543 (Approximately)
Inconclusion the amount of dollars that is needed to be invested in stock B if you want a portfolio beta of 0.90 is $543.
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