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You have a $1,000 portfolio which is invested in stocks A and B plus a risk-free asset. $400 is invested in stock A. Stock A has a beta of 1.30 and stock B has a beta of 0.70. How many dollars need to be invested in stock B if you want a portfolio beta of 0.90

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Parrain

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

abiolataiwo2015

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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