Question

Suppose you have a portfolio that has $100 in stock A with a beta of 0.9, $400 in stock B with a beta of 1.2, and $300 in the risk-free asset. You have another $200 to invest. You wish to achieve a beta for your whole portfolio to be the same as the market beta. What is the beta of the added security? Give an example of a firm that may have such a beta.

Answer 1

Solution :-

Market Beta = 1

So we want the Beta of Our Portfolio = 1

Now Total Investment in Portfolio = 100 + 400 + 300 + 200 = 1,000

Now Weight of Stock A = 100 / 1000 = 0.10

Weight of Stock B = 400 / 1000 = 0.40

Weight of Risk Free Asset = 300 / 1000 = 0.30

Weight of Another Stock = 200 / 1000 = 0.20

Now

Beta of Stock A = 0.90

Beta of Stock B = 1.20

Beta of Risk Free Asset = 0 ( Always )

Beta of Another Asset = ?? ( Assume X )

Now 1 = ( 0.10 * 0.90 ) + ( 0.40 * 1.20 ) + ( 0.30 * 0 ) + ( 0.20 * X )

1 = 0.09 + 0.48 + 0 + 0.20 X

0.43 = 0.20 X

X = 0.43 / 0.20 = 2.15

Therefore Beta of Added Security = 2.15

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