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Homework answers / question archive / A $5,000 portfolio is invested in three stocks and one risk-free asset
A $5,000 portfolio is invested in three stocks and one risk-free asset. Nine hundred dollars is invested in stock A which has a beta of 0.75. One thousand dollars is invested in Stock B which has a beta of 1.25. The rest of the portfolio is divided evenly between stock C and the risk-free asset. What is the beta of stock C if the portfolio is equally as risky as the market?
The beta of stock C is computed as shown below:
Beta of portfolio = Beta of stock A x weight of stock A + Beta of stock B x weight of stock B + Beta of stock C x weight of stock C + Beta of risk free asset x weight of risk free asset
Weight of Stock C is computed as follows:
= (Total amount of investment - Investment in Stock A - Investment in Stock B) / 2
= ($ 5,000 - $ 900 - $ 1,000) / 2
= $ 3,100 / 2
= $ 1,550
Weight of risk free asset is computed as follows:
= (Total amount of investment - Investment in Stock A - Investment in Stock B) / 2
= ($ 5,000 - $ 900 - $ 1,000) / 2
= $ 3,100 / 2
= $ 1,550
Beta of portfolio will be 1, since the beta of portfolio is equally as risky as the market.
Beta of risk free asset is always zero.
So, the beta of stock C will be as follows:
1 = 0.75 x $ 900 / $ 5,000 + 1.25 x $ 1,000 / $ 5,000 + Beta of stock C x $ 1,550 / $ 5,000 + 0 x $ 1,550 / $ 5,000
1 = 0.135 + 0.25 + Beta of Stock C x 0.31 + 0
0.615 = Beta of Stock C x 0.31
Beta of Stock C = 1.98 Approximately