Question

You want to create a portfolio equally as risky as the market, and you have $500,000 to invest. Information about the possible investments is given below:

  

Asset	Investment		Beta
Stock A		$ 85,000	.80
Stock B		$165,000	1.15
Stock C			1.40
Risk-free asset

  

a.	How much will you invest in Stock C? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
b.	How much will you invest in the risk-free asset? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.

Answer 1

Portfolio Beta = Amount Invested in Stock A/Total Investment*Beta of Stock A + Amount Invested in Stock B/Total Investment*Beta of Stock B + Amount Invested in Stock C/Total Investment*Beta of Stock C + Amount Invested in Risk Free Asset/Total Investment*Beta of Risk Free Asset (beta of risk Free Asset is 0.)

we have been provided with the value of investment in stock A and stock B, the rest of the amount would get invested in stock C and risk free asset. The balance amount is $250,000 ($500,000 - $85,000 - $165,000).

Let amount invested in C be X. Thus amount invested in risk free asset = ($250000-X)

Now using the above we get,

1 = 85000/500000×0.8 + 165000/500000× 1.15 + X/500000×1.4 + (250000-X)/500000×0

Solving it,

1 = 0.136 + 0.3795 + X/500000 × 1.4 + 0

A) Hence X = amount invested in stock C = $173035.71

B) amount invested in risk free asset = $250000-$173035.71 = $76964.29

.

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