You want to create a portfolio equally as risky as the market, and you have $500

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 $ 138,000 .83 Stock B 142,000 1.28 Stock C 1.43 Risk-free asset A.) How much will you invest in Stock C? (Do not round intermediate calculations. 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. Round your answer to 2 decimal places (e.g., 32.16).)

Explanation / Answer

Total Value of investment = $500,000

Investment remains in Stock C and risk free = $500,000 - ($138,000 + $142,000)

= $220,000

Investment remains in stock C and risk free is $220,000.

Beta of portfolio is equal to beta of market that is 1.

Beta of risk free security = 0.

Weight of investment = 27.60%

Weight of investment in stock B = 28.40%

Weight of stock Ca nd risk free = 44%

So first calculate beta of combination of stock C and risk free security.

1 = (27.60% × 0.83) + (28.4% × 1.28) + (44% × Beta)

1 = 0.23 + 0.36 + (Beta × 44%)

Beta of stock C = 0.41 / 44%

= 0.93.

Beta of combination stock C and risk free rate is 0.93 while beta of stock C is 1.43 and beta of risk free security is 0.

So, Suppose X amount invested in Stock C and (1 - X) in risk free security.

0.93 = (1.43 × X) + (1- X) × 0

X = 0.93 / 1.43

= 64.75%

So, 64.75% of $220,000 invested in Stock C and 35.25% in Risk free security.

Investment in Stock C = $220,000 × 64.75%

= $142,448.

Investment in Risk Free security = $220,000 - $142,448

= $77,552

So, investment in stock C is $142,448 and investment in risk free security is $77,552.

Related Questions

Navigate

• Browse (All)
• Browse Y
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.