You want to create a portfolio as risky as the market with $500,000 to invest. Fill...

You want to create a portfolio as risky as the market with $500,000 to invest. Fill in the following table:

Asset Investment BETA

stock A $85,000 0.8

stock B $165,000 1.15

stock C ---------- 1.4

Riskfree asset _______ ------

Please fill in the blanks and show all work

Solutions

Expert Solution

Weight of Stock A = Investment in Stock A / Total Investment
Weight of Stock A = $85,000 / $500,000
Weight of Stock A = 0.17

Weight of Stock B = Investment in Stock B / Total Investment
Weight of Stock B = $165,000 / $500,000
Weight of Stock B = 0.33

Let Weight of Stock C be x

Weight of Stock A + Weight of Stock B + Weight of Stock C + Weight of Risk-free Asset = 1
0.17 + 0.33 + x + Weight of Risk-free Asset = 1
Weight of Risk-free Asset = 0.50 - x

Beta of Risk-free Asset = 0.00

Portfolio Beta = Weight of Stock A * Beta of Stock A + Weight of Stock B * Beta of Stock B + Weight of Stock C * Beta of Stock C + Weight of Risk-free Asset * Beta of Risk-free Asset
1.00 = 0.17 * 0.80 + 0.33 * 1.15 + x * 1.40 + (0.50 - x) * 0.00
1.00 = 0.1360 + 0.3795 + x * 1.40
x * 1.40 = 0.4845
x = 0.34607

Weight of Stock C = 0.34607

Weight of Risk-free Asset = 0.50 - x
Weight of Risk-free Asset = 0.50 - 0.34607
Weight of Risk-free Asset = 0.15393

Investment in Stock C = Weight of Stock C * Total Investment
Investment in Stock C = 0.34607 * $500,000
Investment in Stock C = $173,035

Investment in Risk-free Asset = Weight of Risk-free Asset * Total Investment
Investment in Risk-free Asset = 0.15393 * $500,000
Investment in Risk-free Asset = $76,965

jeff jeffy answered 1 year ago

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