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Rf=2%, Rm= 10% An equal weighted portfolio of stock X and Rf yields a return of...

Rf=2%, Rm= 10%

An equal weighted portfolio of stock X and Rf yields a return of 10%

A portfolio of stock Y and Rf with a 75% investment in stock Y yields a return of 6.5%

What is the market beta of a portfolio if we invest 40%in X, 20% in Y, 20% in Rf and 20% in the market?

Solutions

Expert Solution

Beta of Risk-free Asset = 0.00

Portfolio 1:

Weight of Stock X = 0.50
Weight of Risk-free Asset = 0.50

Portfolio Return = Risk-free Rate + Portfolio Beta * (Market Return - Risk-free Rate)
10.00% = 2.00% + Portfolio Beta * (10.00% - 2.00%)
8.00% = Portfolio Beta * 8.00%
Portfolio Beta = 1.00

Portfolio Beta = Weight of Stock X * Beta of Stock X + Weight of Risk-free Asset * Beta of Risk-free Asset
1.00 = 0.50 * Beta of Stock X + 0.50 * 0.00
1.00 = 0.50 * Beta of Stock X
Beta of Stock X = 2.00

Portfolio 2:

Weight of Stock Y = 0.75
Weight of Risk-free Asset = 0.25

Portfolio Return = Risk-free Rate + Portfolio Beta * (Market Return - Risk-free Rate)
6.50% = 2.00% + Portfolio Beta * (10.00% - 2.00%)
4.50% = Portfolio Beta * 8.00%
Portfolio Beta = 0.5625

Portfolio Beta = Weight of Stock Y * Beta of Stock Y + Weight of Risk-free Asset * Beta of Risk-free Asset
0.5625 = 0.75 * Beta of Stock Y + 0.25 * 0.00
0.5625 = 0.75 * Beta of Stock Y
Beta of Stock Y = 0.75

Portfolio 3:

Weight of Stock X = 0.40
Weight of Stock Y = 0.20
Weight of Risk-free Asset = 0.20
Weight of Market Portfolio = 0.20
Beta of Market Portfolio = 1.00

Portfolio Beta = Weight of Stock X * Beta of Stock X + Weight of Stock Y * Beta of Stock Y + Weight of Risk-free Asset * Beta of Risk-free Asset + Weight of Market Portfolio * Beta of Market Portfolio
Portfolio Beta = 0.40 * 2.00 + 0.20 * 0.75 + 0.20 * 0.00 + 0.20 * 1.00
Portfolio Beta = 1.15

jeff jeffy answered 1 year ago
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