Question

# You invest \$1000 in a risky asset with an expected rate of return of 0.14 and...

You invest \$1000 in a risky asset with an expected rate of return of 0.14 and a standard deviation of 0.20 and a T-bill with a rate of return of 0.06. The risky asset has a beta of 1.4. If you have a risk-aversion parameter of 2.5, what is the beta of your complete portfolio? A. 0.28 B. 0.80 C. 1.00 D. 1.12 E. 1.32

The correct answer is option D. 1.12

Using the following equation,

Weight in risky asset= Where E(rp) = Expected Return on Risky Portfolio i.e. 14%

Rf = Risk free Rate i.e. 6%

A = Risk Aversion i.e. 2.5

SD = Standard Deviation i.e. 0.2

Weight in risky asset= = 80%

Weight in risk free asset = 100% - 80% = 20%

Portfolio Beta is weighted average beta of assets, beta of risk free asset is 0.

therefore, beta of portfolio = beta of riksy asset x weight of risky asset

Beta of complete portfolio = 1.4 x 80% = 1.12

Hence, option D. 1.12 is correct

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