Question

2)

You invest $1,500 in a complete portfolio. The complete portfolio is composed of a risky asset with an expected rate of return of 16% and a standard deviation of 20% and a Treasury bill with a rate of return of 7%. __________ of your complete portfolio should be invested in the risky portfolio if you want your complete portfolio to have a standard deviation of 10%.

Multiple Choice

• 9%

• 13%

• 50%

• 33%

Answer 1

- Standard Deviation of Portfolio = 10%

Standard Deviation of risky asset = 20%

As, Treasury Bill have Standard Deviation of 0.

Thus, Formula for Standard Deviation of Portfolio:-

(Standard Deviation of Portfolio)^2 = (Weight of Risk Asset)^2*(Standard Deviation of Risky Asset)^2

(10)^2 = (Weight of Risk Asset)^2*(20)^2

100 = (Weight of Risk Asset)^2*400

(Weight of Risk Asset)^2 = 0.25

Taking 2-root on both sides,

Weight of Risk Asset = 0.50

So, Weight of Risk Asset is 50%

Thus, 50% of your complete portfolio should be invested in the risky portfolio if you want your complete portfolio to have a standard deviation of 10%

Option 3

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