You invest $1,000 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 6%.
-The slope of the capital allocation line formed with the risky asset and the risk-free asset is _________.
A) 1.40
B) 0.80
C) 0.50
D) 0.40

Question

Quizplus · Accepted Answer

The slope of the capital allocation line (CAL) is given by the ratio of the excess return of the risky asset to the standard deviation of the complete portfolio.

Slope of CAL = (E(R) - Rf) / σp

where E(R) is the expected return of the risky asset, Rf is the risk-free rate, and σp is the standard deviation of the complete portfolio.

Plugging in the given values, we get:

Slope of CAL = (0.16 - 0.06) / (sqrt(1)*0.20) = 0.50

Therefore, the slope of the CAL is 0.50.

To make the best choice for the investment, it depends on the investor's risk preference. If the investor is risk-averse, they might choose to invest more in the risk-free asset, whereas if the investor is risk-seeking, they might allocate more to the risky asset. One possible optimal portfolio can be found by determining the point of tangency between the CAL and the efficient frontier. This portfolio offers the highest expected return for the given level of risk.

You Invest $1,000 in a Complete Portfolio