Question

You invest $100 in a risky asset with an expected rate of return of 0.11 and a standard deviation of 0.21 and a t-bill with a rate of return of 0.045. What percentages of your money must be invested in the risky asset and the risk-free asset, respectively, to form a portfolio with an expected return of 0.13?

1) -30.77% and 130.77%
2) 57.75% and 42.25%
3) 130.77% and -30.77%
4) Cannot be determined.
5) 67.67% and 33.33%

Answer 1

To form a portfolio with an expected return of 0.13, you would need to invest approximately 130.77% of your money in the risky asset and -30.77% in the risk-free asset.

Step-by-step explanation:

To form a portfolio with an expected return of 0.13, we can use the formula for the expected return of a portfolio: Expected Return = Weight of risky asset * Expected return of risky asset + Weight of risk-free asset * Expected return of risk-free asset. Let's assume the weight of the risky asset is 'x' and the weight of the risk-free asset is '1 - x'.

Given that the expected return of the risky asset is 0.11 and the expected return of the risk-free asset is 0.045, we can set up the equation as follows: 0.13 = 0.11 * x + 0.045 * (1 - x).

Simplifying the equation, we get 0.13 = 0.11x + 0.045 - 0.045x. Combining like terms, we have 0.13 = 0.065x + 0.045.

Subtracting 0.045 from both sides, we get 0.085 = 0.065x. Dividing both sides by 0.065, we have x = 0.085 / 0.065 = 1.3077.

Therefore, the weight of the risky asset is approximately 1.3077 and the weight of the risk-free asset is approximately 1 - 1.3077 = -0.3077. Since the weights should be expressed as percentages, we can multiply these values by 100 to get the final answer: 130.77% for the risky asset and -30.77% for the risk-free asset.