Question

	Risky Asset 1	Risky Asset 2
Expected Return	0.11	.15
Standard Deviation	0.28	.88

The coefficient of correlation ρ between these two assets is equal to .009, and the risk free rate is 3.8%.

2A. If you wished to construct the optimal risky portfolio using these two assets, what percentage this portfolio would consist of Asset 1?

2B. What is the expected return of the portfolio from 2A?

2C. What is the standard deviation of the portfolio from 2A?

2D. If Rachel has a coefficient of risk aversion of 4.9, what percentage of her money should she invest in the riskless asset if the only risky assets she can invest in are the ones described above?

Answer 1

Markowitz Efficient Portfolio Formula

Where

P(A) is proportion of A security in portfolio

P(A) is proportion of B security in portfolio

is the Standard Deviation of Security A

is the Standard Deviation of Security B

is the coefficient of correlation of Security A and Security B

Portfolio Standard Deviation Formula

is proportion of A security in portfolio

is proportion of B security in portfolio

is the Standard Deviation of Security A

is the Standard Deviation of Security B

is the coefficient of correlation of Security A and Security B

Utility Score = Expected Return - (0.5 x Variance of Security * Risk Aversion Co-efficient)

Solution

The Utility score of Rachael is negative which means she is not getting enough returns that she is expecting for the risk she is taking from risky assets. Therefore, Rachel can invest 100% of her funds in riskless assets.

2A) 91.02%

2B) 0.11

2C) 0.27

2D) 100%