In: Finance
Using sample average returns and standard deviations of the volatility strategy discussed in class, calculate the optimal proportion that a mean-variance utility investor would invest in the volatility strategy in the following scenarios:
Risk-free rate is 0.75% and gamma = 3.
Enter your answer in percentage points with two decimal places.
What is a Mean-Variance Analysis?
Sample Mean-Variance Analysis
It ts possible to calculate which investments have the greatest variance and expected return. Assume the following investments are in an investor's portfolio:
Investment A: Amount = $100,000 and expected return of 5%
Investment B: Amount = $300,000 and expected return of 10%
In a total portfolio value of $400,000, the weight of each asset is:
Investment A weight = $100,000 / $400,000 = 25%
Investment B weight = $300,000 / $400,000 = 75%
Therefore, the total expected return of the portfolio is the weight of the asset in the portfolio multiplied by the expected return:
Portfolio expected return = (25% x 5%) + (75% x 10%) = 8.75%Portfolio variance is more complicated to calculate, because it is not a simple weighted average of the investments' variances. The correlation between the two investments is 0.65. The standard deviation, or square root of variance, for Investment A is 7 percent, and the standard deviation for Investment B is 14 percent.
In this example, the portfolio variance is:
Portfolio variance = (25% ^ 2 x 7% ^ 2) + (75% ^ 2 x 14% ^ 2) + (2 x 25% x 75% x 7% x 14% x 0.65) = 0.0137
The portfolio standard deviation is the square root of the answer: 11.71% i.e. 12%
Coefficient of Risk version
we use the following utility formula U = E(r) – 0,5 x A x σ2
U=Represents the utility or score to give this investment in a given portfolio by comparing it to a risk-free investment.
E(r)= expected Return
σ2=the square of volatility
a) U = E(r) – 0.5 x A x σ2
= 0.08 - 0.5 X 3 X 0.122 = 5.84%
Now we can not say that Risk free Rate and risk aversion coefficient on the optimal allocation to the volatility strategy.