You would like to form a portfolio
What would be the weight that you invest in the optimal risky portfolio?
The weight that you should invest in the optimal risky portfolio can be determined using the formula for the optimal risky portfolio weight. It represents the proportion of your total portfolio that should be allocated to the risky assets. By considering the expected return of the optimal risky portfolio, the risk-free rate, your risk aversion degree, and the variance of the optimal risky portfolio, you can calculate the weight (y) that you should allocate to the optimal risky portfolio. In this case, the weight comes out to be approximately 5.81%.
Calculation of Optimal Risky Portfolio Weight
Where:
y = Weight for the optimal risky portfolio
E(Rp) = Expected return of the optimal risky portfolio
Rf = Risk-free rate
A = Risk aversion degree
Var(Rp) = Variance of the optimal risky portfolio
To calculate the weight that should be invested in the optimal risky portfolio, we will use the provided information:
- Expected return of the optimal risky portfolio (E(Rp)) = 12.19%
- Risk-free rate (Rf) = 5%
- Risk aversion degree (A) = 9
- Variance of the optimal risky portfolio (Var(Rp)) = (12.78%)^2 = 163.0884
Now, substitute these values into the formula:
y = [(12.19 - 5) / (9 * 163.0884)]
y ≈ 0.0581 or 5.81% Therefore, it is recommended to invest approximately 5.81% of your total portfolio in the optimal risky portfolio to achieve the desired level of risk and return.