Calculating the Standard Deviation of the Optimal Risky Portfolio

What is the standard deviation of the optimal risky portfolio?

Answer:

The standard deviation of the optimal risky portfolio is 12.19%.

Explanation:

Given:

Expected return of Origami = 13%

Standard deviation of Origami = 20%

Expected return of Gamiori = 6%

Standard deviation of Gamiori = 10%

Correlation coefficient between returns of Origami and Gamiori = 0.30

Risk-free rate of return = 2%

Formula used:

Standard Deviation of Optimal Risky Portfolio = √[(Weight of Origami)²*(S.D. of Origami)² + (Weight of Gamiori)²*(S.D. of Gamiori)² + 2*(Weight of Origami)*(Weight of Gamiori)*(Correlation Coefficient)*(S.D. of Origami)*(S.D. of Gamiori)]

Here, the standard deviation of the optimal risky portfolio can be calculated by determining the weights of Origami and Gamiori in the portfolio. The total weight of the portfolio is 1, so we can calculate the weights as follows:

W1 = Weight of Origami, W2 = Weight of Gamiori

Expected return of the portfolio (Rp) = W1*R1 + W2*R2

Where,

R1 = Expected return of Origami = 13%

R2 = Expected return of Gamiori = 6%

Rp = 2% + W1*(13% - 2%) + W2*(6% - 2%)

After solving the equations, we find:

W1 = 0.7333

W2 = 0.2667

Substitute these weights into the formula of the standard deviation of the optimal risky portfolio, we get:

S.D. of Optimal Risky Portfolio = √[(0.7333)²*(20)² + (0.2667)²*(10)² + 2*(0.7333)*(0.2667)*(0.30)*(20)*(10)]

The final result is 12.19%, which means the standard deviation of the optimal risky portfolio is 12.19%.