Question

We have only two risky assets in the market with the following risk and return:

	Expected Return	Standard Deviation
Stocks	20%	25%
Bonds	15%	15%

The correlation between the two risky assets is: 0.5 and the risk free in the market is 8%.

1. Find the weight of Stocks and Bonds in the optimal portfolio. Calculate the return and standard deviation of the optimal portfolio.

2. Calculate the standard deviation of portfolio (P) with an expected return of 15% on the CAL.

3. Find the weight of Stocks, Bonds and risk free on portfolio P.

Answer 1

The weight of Stocks and Bonds in the optimal portfolio: 39.50% in Stock and 60.50% in Bond

The return of the optimal portfolio : 16.98%

The standard deviation of the optimal portfolio : 0.164

The standard deviation of portfolio (P) with an expected return of 15% on the CAL : 0.128

The weight of Stocks, Bonds and risk free on portfolio P : Stocks =30.81%; Bonds = 47.18%; Risk Free = 22.01%

Workings:

Notes:

Step 1: Risk Premium on both stock and bond fund is computed by reducing Risk Free rate from the expected returns

Step 2: Covariance of stock and bond is computed by multiplying Correlation with the standard deviation of bond and stock

Step 3: Basis the above 2 steps, investment propotion in stock and bond is computed which represent the optimal risky portfolio

Step 4: Expected return of optimal risky portfolio comprising stock and bond is the expected return of stock and bond multiplied with the weights (investment propotion) in stock and bond

Step 5: Standard deviation of optimal risky portfolio is computed basis the weights, covariance and individual standard deviation of bond and stock

Step 6: Sharpe Ratio (reward to variability ratio) of the best feasible CAL is computed by reducing the risk free rate from the expected return of portfolio and then dividing by the portfolio standard deviation

Step 7: The portfolio is expected to yield a return on 15% on the CAL. The standard deviation of the portfolio is estimated by reducing the risk free rate from 15% and then dividing by Sharpe Ratio

Step 8: With the expected return of 15%, the propotion of investments in stock and bond (excluding risk free) is calculated by reducing the risk free rate from 15% and then dividing by the market premium.

The resultant number is then multipled with the weights derived in step 3 to calculate the investment propotion in stock and bond.

The balance investment will be in the risk free. This is because the return of the portfolio (15%) is the average of risk free and the optimal propotion of stock and bond.