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.

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

Answer 1

1. Find the weight of Stocks and Bonds in the optimal portfolio : 39.5% in Stock and 60.5% in Bonds
2. Calculate the return and standard deviation of the optimal portfolio : Return of optimal portfolio = 16.98%; standard deviation of the optimal portfolio = 0.164
3. Calculate the standard deviation of portfolio (P) with an expected return of 15% on the CAL: standard deviation of portfolio (P) = 0.128
4. Find the weight of Stocks, Bonds and risk free on portfolio P : Weight of Stock = 30.81%; Weight of Bond = 47.18%; Weight of Risk Free = 22.01%

Workings:

Note:

Step 1: Risk Premium on both stock and bond fund is computed as : Expected Return - Risk Free Rate

Step 2: Covariance of stock and bond is computed as : Correlation * standard deviation of bond * standard deviation of stock

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

Step 4: Expected return of optimal portfolio comprising stock and bond is computed as : expected return of stock * weight of stock (as per step 3) + expected return of bond * weight of bond (as per step 3)

Step 5: Standard deviation of optimal portfolio is computed basis the weights (as per step 3), covariance and individual standard deviation of bond and stock

Step 6: Sharpe Ratio (reward to variability ratio) of the best feasible CAL is computed as : (Expected return of portfolio (as per Step 4) - risk free rate ) / portfolio standard deviation (as per step 5)

Step 7: The expected return on portfolio is 15% on the CAL. The standard deviation of the portfolio is computed as : (15%-Risk Free Rate)/Sharpe Ratio (as per step 6)

Step 8: With the expected return of 15%, the propotion of investments in stock and bond (excluding risk free) is calculated as: (15%-Risk Free Rate)/(Expected Return on optimum portfolio (as per step 4)- Risk Free Rate).

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

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