Suppose that economy A is growing rapidly, and you are managing a global equity fund and so far you have invested only in developed-country stocks…
CA Final · Advanced Financial Management · MTP · May 2024
Suppose that economy A is growing rapidly, and you are managing a global equity fund and so far you have invested only in developed-country stocks only. Now you have decided to add stocks of economy A to your portfolio. The table below shows the expected rates of return, standard deviations, and correlation coefficients (all estimates are for aggregate stock market of developed countries and stock market of Economy A). Developed Country Stocks Stocks of Economy A Expected rate of return (annualized percentage) 20 30 Risk [Annualized Standard Deviation (%)] 16 30 Correlation Coefficient (ρ) between stock of two economies 0.30 Assuming the risk-free interest rate to be 6%, you are required to determine: (i) What percentage of your portfolio should you allocate to stocks of Economy A if you want to increase the expected rate of return on your portfolio by 1%? (ii) What will be the standard deviation of your portfolio assuming that stocks of Economy A are included in the portfolio as calculated above? (iii) Also show how well the Fund will be compensated for the risk undertaken due to inclusion of stocks of Economy A in the portfolio?
Suggested Answer and Working Notes:
(i) Let the weight of stocks of Economy A be expressed as w, then (1- w) × 20% + w × 30% = 21% i.e. w = 0.1 or 10%. (ii) Variance of portfolio shall be: (0.9) 2 (0.16) 2 + (0.1) 2 (0.30) 2 + 2(0.9) (0.1) (0.16) (0.30) (0.30) = 0.02423 Standard deviation is (0.02423) 1/2 = 0.15565 or 15.56%. (iii) The Sharpe ratio will improve by approximately 0.09, as shown below: Sharpe Ratio = (Expected Return - Risk Free Rate of Return) / Standard Deviation Investment in stock of developed countries only: (20-6) / 16 = 0.875 Investment with inclusion of stocks of Economy A: (21-6) / 15.56 = 0.964
Topics: Portfolio Management
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