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…

Let the weight of stocks of Economy A be expressed as w. Expected return of portfolio = w * E(R A ) + (1-w) * E(R DC ) Current expected return (Developed Country Stocks only) = 10% Desired expected return = 10% + 0.5% = 10.5% (i) Percentage allocation to stocks of Economy A: 10.5 = 15 w + 10(1-w) 10.5 = 15 w + 10 - 10w 0.5 = 5 w w = 0.1 or 10% So, 10% of the portfolio should be allocated to stocks of Economy A, and 90% to Developed Country Stocks. (ii) Standard deviation of the portfolio: σ p 2 = w A 2 σ A 2 + w DC 2 σ DC 2 + 2 w A w DC ρ A,DC σ A σ DC w A = 0.1, w DC = 0.9 σ A = 30% = 0.30, σ DC = 16% = 0.16 ρ A,DC = 0.30 σ p 2 = (0.1) 2 (0.30) 2 + (0.9) 2 (0.16) 2 + 2 (0.1) (0.9) (0.30) (0.30) (0.16) σ p 2 = (0.01)(0.09) + (0.81)(0.0256) + 2(0.09)(0.30)(0.30)(0.16) σ p 2 = 0.0009 + 0.020736 + 0.002592 σ p 2 = 0.024228 Standard deviation (σ p ) = √0.024228 ≈ 0.15565 or 15.57% (iii) Compensation for risk (Sharpe Ratio): Sharpe Ratio = (Expected Return - Risk Free Rate) / Standard Deviation Investment only in developed countries: Expected Return = 10% Risk Free Rate = 3% Standard Deviation = 16% Sharpe Ratio DC = (10 - 3) / 16 = 7 / 16 = 0.4375 With inclusion of stocks of Economy A: Expected Return = 10.5% Risk Free Rate = 3% Standard Deviation = 15.57% (from part ii) Sharpe Ratio Portfolio = (10.5 - 3) / 15.57 = 7.5 / 15.57 ≈ 0.4817 The Sharpe ratio improves from 0.4375 to 0.4817, an increase of approximately 0.0442. This indicates that the fund is better compensated for the risk undertaken with the inclusion of stocks from Economy A, as the portfolio offers a higher risk-adjusted return.