Question 1: We use the following formulae to get the anticipated returns and standard deviations of the portfolios: Weight of asset A * Expected Return of Asset A + Weight of asset B * Expected Return of Asset B equals the portfolio's anticipated return. The formula for calculating a portfolio's standard deviation is sqrt(Weight of Asset A * SD of Asset A * Weight of Asset B * SD of Asset B * + 2 * Weight of Asset A * Weight of Asset B * Correlation * SD of Asset A * SD of Asset B). I 20% in Spain, 80% in the United States: Return anticipated: 10.6% (0.8 * 10% + 0.2 * 15%). Standard deviation is calculated as sqrt(0.8 * 20% * 0.2 * 30% * 2 * 0.8 * 0.2 * 20% * 30%) = 22.07%. (ii) Half in the US and half in Spain: Return anticipated is 0.5 x 10% plus 0.5 x 15%, or 12.5%. Standard deviation equals sqrt(0.5*2*20*0.5*2*30*2*2*0.5*5*5*0.3*20*30) = 24.50% (iii) 80% in Spain and 20% in the US: Estimated return = 0.2% * 10% + 0.8% * 15% = 13.6% Standard deviation equals square root (0.2 * 20% * 0.8 * 30% * 2 * 0.2 * 0.8 * 0.3 * 20% * 30%) = 27.32% We must use the following formula to solve for the weights in order to get the weights for a portfolio with an anticipated return of 25%: 0.25 = Weight of the US times 10% plus Weight of Spain times 15% Also, we must use the following formula to determine the standard deviation of a portfolio: SD of the portfolio is equal to sqrt(Weight of US * 0.3 * 20% * 30% + Weight of Spain * 0.2 * 20% * 30% + Weight of US * 0.3 * 30% * Weight of Spain). To find the weights, we may apply substitution. When we rewrite the equation above, we obtain: Weight of US is equal to 0.25 minus 0.15 and 0.10 minus 0.15. Spain weighs one pounds whereas the US weighs zero. Hence, the only way to build a portfolio with a 25% projected return is to invest exclusively in the US market. This portfolio has a 20% standard deviation. Question 2: (i) Weight(Rf Asset) = 0.75 , Weight(B) = 0.25 ER(portfolio) = { ER(Rf Asset) * Weight(Rf Asset) } + { ER(B) * Weight(B) } = { 4 * 0.75 } + { 20 * 0.25 } =8% SD(portfolio) = SD(B) * Weight(B) FORMULA of SD in case portfolio consists Rf Assets = 50 * 0.25 = 12.5 % (ii) Weight(Rf Asset) = 0.25 , Weight(B) = 0.75 ER(portfolio) = { ER(Rf Asset) * Weight(Rf Asset) } + { ER(B) * Weight(B) } = { 4 * 0.25 } + { 20 * 0.75 } = 16 % SD(portfolio) = SD(B) * Weight(B) = 50 * 0.75 = 37.5 % (iii) Weight(Rf Asset) = 0.50 , Weight(Portfolio in Q1 aii) = 0.50 ER(portfolio) = { ER(Rf Asset) * W(Rf Asset) } + { ER(Portfolio in Q1 aii) * W(Portfolio in Q1 aii) } = { 4 * 0.50 } + { 15 * 0.50 } = 9.5 % SD(portfolio) = SD(Portfolio in Q1 aii) * Weight(Portfolio in Q1 aii) = 30.29 * 0.50 = 15.15 % (i) Asset A Sharpe Ratio = (10 - 4) / 30 = 0.2 (ii) Asset B Sharpe Ratio = (20 - 4) / 50 = 0.32 (iii) Portfolio in Q.1a(i) Sharpe Ratio = (12 - 4) / 27.35 = 0.29 (iv) Portfolio in Q.1a(ii) Sharpe Ratio = (15 - 4) / 30.29 = 0.36 (v) Portfolio in Q.1a(iii) Sharpe Ratio = (18 - 4) / 41.33 = 0.34 Question 3: