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: