Problem $1$:

The $($annual$)$ expected return and standard deviation of returns for $2$ assets are as follows:

Asset A Asset B

E$[$r$]10\%20\%$

SD$[$r$]30\%50\%$

The correlation between the returns is $0\mathrm{.}15.$

a$)$ Calculate the expected returns and standard deviations of the following portfolios:

$($i$)80\%$ in A$,20\%$ in B

$($ii$)50\%$ in A$,50\%$ in B

$($iii$)20\%$ in A$,80\%$ in B

b$)$ Find the weights for a portfolio with an expected return of $25\%.$ What is the standard

deviation of this portfolio?

c$)$ Find the weights for a portfolio with the same standard deviation as asset A but a

higher expected return? $($Trial and error may be a viable strategy; however, there is

an analytical solution.$)$ What is the expected return of this portfolio?

d$)$ What is the correlation between the returns on the portfolios in parts a$($i$)$ and a$($iii$)?$

$($Recall that the correlation is the covariance divided by the product of the standard

deviations.$)$

$1$