You have taken out a $5-$year car loan for $$50,000($nice car!$)$ with equal semi$-$annual

payments. The loan requires no payments in the first year, i$.$e$.,$ the first payment is in $18$

months, but interest continues to accrue during this period. The last payment is in $5$ years.

If the APR on the loan is $8\%($semi$-$annual compounding$),$ what are the payments?

$($Problem Set $1$ revisited$)$ You bought Coca$-$Cola stock $3$ years ago for $$\frac{45}{?}$ share. It paid

dividends at the end of the first, second and third years of $$\frac{2}{?}$ share, and you sold it for

$$\frac{50}{?}$ share. Assuming you could reinvest the dividends at $2\%$ per year, what is the

annualized HPR on Coca$-$Cola stock over this $3-$year period?

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

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$.($Difficult$)$ 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$.($Optional$)$ 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.$)$