A pension fund manager is considering three mutual funds. The first is a stock fund, the second is

a long$-$term bond fund, and the third is a money market funds that provides a risk free return of

$4\%.$ The characteristics of the risky funds are as follows.

Stock Fund: Ret. $(14\%),$ Std$.$ Dev $(20\%)$

Bond Fund: Ret $(7\mathrm{.}5\%),$ Std$.$ Dev $(10\%),$ Correlation w stock fund $=0\mathrm{.}35$

a$.$ What are the investment proportions in the minimum variance portfolio of the two

risky funds, and what are the expected value and standard deviation of its rate of

return.

b$.$ Solve numerically for the proportions of each asset and for the expected return and

the standard deviation of the optimal risky portfolio.

c$.$ You require that your portfolio yield and expected return of $10\%,$ and that it be

efficient, that is$,$ on the steepest feasible CAL. What is the standard deviation of your

portfolio? What is the proportion invested in the money market fund and in each of

the two risky assets

Suppose Stock XYZ is selling at $$49$ per share. You buy $10,000$ shares, using $$220,000$ of your

own money, and borrow the remainder. The rate on the margin loan is $6\%$ per year

a$.$ What is your total return on the investment if in $12$ months, the price changes to $$45,$$$48,$

$$55$ per share.

b$.$ If the maintenance margin is $30\%,$ at what price will you get a margin call?

If a large pension fund wanted to buy $175,000$ shares of Amazon, describe how a high frequency

trading firm, may try and profit from that trade. Assume there are two different exchanges that

can be traded on$,$ and the first exchange only has $100,000$ shares of Amazon.

We discussed the four main roles of capital markets. Please explain the informational role in

capital markets and how it contributes to the growth in the productive capacity of the economy.