Problem $3\mathrm{.}27$

It is July $16.$ A company has a portfolio of stocks worth $$100$ million. The beta of the portfolio is

$1\mathrm{.}2.$ The company would like to use the December futures contract on a stock index to change

the beta of the portfolio to $0\mathrm{.}5$ during the period July $16$ to November $16.$ The index futures price

is currently $2,000$ and each contract is on $$250$ times the index.

a$)$ What position should the company take?

b$)$ Suppose the company changes its mind and decides to increase the beta of the portfolio

from $1\mathrm{.}2$ to $1\mathrm{.}5.$ What position in futures contracts should it take?

Problem $4\mathrm{.}27$

An interest rate is quoted as $5\%$ per annum with semiannual compounding. What is the

equivalent rate with $($a$)$ annual compounding, $($b$)$ monthly compounding, and $($c$)$ continuous

compounding.