Suppose that the BIST$100$ Index has a level of $9,000.$ The continuously compounded rate of

return on a $1-$year Treasury bill is $45\%.$ You wish to hedge an $10$ million portfolio that has

a beta of $1\mathrm{.}1$ and a correlation of $0\mathrm{.}95$ with BIST$100.$ One index futures contract is on $100$

times the index and the index has a $15\%$ expected dividend yield this year.

a$.$ What should be the $1-$year futures price for the BIST$100$ index?

b$.$ How many index contracts should you short to hedge your portfolio?

c$.$ What is the expected value and variance of the rate of return on the hedged

portfolio?