Max Houck holds $800$ shares of Boulder Gas and Light. He bought the stock several years ago at $ $51\mathrm{.}64,$ and the shares are now trading at $ $78\mathrm{.}00.$ Max is concerned that the market is beginning to soften. He$$ doesn't want to sell the$$ stock, but he would like to be able to protect the profit$$ he's made. He decides to hedge his position by buying $8$ puts on Boulder$$ G&L$.$ The$$ three$-$month puts carry a strike price of $ $78\mathrm{.}00$ and are currently trading at $ $3\mathrm{.}42.$

a$.$How much profit or loss will Max make on this deal if the price of Boulder$$ G&L does indeed$$ drop, to $ $61\mathrm{.}00$ a$$ share, by the expiration date on the$$ puts?

b$.$How would he do if the stock kept going up in price and reached $ $85\mathrm{.}50$ a share by the expiration$$ date?

c$.$What do you see as the major advantages of using puts as hedge$$ vehicles?

d$.$Would Max have been better off using$$ in$-$the$-$money putslong dashthat $$is$,$ puts with an $ $87\mathrm{.}00$ strike price that are trading at $ $10\mathrm{.}34?$ How about using$$ out$-$of$-$the$-$money putslong dash$$say$,$ those with a $ $72\mathrm{.}50$ strike$$ price, trading at $ $1\mathrm{.}00?$ Explain.