$.$ You expect the stock market to decline, but instead of selling

stocks short, you decide to sell a stock index futures contract

based on an index of New York Stock Exchange common stocks. The

index is currently $600$ and the contract has a value that is $$250$

times the amount of the index. The margin requirement is $$2,000$ and

the maintenance margin requirement is $$1,000.$ a$.$ When you sell the

contract, how much must you put up$?$ b$.$ What is the value of the

contract based on the index? c$.$ If after one week of trading the

index stands at $601,$ what has happened to your position? How much

have you lost or profited? d$.$ If the index rose to $607,$ what would

you be required to do$?$ e$.$ If the index declined to $594(1$ percent

from the starting value$),$ what is your percentage profit or loss on

your position? f$.$ If you had purchased the contract instead of

selling it$,$ how much would you have invested? g$.$ If you had

purchased the contract and the index subsequently rose from $600$ to

$607,$ what would be your required investment? h$.$ Contrast your

answers to parts $($d$)$ and $($g$).$ i$.$ At the expiration of the contract,

do you deliver the securities you contracted to sell?