Margins related to Futures Contracts

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Initial futures price on Day 0 $100
Initial margin requirement $5
Maintenance margin requirement $3
Settlement price on Day 1 $103
Settlement price on Day 2 $96
Settlement price on Day 3 $98
If no funds are withdrawn and margin calls are met at the beginning of the next day, the ending margin account balance on Day 3 for an investor with a short position of 10 contracts is closest to:
A. $70. B. $80. C. $100.
I do not get how to compute the answer for this. The solution does not provide a clear answer, either.
 
Remember first of all that margin accounts in future markets are different from margin accounts in equity markets in the sense that, in future markets you don’t use the margin account as leverage (e.g. put down x% and borrow the rest). Instead, the margin accounts are rather used as a buffer, given that futures are settled on a daily basis (aka mark to market) in case the position incurs too many losses. That is, at the end of the day, you either receive the gains you made or you have to pay for the losses you made.
Remember also that:
Rising (falling) prices, of course, benefit (hurt) the long and hurt (benefit) the short. So since we are short here, any increase in the price is a loss to the trader.
Let’s look at your example:
Initial margin is $5 and maintenance margin is$ 3, this means the investor puts down $5 per contract, thus $50 at the beginning of the trade.
First day, the trader loses $3 per contract (so he loses $30 total), ($100-$103=-$3), Margin account is at $50-$30=$20.
Second Day: The trader gains $7 per contract (thus 70 total), $103-$96=$7. Margin account is at $20+$70=$90
Third day: Trader loses $2 per contract (20 total), ($98-$96=$2). Margin account is at $90-$20=$70.
(Note: The losses on the first day would trigger a Margin Call, and the margin account would need to be increased up to the initial margin again, but we ignore the margin calls here as requested in the question)
By the way, the whole thing is described in a nice and short paragraph in Reading 58, 4.1.2. Futures and in Example 9 Reading 46.
Hope this helps.
 
My apologies, I just re-read the question and noticed that margin calls are being met.
In that case after the 1st day, the trader does receive the margin call and has to increase the funds on the margin account back to the initial margin (not to required margin), so in my post above, after the first day the account is at 50 again, $30 have to be paid in.
2nd Day:50+70=120
3rd Day: 120-20=$100
So C) is correct.
 
Got it. So basically, when the margin account falls below the maintainence margin requirement, the investor must put up cash or collateral that would refill his account to the initial margin requirement?
 
Precisely.
I think it must be Cash though, not sure about Collateral.
 
I learned in class it can also be short term liquid securities, but not sure if this is right though.
Thanks for the help!
 
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