Question

Question 1-6 are based on the following series of futures price (F(0), F(1),... F(6)):

Day 0: F(0)=$212

Day 1: F(1)=$211

Day 2: F(2)=$214

Day 3: F(3)=$209

Day 4: F(4)=$210

Day 5: F(5)=$202

Day 6: F(6)=$200

Suppose you are going to long 20 contracts. The initial margin=$10 per contract, and the maintenance margin is $2.

1) from the set of information: how much do you need to deposit in the trading account at Day 0?

2) Using the same set of information from Question 2,  what is the ending balance in Day 1?

3) Using the same set of information from Question 2, figure out what is the first day, on which, you receive margin call and need to put extra money into the trading account?

4) Using the same set of information from Question 2, answering what is the additional fund that needs to put into account on Day 6?

5) Using the same set of information from Question 2, answering what is the ending balance at Day 6?

6) Using the same set of information from Question 2, answering which day has the largest gain among the 6 days?

Answer 1

Initial Margin = $ 10 per contract

Answer to 1:

How much you need to deposit in the trading account at day 0 :

We need to deposit Intial Margin of $ 10 * 20 contracts = $ 200.

Initial Margin is the minimum amount which the buyer and seller has to maintain with their respective broker if they want to enter into a future contract.
The Initial Margin is only a security provided by the client to the exchange. It can be withdrawn in full after the position is closed i.e after the contract expires.Initial Margin deposited is not an expense it is just like security deposit .

So, since it is the minmum amount which we require to maintain and no of long contracts to be entered is 20. Therefore, need to deposit $ 200 in the trading account at day 0 .

Answer to 2.

What is the ending balance in day 1 ?

Day 1 Future price has fallen to $ 211 from $ 212 (day 0), so, loss of $ 1 per contract will reduce our Initial balance deposited with the broker of $ 200 .

so, loss of $ 20 ($ 1 loss * 20 contracts) will reduce the Initial margin to $ 180 . ($200 - $ 20).

Ending balance in day 1 = $ 180

Answer to 3.

Which is the first day on which you receive margin call and need to put extra money into the trading account ?

Maintenance Margin :

Maintenance Margin is not any account which is to be maintained.

It is just a limit or deadline below which balance should not drop .

This is lower than the initial margin .This is to ensure that if balance in the margin account falls below the maintenance margin,the investor receives a margin call and is expected to top up the margin account to the initial margin level.

In other words Whenever balance fell below Maintenance Margin, we have to bring back the balance to Initial Margin
.The extra fund which is deposited is known as Variation Margin.

M To M is the Marked to Market Margin where prices are set on daily basis as per the closing future price and difference is adjusted from the Initial Margin deposited with the broker.It is like a profit and loss account.

(in $ )

Days	Opening Price	Closing Price	MTo M	Margin Call	Closing balance
1	212	211	-20 notional loss (-1* 20 contracts)	0 (because our Initial Margin has not touched the level of Maintenance margin)	180 (Intial Margin left at the end of 1st day ).
2	211	214	+ 60 notional profit (+3* 20 contracts)	0 (because our Initial Margin has not touched the level of Maintenance margin)	240 (180 + 60) , our Intial Margin increased by $ 60.
3	214	209	- 100 notional loss (-5* 20 contracts)	0 (because our Initial Margin has not touched the level of Maintenance margin)	140 (240-100) , our Intial Margin decreased by $ 100.
4	209	210	+ 20 notional profit (+1* 20 contracts)	0 (because our Initial Margin has not touched the level of Maintenance margin)	160(140 + 20) , our Intial Margin increased by $ 20.
5	210	202	- 160 notional loss (-8* 20 contracts)	200 (because our Initial Margin has reached 0 , even crossed the maintenace margin of 40, so, broker will give margin call for maimtaining Initial Margin of $ 200 ($10 per contract for 20 contracts)).	0 (160-160) + 200 our Intial Margin decreased by $ 160 and stands to 0 now so, broker will give margin call and again our closing balance with broker will be $ 200.
6	202	200	-40 notional loss (-2* 20 contracts)	0 (because our Initial Margin has not touched the level of Maintenance margin)	160 (200-40) , our Intial Margin decreased by $ 40 and stands at $ 160 at the end of day 6 .

Maintenance Margin is $ 2 * 20contracts = $ 40 for 20 contracts.

SO, DAY 5 is the First day on which we receive margin call and need to put extra money into the trading account of $ 200. (Intial Margin will be put back in the trading account).

Answer to 4.

What is the aditional fund that needs to put into account on Day 6?

Additional fund of $ 4000 ( 20 contracts * $200 future price ) needs to be put into account on DAY 6.

Since till now we were paying only the margin money , now we also need to Put $ 4,000 in order to buy the 20 future contracts @ $ 200 prevailing at the end of day 6.

Answer to 5.

what is the ending balance at Day 6?

Ending Balance at Day 6 = $ 160.

$ 160 can withdraw by us aince it is a security deposited with the broker/exchange.

Answer to 6.

which day has the largest gain among the 6 days?

DAY 2 has the Largest Gain by $ 60 ($ 3 per contract * 20 contracts).