Question

For all problems assume an effective monthly interest rate of 1% unless otherwise indicated in the problem.

3. In the CME’s silver futures market, the current silver price is $33.41 per troy ounce, and the contract size is 5000 troy ounces

(a) If a hedge fund wanted to be long $835,250 worth of silver futures, how many contracts should they buy?

(b) If the CME requires an 12% initial margin, how much does the hedge fund need to post in the margin account?

(c) If the price of silver closes tomorrow at $33.50 per troy ounce, what is the balance in the margin account?

(d) Assuming the account earns no interest and the broker requires margin maintenance of 70% of initial margin, what is the highest silver price that will trigger a margin call

Answer 1

a)	Value of one contract			=	Current future price*no. of troy ounce per contract
				=	$33.41*5000
				=	$ 167,050.00
	No. of contracts			=	Total value/Value of one contract
				=	$835,250/$167,050
				=	5
b)	Initial margin			=	Total amount of long position*margin rate
				=	$835,250*12%
				=	$ 100,230.00
c)	Gain/(loss) in a day			=	(closing price-purchase price)*contract size*no. of contracts
				=	($33.5-$33.41)*5000*5
				=	$0.09*5000*5
				=	$      2,250.00
	Balance in margin			=	Initialmargin +gain
				=	$100,230+$2,250
				=	$ 102,480.00
	The gain is $2,250
d)	If broker requires 70% of initial margin
	70% of initial margin			=	70%*$100,230
				=	$70161
	i.e loss for margin call to be triggered
				=	Initial margin-maintenance margin
				=	$100,230-$70,161
				=	$    30,069.00
	Price at which this loss happens			=	current price-[{Loss amount/(no. of ounce per contract*no. of contracts)}]
	Price			=	$33.41-[$30,069/(5000*5)]
	Price			=	$33.41-[$30,069/25000]
	Price			=	$33.41-1.20276
	Price			=	$ 32.21
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