Question

1) It is now January. The current interest rate is 3%. The storage cost of silver is 2%. The June futures price is 1246.3, while the spot price of silver is $1200. Is there any arbitrage opportunity here? If so, how would you exploit it? How much is the profit? Show the steps

Answer 1

	Equilibrium Future Price of Silver
	= Spot Price*e^(Interest Rate*Period) + Storage Cost*e^(Interest Rate*Period)
	Where,
	e^(Interest Rate*Period)
	= e^(3%*6 months / 12 months)
	= e^(0.015)
	Using Excel Formula = EXP(0.015)
	= e^(0.015)
	= 1.01511
	Equilibrium Future Price of Silver
	= Spot Price*e^(Interest Rate*Period) + Storage Cost*e^(Interest Rate*Period)
	= Spot Price*e^(Interest Rate*Period) + (Spot Price*Storage Cost %)*e^(Interest Rate*Period)
	= $1200*1.01511 + ($1200*2%)*1.01511
	= $1218.13 + $24*1.01511
	= $1218.13 + $24.36
	= $1242.49
	The actual Future Price is $1246.30 whereas equilibrium price is $1242.49.
	Therefore, Future Value is overvalued.
	Arbitrage Strategy
	1) Sell June Future @ $1246.30
	2) Borrow $1200 for 6 months @ 3%.
	3) Buy Silver in the Spot market for $1200.
	Calculation of Arbitrage Profit
	Sell Amount of June Future	$1,246.30
	Repayment of Borrowed Amount with Interest	$(1,218.13)
	($1200*e(0.15) = $1200*1.01511)	$     (24.36)
	Storage Cost ($24*e(0.15) = $24*1.01511)
	Arbitrage Profit ($1246.30 - $1218.13 - $24.36)	$3.81