Question

A security is currently trading at $100. The six-month forward price of this security is $104.00. It will pay a coupon of $6 in three months. The relevant interest rate is 10% p.a. (continuously compounding). No other payouts are expected in the next six months. Show the exact strategy you will use to make an arbitrage profit. State the profit and show all cash flows arising from the strategy.

Answer 1

A	Current Price = $ 100
B	Computation of Fair Price of Security:
	6 Month Forward Price = $ 104
	Coupon Payment in 3 Months = $ 6
	Interest Rate = 10%
	Fair Value of Bond = PV of Coupon Payment + PV of Price after 6 Months
	Fair Value of Bond = ($ 6 * PVF(10%, 3 Month)) + ($ 104 * PVF(10%,6 Months))
	Fair Value of Bond = ($ 6 * e^(-0.10*3/12)) + ($ 104 * e^(-0.10*6/12))
	Fair Value of Bond = ($ 6 * e^(-0.025)) + ($ 104 * e^(-0.05))
	Fair Value of Bond = ($ 6 * 0.9753) + ($ 104 * 0.9512)
	Fair Value of Bond = $ 5.85 + $ 98.93
	Fair Value of Bond = $ 104.78
C	From the above, the Fair Price of Security is $ 104.78 while it is Currently Trading at $ 100.
	i.e., The Security is Underpriced.

	To take the arbitrage Oppurtunity, We have to buy the bond.
	For this we can borrow $ 100
I	Amount Borrowed	$        100
	Amount Required for Repayment after 6 Months	$ 105.13
	($ 100 * e^(0.10*6/12) = $ 100 * 1.0513
	Total Expense	$ 105.13
II	Amount Received after 3 Months	$6
	Deposit the amount received for the period of 3 Months	$6.15
	Amount Received on Depoist = $ 6 * e^(0.10*3/12)
	= $ 6 * 1.0253
	6 Months Forward Price of Security	$104
	Total Income	$110.15
III	Arbitrage Profit (II - I)	$5.02