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

There is an arbitrage profit to be made from this, the cash flow is detailed below:

At t = 0:

Borrow 100$ from the bank at 10% p.a

Buy the security at $100

Buy the forward to sell at $104 in 6 months

At t = 3 months:

Collect coupon of 6$ on security

Deposite coupon in bank at 10% p.a

At t = 6 months:

Using forward contract, sell security for 104$

Interest accumulated on loan = 100 * exp ( 0.1*0.5)

= 100 * 1.0513

= 105.13$

Pay back loan + interest of 105.13$

Interest accumulated on coupon deposited = 6* exp(0.1*0.25)

= 6 * 1.025

= 6.15$

Cash flows at t = 6 months :

+ 104$ (Sale of security)

+ 6.15 (return for depositing coupon)

- 105.13 ( Bank loan + interest)

= 5.02$ profit

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