Question

Consider the following three bonds and bond prices (0s denotes 0% annual coupon rate):

Bond Price

0s of 5/15/2012 (expiration date) 96-12

7.5s of 5/15/2012 103-12

15s of 5/15/2012 106-02

All bonds have identical face values and the same (but uncertain) settlement dates. Do these prices imply any arbitrage opportunity? If so, what are the weights of each security in an arbitrage portfolio (normalize the weight of the 15s bond to 1)? What is the arbitrage profit?

Answer 1

The Prices imply an Arbitrage Opportunity. The Arbitrage Strategy is to:

• Buy ONE 0s bond and ONE 15s bond.
• Simultaneously, sell TWO 7.5s bonds.

i.e. the weights of the bonds in the arbitrage portfolio are as below:

0s Bond: 7.5s Bond: 15s Bond= 1 (Buy): 2 (Sell): 1 (Buy)

The profit for such strategy would be= 2x 103.12- 96.12- 106.02= $4.1

(If you sell 2N no. of 7.5s Bonds and buy N no. of 0s Bond+ N no. of 15s Bond, then the Profit will be $4.1x N)

Explanation:

Let us assume all the bonds have a face value of $100.

You have to match the cash flows from the coupon payments and the payments at maturity.

At Maturity you will get

(1) $100 from the 0s and

(2) $15 coupon+ $100 from the 15s

From which you can pay

2x ($100+ $7.5) for the two 7.5s you have sold

(Basically coupon amount for TWO no. 7.5s Bonds is equal to coupon amount for ONE 15s Bond)