Arbitrage in the Government Market Case Assignment

Xiaoxue Lu

Fixed Income Securities

Professor Natalia Reisel

10/03/2017

Arbitrage in the Government Market Case Assignment

1. Create the two synthetic bonds described in the case.   How should the price of these synthetics relate to the callable bonds?  Why?  On January 7, 1991, how much would it cost to create the synthetic using the ‘05s?  the ‘00s?

Thompson created two synthetic bonds imitated the cash flow of the 8 ¼ May 00-05 bond. The first synthetic bond describe in the case is the combination of noncallable bonds maturing in 2005 and zero-coupon Treasuries (or STRIPS) maturing in 2005. This synthetic bond can provide with semiannual interest payments of $4.125 per $100 face value and whose final payment of $100 at maturity exactly matched those of the callable bond.

1. According to Exhibit 2, the bond’s ask prices are:

We assume the non-callable bond coupon rate is s, and the callable bond coupon rate is c.

For the synthetic bond, the proportion of the non-callable bond is c/s and the proportion of STRIPS is 1-c/s.

Synthetic bond 00: c/s= 8.25/8.875=0.9296, 1-c/s=0.0704

Price of synthetic bond (using ask price): 104.5*0.9296 + 46.66*0.0704 = 100.43

Price of synthetic bond (using bid price): 104.38*0.9296 + 46.25*0.0704 = 100.28

Synthetic bond 05: c/s= 8.25/12=0.6875, 1-c/s=0.3125

Price of synthetic bond (using ask price): 129.91*0.6875 + 30.31*0.3125 = 98.785

Price of synthetic bond (using ask price): 129.72*0.6875 + 29.91*0.3125 = 98.53

Non-callable Synthetic Bonds:

8.25 May ’00: Bid: 100.28 Ask: 100.43

8.25 May ‘05: Bid: 98.53 Ask: 98.785

b) The price of the callable bond should always be lower than the synthetic bonds since the risks of callable bonds are higher. However, this is not true for out Callable 8.25 May 00-05 bonds. Therefore, we have a price discrepancy.

c) On Jan 7, 1991. If the government decide not to call until maturity, the callable and non-callable bonds will generate same cash flows, therefore same cost to create. If the government decide to call the bond, the callable bond’s cash flow will be less than non-callable bond’s cash flow. Therefore, the non-callable bonds are more valuable than callable bonds with same coupon rate and maturity. For 8.25 May ’05 and 8.25 May ’00, if government buy back the bond at the first possible date, the cash flows of these two bonds are identical; if not, cash flows of the callable bonds will less than that of non-callable. Therefore, callable bonds price will be lower than non-callable bonds price with same coupon and expiration of its first redeem date.