Fixed Income

Fixed Income

Homework 2 Case Study

Xiaofeng Jiao (A13102792)

Bin Xu (A12258325)

Beibei Zhang (A13059866)

The price of the synthetic bonds should be higher than those of callable ones. There are two major reasons behind this. Firstly, callable bonds offer the government an option to buy back the bond if the interest rate declines, after which the government can refinance at a lower rate. The value of this option will never be negative. Secondly, if the interest rate increases, the government will not call the bond because it will be costly to do so. Therefore, the price of callable 00-05 bond will be lower than a 00 non-callable bond.

To construct the non-callable 8 1/4 May synthetic bonds, we either combine 12 May 05 Treasury Bond with May 05 STRIP if the bond is not called or combine 8 7/8 May 00 Treasury bond with May 00 STRIP if the bond is called at the first possible date. For 8 1/4 May 05 non-callable bond, since the STRIP does not offer coupon payment, the portion of 12 May 05 Treasury Bond should be (8 1/4)/(12), which is 68.75%. The rest 31.25% belongs to 05 STRIP. Thus, the cost to buy at ask is 68.75%*(129 29/32)+31.25%*(30 10/32)= $98.78, and the cost to sell at bid is $98.53. Similarly, the cost to buy at ask for 8 1/4 May 00 non-callable bond is $100.43 and the cost to sell at bid is $100.28.

On January 7, 1991, for investors who own the 8.25 May 00-05 bond, Thompson can sell the bond at $101 4/32 ($101.125) and buy the 8 1/4 May 05 non-callable bond at $98.78 to realize a $2.345 profit. Alternatively, she can also buy 8 1/4 May 00 at $100.43 and sell May 00-05 at $101.125 to realize a $0.695 profit. On the other side, if investors do not own the callable bonds, they can short sell at a higher price and buy back at a lower price to gain profit. In this case, for instance, investors can short sell May 00-05 to receive $101.25 upfront and buy either May 05 at $98.78 or May 00 at $100.43. However, short sell is not common in Treasury Bond market. Thompson can enter into a reverse repo by selling the bond at high and purchase back at low. Either way works, but the latter is more commonly used.

Although price discrepancy is rare in the Treasury market, there are several reasons to explain this situation:

1. Liquidity premium: it is common that asset with high liquidity has high price. However, research of 1992 shows that the ask-bid spread of callable bonds is very big, which makes a low liquidity;
2. Tax consideration: Investors who pay tax will concern with tax ramification;
3. Transaction costs of short sale and reversed repo: margin requirement and transaction cost may be relatively high, which make the arbitrage opportunity exists;
4. Market disequilibrium: this market is not a strong efficient market, and it is in an unbalanced situation. Although a large number of investors will catch the arbitrage opportunity, then the profits will decrease, for the asymmetrical information of the market, there will be new arbitrage opportunity emerges.
5. Supply and demand: the shortage of callable bond and strong demand may increase the price of callable bonds. Also, the expectation of interest rates to fall draws the price of callable bonds higher.

The primary reason that the treasury and corporations issue callable bonds rather than non-callable bonds is to protect them in the event that interest rates drop.

Treasury bond is an important tool for the federal government to implement monetary policy. For example, if the government want to go monetary easing, callable bonds should be redeemed from the market so that more money can liquid in the whole market. Also, it gives the government more flexibility to do financial budget. When the government has budget surplus, it can redeem callable bonds easily.