# Bond mispricings?

1. Mar 23, 2012

### the4thamigo_uk

Ive been looking at quotes for two US government bonds maturing on 31/5/2012. Im trying to understand why they differ so much?

5/31/2012 0.750 100.1250 100.1328 0.0078 0.045
5/31/2012 4.750 100.8750 100.8828 -0.0078 0.066

Source : http://online.wsj.com/mdc/public/page/2_3020-treasury.html
(select historical data and choose Thursday, March 22, 2012)

As I understand both these bonds have only one coupon remaining (i.e. the last one payable at maturity). The difference in the final payments between the two bonds is therefore: 4.75/2 - /75/2 = $2. The discount rate for the payment of the principal and final coupon is the same for both bonds. I can approximate this by looking at the rates for the zero coupon treasury bill Maturity Bid Asked Chg Asked yield 5/31/2012 0.065 0.060 -0.0100 0.0610 Source : http://online.wsj.com/mdc/public/page/2_3020-treasury.html (select historical data and choose Thursday, March 22, 2012, then click Goto Bills) The yield of the zero bond is very low (0.061% annualized) and we are fairly close to maturity, so the discount factor is very close to 1. The difference in price of the two bonds, should therefore be roughly the difference in the value of the final coupon. i.e.$2. But the difference in price is only \$0.75.

As I understand it market convention is to quote prices as 'clean'. I am assuming WSJs quotes are clean. If so, what explains the large discrepancy?

2. Mar 23, 2012

### BWV

two issues:

1) the quoted bond prices do not include accrued interest - if you bought the higher coupon bond on April 1 you would pay an additional amount equal to 5/6 of the semiannual payment

2) its not uncommon for Treasuries of similar maturities with different coupons to trade at small spreads , in this case 2.1 basis points

3. Mar 23, 2012

### the4thamigo_uk

Ok, so the quotes are clean...

31st may is maturity, this is about 10 weeks ~ 70 days, so I add 70/180 of the coupon onto the clean price of the bonds i.e. taking the bid price we get dirty/cash prices of

100.1250 + .75/2 * (180-70)/180 = 100.3542
100.8750 + 4.75/2 * (180-70)/180 = 102.3264

difference = 1.9722 (which is more like what I expected)

ahh... right I got it.... so if i bought the bond now I would forfeit most of the coupon