Question

8) a. Suppose a 7.6% semi-annual coupon 20-year Treasury issue with a par value of $100 issue is priced in the market based on the on-the-run 20-year Treasury yield. Assume further that this yield is 6.20%, so that each cash flow is discounted at 6.20% divided by 2. What is the market price of the Treasury issue based on this assumption?

b. Suppose also that the price of the same Treasury issue would be $108.462 if it is calculated based on the prevailing Treasury spot rate curve. What action would a dealer take and what would the arbitrage profit be? Can this situation persist in the long run?

Answer 1

a ) Market price of the bond willl be the Future Cash flows discounted at the Yield rate. the current market price is $115.92

given,

Par Value (FV)       =    $100.00

coupon rate    = 7.6%

Coupon amt (PMT) = $3.80 (100 X 7.6% X 1 / 2)- since semi annual

Period (n)    =    40 (20 years X 2 ) since semi annual

YTM                      =3.10%   (6.20% X 1/2) since semi annual

based on the above, price of the bond is determined using PV function as show below

current Price of the bonds
Par Value (FV)	$                     100.00
coupon rte	7.60%
Coupon amt (PMT)	$                          3.80
Years (n)	40
YTM	3.10%
Bond price (PV)	$                     115.92

excel formulas

b)     suppose the Bond which is to be priced at $ 115.92 is available for   $108.462, then it means the Bond is undervalued in the Spot market. This makes the investment in Bond attractive since $115.92 worth of bonds is available for $108.462 , there by resulting in an instant gain of $7.46 per bond. the dealer will buy the bond at $108.462 to make an arbitrage profit of $ 7.46

the situation wont persist in the long run, since the arbitrage traders trying to take advantage of the situation, will lead to an increase in demand for the bond, moving its price above till it reaches its equilibrium price of $108.462