Arbitrage-free valuation for bonds

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bigfin

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In general, I have no idea how to do these calculation to figure out if there is an arbitrage opportunity and how much profit there would be. I understand that you could buy the bond then create STRIPS, or vice versa to create a profit. But, how do you compare the two values? For bonds, you just do the simple PV on the calculator. But, for the STRIPS, how do you calculate the PV?
Consider a 6% Treasury note with 1.5 years to maturity. Spot rates (expressed as semiannual yields to maturity) are: 6 months= 5%, 1 year= 6%, 1.5 years= 7%. If the note is selling for $992, compute the arbitrage profit, and explain how the dealer would perform the arbitrage.
Also, Is there a way to figure out the PV of the spot rates in the calculator?
 
Calculate the fair MV of the bond
30/(1.025) + 30/(1.03)^2 + 1030/(1.035)^3 = 986.55
Since FV < MV, one way you can profit is , by selling it short.
 
you calculate the PV of the cashflow according to spot rate.
PV: 6/(1+5%)+6/(1+6%)^2+106/(1+7%)^3=x
then u compare x with the note price ( $992)
if x>$992, profit: x-992: you should buy the note and short the STRIPS
if x<$992, prift: $992-x: you should buy the strips and short the note.
by shorting, i mean borrow strips and use the money to buy note. does it work that way?
Thanks!
 
couldn’t you just calculate the yield to maturity in our case 6.56?
if you can get for 1.5 years 7% you should sell the note and invest at 7%
is that incorrect thinking?
 
florinpop
I am not sure on this, but others may chime in (I haven’t looked at this in many months). YTM assumes that all cash flows are reinvested at one rate. When comparing to a STRIP you have to discount each cash flow at the approiate spot rate. If you don’t you aren’t really comparing apples to apples.
The whole idea here is that you are trying to figure out if you are better off buying the bond (whole) or the STRIP (pieces) that make up the bond. To do so you need to discount each cash flow (pieces) by the appropriate spot rate and see if it equals the current bond price (whole).
It may become more clear if you go back and look at the assumptions embedded in the YTM.
 
florinpop Wrote:
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> couldn’t you just calculate the yield to maturity
> in our case 6.56?
> if you can get for 1.5 years 7% you should sell
> the note and invest at 7%
> is that incorrect thinking?
Suppose that you short the note and put all the money in the 1.5 year strip. What are you going to do at the 6 month point when you have to make a coupon payment on your short bond position? If you borrow it for a year, it’s not arbitrage anymore.
If you had shorted thye 6 month strip equal to the coupon payment you would just turn that over for the coupon payment (since it would probably just be a coupon interest strip anyway).
 
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