Can a dealer generate an arbitrage profit?

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kpollar1

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T spot rates are 2.2% for 6 months and 2.8% for 1 year. A 4% coupon T note with one year remain until maturity is priced at $1013.73. Can a dealer earn an arbitrage profit?
I’m unsure how to answer this one…can anyone help? Thx
 
FV = 1000
coupon semiannual = $20
20 discounted by 2.2% spot rate (PV of first coupon with 6 months spot rate)
1020 discounted by 2.8% spot rate. (PV of final cash flow with 1 year spot rate)
if sum of above two is different from 1013.73 which is the price of security, then Yes arbritrage profit is possible.
Sorry, no time to do calculations myself but give it a try.
 
Yes, he can.
There is a discrepancy in the rates implied by the bond and the spot rates
For the bond:
FV 1000, PV, 1013.73, PMT 20, N 2, IY 1.3%
for the spot rates:
1.011 * 1.014 ^1/2 -1 = 1.25%
 
So i calculated (20/1.011) + (1020/1.014^2) = 1011.81
Since this is lower than 1013.73, I would earn an arbitrage profit by purhasing the the strips, assembling them into a note then selling them.
Am I getting this right? Thanks in advance
 
robjames1984 wrote:Yes, he can.
There is a discrepancy in the rates implied by the bond and the spot rates
For the bond:
FV 1000, PV, 1013.73, PMT 20, N 2, IY 1.3%
for the spot rates:
1.011 * 1.014 ^1/2 -1 = 1.25%
Click to expand...
Unfortunately, it’s more complicated than that (i.e., this calculation doesn’t prove that there is an arbitrage opportunity, nor that there isn’t).
 
Magician - is the way I calculated it correct? Thanks
 
S2000magician wrote:
robjames1984 wrote:Yes, he can.
There is a discrepancy in the rates implied by the bond and the spot rates
For the bond:
FV 1000, PV, 1013.73, PMT 20, N 2, IY 1.3%
for the spot rates:
1.011 * 1.014 ^1/2 -1 = 1.25%
Click to expand...
Unfortunately, it’s more complicated than that (i.e., this calculation doesn’t prove that there is an arbitrage opportunity, nor that there isn’t).
Click to expand...
well don’t leave me in suspense… :) what else do I need to do here?
 
Ok, let me redo this:
$20 / 1.011 + 1020 / (1.014)^2 = 1,011.81
Which is different from the current price of 1013.73.
 
pivpomars wrote:I think it must be
$20 / 1.011 + 1020 / (1.028) = 1,012.00
?
Click to expand...
Nope: these are Treasury spot rates: BEY. You divide by 2 to get the effective semiannual yield, then compound.
You may be thinking that they’re LIBOR spot rates, which are nominal; if they were, your formulation would be correct.
 
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