Theoretical Futures Price V Actual Futures Price

[Brackers27]

Hi

I have tried to calculate the theoretical futures price for 2 year Treasuries September contract but the resulting figure is 11.5/32nds higher than the actual quoted futures price (based on Monday's settlement prices- 7/12/10). Does anyone know why this could be? I used the figures below

—————————————————————————————————————————————————————————-
Settlement price of 2 yr Treasury futures = 109 12-5/32nds
Settlement price of Cheapest to deliver = 99 31/32nds
Coupon rate (paid semi-annually) = 0.625%
CTD Issued on 30/6/10, days of accrued interest = 12 days
Days until next Coupon = 171 days

Days until expiry (september 30th) = 80days
(I have assumed the last delivery day,correct?)

Conversion Factor = 0.9119

Risk Free Rate = 1.14375%
(I have used the 1 Year US LIBOR rate, is this correct?
The 12 month treasury is trading at a yield of 0.28)
——————————————————————————————————————————————————————————————
Accrued Int. = 12/183 x 0.625/2 = 0.0204918
Dirty Price = 99.989242

Since no coupon is issued during the life of the futures contract, I have excluded it:

Cash Futures Price =(Dirty Price - PV of Coupon) x exp(days until expiry/days in year x r)
= (99.989242 - 0) x exp(80/183 x 1.14375%) = 100.24021


Quoted Futures Price SHOULD BE = (cash futures price - accrued int at delivery)/Conversion Factor

= (100.24021 - (92/183)x0.625/2)/0.9119 = 109.7522869 ~ 109 24/32


Thus the theoretical futures price I have calculated is 11.5/32nds higher than the quoted settlement price (109 12.5/32nds).

Any ideas why this is? I thought it may be delivery options impacting on the price somehow but from the research I’ve done, it is highly unlikely that the value of the timing or quality option can explain all of the discrepancy. I suspect I am using the wrong rate, perhaps a repo rate should be used or perhaps there are other borrowing costs to take into account. I have included an excel worksheet for clarity.


Any help would be great.


Thanks

Brackers27

 

[A Dashing Blade]

Lazy student wanting homework checked?

 

[Martinghoul]

Hmmmm, the CTD I see for the 2yr Sep10 contract isn't the 0.625 Jun12s, but rather the 4.875% Jun12s. Where did you get your CTD?

 

[Brackers27]

Lazy student wanting homework checked?

I wish Dashing Blade, no my boss is short 2 Year Treasuries and the current losses he is experiencing are greater than I expected. I had calculated the expected DV01 and associated convexity but the move in yields and the resulting price change does not match what I predicted. So, I just went back to the drawing board and started from scratch and realised that when i tried to calculate the theoretical futures price It didn't match the actual price and this is why I'm here.

My figures seem correct but when I calculate today's future price or use figures from a month ago I seem to be off by 10 or more 32nds and I can't see why. Any help would be much appreciated

 

[Brackers27]

Hmmmm, the CTD I see for the 2yr Sep10 contract isn't the 0.625 Jun12s, but rather the 4.875% Jun12s. Where did you get your CTD?

Hi Martinghoul

Well I calculated the CTD, as you would normally....

Min( Quoted Price - (Futures Price x Conversion factor) for eligible bonds.

I've just repeated the calculation and came up with the same result. It's matching what I'm seeing on bloomberg (http://www.bloomberg.com/markets/rates-bonds/government-bonds/us/....................2-Year 0.625 06/30/2012 99-31 / .64). Is this not correct?


Thanks

Brackers27

 

[Martinghoul]

Well, I am staring at my BBG right now and I see the current CTD as the 4.875 Jun12s. Note that the CTD is not be confused with the current 2s, the on-the-run 2y issue, which is, in fact, the 0.625 Jun12s.

 

[scose-no-doubt]

Hi. I'm just a learner who is interested in this stuff so I can't really help you. Can I ask why you have halved the interest rate in your calculation of the 12 days accrued interest? Also how did you calculate dirty price? I understand the rest.

Thanks

 

[Martinghoul]

Hi. I'm just a learner who is interested in this stuff so I can't really help you. Can I ask why you have halved the interest rate in your calculation of the 12 days accrued interest? Also how did you calculate dirty price? I understand the rest.

Thanks

Don't mean to usurp the thread, but...

The 0.625% coupon is annual, but USTs pay semi-annually, so every year you get 0.3125% twice. Dirty px is just clean px plus accrued interest.

 

[Brackers27]

Well, I am staring at my BBG right now and I see the current CTD as the 4.875 Jun12s. Note that the CTD is not be confused with the current 2s, the on-the-run 2y issue, which is, in fact, the 0.625 Jun12s.

Hi.

Crap, so maybe my calculations for CTD were incorrect.I can't see where I made my mistake but I'll replace the CTD in the previous example to see what happens (based on July 12th figures again):
------------------------------------------------------------------------------------
NEW FIGURES
Settlement price of Cheapest to deliver = 108 13.5/32nds
Coupon rate (paid semi-annually) = 4.875%
Conversion Factor = 0.9815
_________________________________________________________

Accrued Int. = 12/183 x 4.875/2 = 0.1598361
Dirty Price = 108.58171

Since no coupon is issued during the life of the futures contract, I have excluded it:

Cash Futures Price =(Dirty Price - PV of Coupon) x exp(days until expiry/days in year x r)
= (108.58171 - 0) x exp(80/365 x 1.14375%) = 108.85425


Quoted Futures Price SHOULD BE = (cash futures price - accrued int at delivery)/Conversion Factor

= (108.85425 - (92/183)x4.875/2)/0.9815 = 109.6575045 ~ 109 21/32


This is still 8.5/32nds off the July 12th SEP futures settlement price of 109 12.5/32nds

Again off, anyone see an error in my calculations

Thanks


Brackers27

 

[Brackers27]

Well, I am staring at my BBG right now and I see the current CTD as the 4.875 Jun12s. Note that the CTD is not be confused with the current 2s, the on-the-run 2y issue, which is, in fact, the 0.625 Jun12s.

Hi Martinghoul

Thanks for all the replies. By the way I've included an Excel attachment of my CTD calculation. I'm not arguing with your BBG but I'm still coming up with the same CTD the 0.625. Maybe you might identify where I'm messing up

Thanks


Brackers27

 

[Brackers27]

Hi. I'm just a learner who is interested in this stuff so I can't really help you. Can I ask why you have halved the interest rate in your calculation of the 12 days accrued interest? Also how did you calculate dirty price? I understand the rest.

Thanks

Sorry Scose no doubt for not getting back to you sooner but looks like Martinghoul has answered all your queries

 

[Martinghoul]

Hi Martinghoul

Thanks for all the replies. By the way I've included an Excel attachment of my CTD calculation. I'm not arguing with your BBG but I'm still coming up with the same CTD the 0.625. Maybe you might identify where I'm messing up

Thanks


Brackers27

Lemme look at the calculation, brackers, but I can tell you that the current 2s are definitely not the CTD for the Sep TU contract.

 

[scose-no-doubt]

Don't mean to usurp the thread, but...

The 0.625% coupon is annual, but USTs pay semi-annually, so every year you get 0.3125% twice. Dirty px is just clean px plus accrued interest.

Right sorry I was using 183/365 x .625 so didn't understand rate/2. Accountancy for you

Sorry for disrupting Brackers.

 

[Brackers27]

Lemme look at the calculation, brackers, but I can tell you that the current 2s are definitely not the CTD for the Sep TU contract.

Thanks, I'm sure you're correct so I'd just like to identify whatever mistake I'm making so it wont happen again.

 

[Brackers27]

Lemme look at the calculation, brackers, but I can tell you that the current 2s are definitely not the CTD for the Sep TU contract.

Actually if I use the CTD you suggest and use the 12 month Treasury rate of 0.28 instead of 1 year LIBOR (1.14%) as the risk free rate the theoretical price is close to the actual price. I thought I should use LIBOR as the risk free rate but maybe not. Apologies for the repeated messages!

 

[Martinghoul]

Actually if I use the CTD you suggest and use the 12 month Treasury rate of 0.28 instead of 1 year LIBOR (1.14%) as the risk free rate the theoretical price is close to the actual price. I thought I should use LIBOR as the risk free rate but maybe not. Apologies for the repeated messages!

Sorry, I didn't look at the LIBOR question... LIBOR is def the wrong rate to use. My guess is that the right rate should be a term repo rate, but 1y UST yield should certainly get you closer. I am still not sure about your CTD calc.

 

[Brackers27]

Sorry, I didn't look at the LIBOR question... LIBOR is def the wrong rate to use. My guess is that the right rate should be a term repo rate, but 1y UST yield should certainly get you closer. I am still not sure about your CTD calc.

Well that's good, at least I know LIBOR is not right, I figured as much. Where would I find the term repo rate??

 

[Martinghoul]

Well that's good, at least I know LIBOR is not right, I figured as much. Where would I find the term repo rate??

You need to ask the mkt . But using smth like the FedFunds OIS term rate should be close enough.

 

[Brackers27]

You need to ask the mkt . But using smth like the FedFunds OIS term rate should be close enough.

Where are these rates published? Sorry I've searched but to no avail!

 

[Martinghoul]

Where are these rates published? Sorry I've searched but to no avail!

On BBG... If you can't get them, just use the UST yield.