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Discussion in 'Financial Futures' started by AntelopeStew, Jan 16, 2008.

1. ### AntelopeStew

Hi. On the CBOT site, the ratio for this futures spread is listed as 5 10-year notes to 3 30-year bonds.

How do they calculate this ratio and what is the rationale behind it?

Any and all insights appreciated. Thank you.

2. ### Pa(b)st Prime

It's an approximate duration ratio.

You need to discover each instruments tick value as expressed in yield. The shorter the duration (i.e. maturity) the more each 32nd moves the yield.

IOW's, NOB spreaders are NOT trading the price diff of ZB vs. ZN rather they're trading the yield diff. Since 1 tick in 10's accounts for greater yield variance than 1/32nd in Bonds the spread needs to be weighted.

3. ### FullyArticulate

Essentially the steps are:

1) Pick any bond which is eligible for delivery. (You should pick the Cheapest-to-Deliver, but Bloomberg's pay service is one of the few places that has that data. You can compute it yourself, but be prepared for several hours of work. Fortunately, CBOT publishes conversion factors for arbitrary bonds and notes that should get you pretty close to par. So, just pick one)

2) Get a price quote for that bond (I used Schwab to get a quote for a specific treasury)

3) Compute the Modified Duration and the accrued interest. (Excel and some simple math will get you those two values)

4) DV01 = ((.01 * ModifiedDuration)*(PriceOfBond + Accrued Interest)*.01)

5) Futures DV01 =( (Contract \$ value)/1000)*DV01/Conversion Factor

That will give you the price move for a 1 basis point move in yield on the futures contract.

Do the same for the 10 year note, and then divide one by the other.

A typical DV01 for a 10 year note at 4.75% yield to maturity is about \$80. A 2 year note is around \$18.84. The two year contract is \$2000 per point, whereas the 10 year is \$1000 per point.

Taking into account the conversion factors for the specific bonds I chose, you end up with a 10 year Futures DV01 of \$86.36, 2 year is \$38.42. Or, about 2.25 2 years for every 1 10 year.

Long-winded enough? After all of that work, it's easier to just look at where CBOT will give you a price break. Unless you're doing HUGE trades, slight variances in your DV01 neutrality probably won't bother you much.

4. ### nazzdack

The ratio of bonds to 10-years tends to range from 0.6 to 0.7, i.e. 3/5, 5/8, 13/20, 2/3, 17/25 or 7/10 depending on volatility and your expectations of yield curve movement.

5. ### Bernard111

Pa(b)st Prime,

Your post make me think about the 30Y cut tick that we will have next March from \$31.25 to \$15.625.

You wrote that the NOB spreaders do not trade the ZB vs. ZN price difference but in March will be still good the affirmation that "Since 1 tick in 10's accounts for greater yield variance than 1/32nd in Bonds the spread needs to be weighted. "? Maybe it's a newbie question...

6. ### FullyArticulate

The tick size has no impact on the proper ratio to spread bonds to match yield DV01.

No comment!

el surdo

8. ### Bernard111

Well, clearly, I'm newbie enough to don't know in my ignorance 'that the tick size has no impact on the proper ratio to spread bonds to match yield DV01.'

Thanks FullyArticulate.
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