# Conversion Factor and Yield Beta

These two terms are found in both Reading 29 and Reading 42 but it seems some inconsistence existed. Can anyone explain clearly these two terms ? What are their definitions and practical usages ? I am confused by them !

Conversion Factor (CF) refers the denominator must be applied toward converting the price of cheapest to deliver (CTD) to the specified underlying in the treasury bond future’s contracts. Price used in settlement = Price of CTD / CF Yield Beta refers to the ratio of change in yield on the bond over change in the implied yield of futures contract. Yield beta = delta yield of bond / delta implied yield of futures

yield beta is beta, just like the beta for stock. it is the sensitivity of the price of a security to the changes in a benchmark price. This is about concept. conversion factor, as pointed above, is how many bad apples you need to give up for a good apple. it is about practice.

In checking over my potential calculations using either the ‘Conversion Factor’ or ‘Yield Beta’ I get the same result. Is it wrong to look at both concepts as an adjustment that is needed in order to sync the portfolio movement with the movement of the underlying future?

Conversion Factor: The Treasury future is based on delivering a \$100,000 par value bond yielding 6% and having a maturity of 15 years (I might be wrong on the exact maturity date). In practice, it can be hard to find a bond exactly like that, and so any Treasury bond with a maturity longer than (I think) 10 years is acceptable for delivery. That doesn’t mean, however, that \$100k of any of these bonds is equivalent to the \$100k/6%/15y contracted bond. The conversion factor is just a number you divide the price by in order to convert the value of another bond into an “equivalent” amount of \$100k/6%/15y bond. Yield Beta: When Treasury yields change, most yields move up or down more or less in sync. However, they may not move in an exact 1-1 relationship, particularly if the maturity of the bond you are trying to deliver is substantially different from the hypothetical \$100k/15y rate. The Yield Beta tells you how much your bond’s Yield changes, given a change in the benchmark bond’s yield. You will not need to compute Conversion Factors - they will be given to you if needed (and perhaps if not needed too). You will likely not need to compute Yield betas, although it’s possible that they might throw you a regression equation of CTD bond Yield vs. 15y yield, and then the Yield beta is just the regression coefficient (not the constant).

bchadwick, Thanks for your explanation. Refering to Example 11 on P.109 of Vol 4 text, can you advise if the CF of 1.1 is used to calculate the # of futures contracts just because CTD bond is used in denominator ? Is it that because non-CTD bonds are used in reading 42 so that no CFs are required to be multiplied ? Futhermore, is there any relationship between CF & Yield Beta (I mean if you know only the CF can you figure out the Yield Beta or vice versa) ? Your further advice is appreciated !

I don’t have the material in front of me, since I’m not taking the exam this year. So I don’t know the problem you’re referring to. As for whether there is a relationship between CF and Yield Beta, I’m sure there is some relationship, but it is probably fairly complex and in any case won’t be something required for the exam.

bchadwick, Anyway, thank you so much. I am very much surprised to know that you are not a current candidate but you are so kind to explain to us !

bchadwick, so helpful and you seem to really have a knack for explaining things so thank you! i think your name is familiar from level 2 forum too last year!