# Question on Yld beta or Conversion Factor

When do you use yld beta or when do you use conversion factor if both is given. Ex. Trying to modify the duration to 5 while my current portolio is 8 and Market Value is \$100 Million. The US Treasury Futures contract to be used has a duration of 6 priced at \$100,000. The conversion factor for the CTD bond is 0.90 and the yield beta is 1.2 What is the number of contracts needed to change the duration?

short 540?

It should be 450 contracts, why i need someone to explain why it’s not 600 contracts

It should be 450 contracts, but i need someone to explain why it’s not 600 contracts

Alright book says that yield beta for adjusting duration is that you are typically using treasury futures to adjust the duration of a non-treasury bond portfolio.

so basically you didn’t multiply it with yield beta. Why? I believe for bond, you do calculate it with yield beta Formula is 5-8/6 X 100M/100K/0.90 = -450

I Believe the formula is (5-8)*100MM/6*100K*0.9*1.2 5 represents the target duration, 8 the current portfolio duration, 100MM is value of the portfolio, 6 is duration of the futures contract, 100K the value of each future contract, CTD=0.9, Yield Beta is 1.2 The above equals to around 462 which is close to the 450 answer you refer to in the post. Short 462 contracts

BTN - your calculation doesn’t make sense. I am getting 540

My bad, THe forumal for number of contract is (Yield Beta*(Duration Target-Portfolio Duration)*Value of portfolio)/(duration of future*price of future*multiplier) Where duration is modified duration, multiplier is CTD. 1.2*(5-8)*100MM/(6*100K*0.9) =667 contracts (short). Apologize for the earlier post.

My bad, THe formula for number of contract is (Yield Beta*(Duration Target-Portfolio Duration)*Value of portfolio)/(duration of future*price of future*multiplier) Where duration is modified duration, multiplier is CTD. 1.2*(5-8)*100MM/(6*100K*0.9) =667 contracts (short). Apologize for the earlier post.

BTN again - you do not multiply 0.9 with 100K. You need to divide here

If the bond to be hedged is the same as the CTD bond then… ((5-8)/6)*(100M/0.1M)*0.9 = - 450 If the bond to be hedged is different from the CTD bond then… ((5-8)/6)*(100M/0.1M)*0.9*1.2 = - 540. because you need to multiply by yield beta to account for the yield difference

B_C - How would you know whether it is going to be hedged same or different from the CTD in the above problem?

I am sorry AFers, seems like I muddied the waters so to speak. I was referring to my notes and I seem to have possibly written the formula incorrectly. Is there a reference in the CFAI text with the correct formula. TIA. Apologize again.

Has whystudy posted all details on the question ? I guess it should say in the question.

check SS 15 - Futures section in Book 5 for correct formula

cfaboston28 Wrote: ------------------------------------------------------- > Alright book says that yield beta for adjusting > duration is that you are typically using treasury > futures to adjust the duration of a non-treasury > bond portfolio. Treasury and non-treasury bond portfolio will react slightly different to interest rate change. When use Treasure future to hedge non-treasury bond, it is a cross hedge, not a 100% prefect hedge, however , still the best one available in market. There is probably not exactly future of the bond portfolio. the yield beta reflects the different reaction between them, and should be applied in this case. When hedging a pure treasury portfolio w/treasury future, the yield beta is not needed.

To summarize… If the bond to be hedged is different from the CTD bond then you need yield beta. If the bond to be hedged is different from the bond underlying the futures then you need yield beta. because you need to account for the yield change difference. Yield beta = % change of yield of bond to be hedged/ % change of yield of CTD bond.

whystudy Where is this Q from?? I think cfaboston is correct. You do need to multiply with yield beta. It is shown on pg. 120 CFA V4. Schwezer V1 practice exam3 PM Q18.4 also confirms that.

Conversion factor is determined by pricing the deliverable as if it had a 6% coupon ( cheapest to deliver bond on future) Conversion factor = price at 6% / current price Yield beta is a modifier which is like a regression between a bond and a future. If the underlying and the future are identical there is no need to use Yield beta