Yield Beta - Reading 28 Question 20

CFA Level III
#1

Hi all, Question on yield Beta. In Reading 28 question 20, the dollar amount is divided by the yield beta of 0.97 <=> 5.340.000/0.97 However, it is my understanding that if the yield beta <1 ==> The yield on the portfolio is less volatile ==> fewer futures contracts are needed. Then why is it that the portfolio value is divided by the yield beta (times futures price) and not multiplied? Thanks in advance! A

#2

The yield beta describes the futures contract; if the beta is less than 1 then the futures contract is less volatile than the bond itself, so you need more futures contracts, not fewer.

#3

I get it.

So going back to the fixed income part of the curriculum and the formula : (Dt-Dpf)/(Dctd) x [Ppf / Pctd] x Conversion factor x yield Beta,

The yield Beta in this formula describes the portfolio and not the CTD contract?

Thanks!

#4

Awesome! That’s the goal.

That’s correct. If you look in the middle of p. 222 in volume 5 of the curriculum, the formula is:

Δ_y_B = βy × Δ_y_f

Thus, the yield beta (βy) is the beta of the portfolio compared to the futures contract. In the problem you originally cited, they gave you the yield beta of the futures contract compared to the portfolio, which is the reciprocal of the beta of the portfolio compared to the futures contract. They were being sneaky; you have to be careful when you read the information given.

You’re quite welcome. I’m glad to help.

(In fact, you helped me, too. On my website I have an article on changing the beta of a bond portfolio using bond futures. In the formula I present, I multiply by the yield beta. Your question prompted me to edit that article to add a note that you need to be careful about which beta they give you, and multiply or divide by that beta accordingly.)

#5

Trust me, this doesn’t settle the bill. You helped my quite a bit more over the last 2 years. Thanks again.

#6

By default (except the case question gives explicitly a contrary definition of yield beta) , the yield beta is always the one in your formula, right?

#7

If they simply say yield beta, yes.

#8

Thank you :).

#9

D’accord.