# FI SS8 Portfolio Dollar Duration Schweser vs CFAI

CFAI book Volume 3 for SS6-8 Page 340 states that a portfolio’s dollar duration is a weighted average of the dollar durations of the component securities Conversely, Schweser Book 3 page 25 states unlike the duration of the portfolio, which is a weighted average of the individual bond durations, the dollar duration of the portfolio is the sum of the individual dollar durations. What is the right one, CFAI solves all the problems using a weighted average but schweser sums the DDs. Any thoughts?

I think you could look at it both ways but Schweser’s is much more natural. Suppose that you had a \$1Million portfolio of ten bonds, you could get the dollar duration of the portfolio by summing the dollar durations of a million dollars worth of each bond times its weight in the portfolio. This would look like a weighted average and would be the same as Schweser’s

I see what you are saying, but schweser simply does’t weight it by market value…

Hmm… Are the definitions equivalent so this is a semantic discussion or do they really give different results?

The results are completely different…

I think I ran in to the same thing and asked it on here a little while back. looks like the are equal weighting them: http://www.analystforum.com/phorums/read.php?13,628291,628703#msg-628703

errata update! CFAI realized this is an error and revised “the weighted average…” to “the sum of …” It wasted me half an hour yesterday to be confused by this! http://www.cfainstitute.org/cfaprog/resources/pdf/Level_III_Errata.pdf “Study Session 8, Reading 27: On p. 340, the text immediately above Example 6 should be changed to say, “A portfolio’s dollar duration is equal to the sum of the dollar durations of the component securities” (instead of “a weighted average”). As a result of this correction, the calculated dollar durations in Examples 6 and 7 should be \$111,945 and \$82,579 respectively.”

However this brings me to another question related to example 6&7 on CFAI volume book3 page 341. A t the bottom paragraph about “controlling position”. It says we could use bond 2 as our controlling position. Bond 2 has the shortest duration, so by selling a portion of this bond position, we would in effect lengthen our portfolio duration. Then it says, the bond2 position must be reduced by approx. 87% in order to bring the portfolio dollar duration back to its original value. How could it be? after one year, all the bond’s duration has declined and how reduce the bond 2 even with the shortest duration could bring portfolio DULLAR DURATION back to its original value? Maybe I’m too dump and I just didn’t get it. While in Schweser notes bk3 page 28, it use bond 1 with the longest duration as controling position. By increasing the holding in bond 1, it returns the portfolio dollar duration back to its original level. This makes much sense to me!!! You can only increase the bond holding but not selling in order to brings the portfolio dollar duration back to it’s original value as time passes. Am I right?

B/c Bond 2 has the Shortest duration and is probably a large % of the overall portfolio weight, thus bringing down teh overall Dollar Duration. If you decrease the % from say 50% to 10% and spread that capital over the other issues you have now increased the portfolios dollar duration.

I see what you are saying, you are assuming increase the holdings for other bonds besides selling bond 2 so the portfolio dollar duration could still come back to its original value. But I thought the book is referring to reduce Bond 2’s holding only (that’s what controlling position is about, right?) not by increasing other bonds. And also, how this 87% reduction for Bond 2 is calcuated?

It solved via: DDportfolio = DD1W1 + DD2W2 + DD3W3 +…+DDnWn. Use algebra to solve. Also, let me correct myself you don’t buy new bonds, you maintain the positions and only adjust the “controlling” position. You can also use derivatives to adjust dollar duration.

You posted effective duration’s formula not dollar duration’s for portfolio. Although they look similiar. the calculation will be slightly differ. According to both schweser and CFAI’s errta updtae, DDportfolio=DD1+DD2+DD3+…+DDn DDbond=market value*duration*0.01 I don’t mean you should buy new bonds, I mean you could increase the holdings of your existing bonds with higher duration. I don’t know how you could bring DDportfolio back by just adjusting controlling position (I would guess you mean the weight of bond 2) while not adjusting other existing bond’s weights. How math works? if you sell bond 2, DD2 is dropped because the market value is decreased. Without adjust DD1 or DD3’s holdings, how could you still remain the equation balance? I guess the only possible answer is to increase holdings for either bond 1 or 2 combined by selling bond 2 to bring back porfolio dollar duratoin.

LOL! Good thing i found this thread, i was going over CFAI text and was going nuts!