Please correct me if I’m wrong: Bond KRD = bond value % change for 1% change in the key rate Bond Effective Duration = sum of the KRDs Portfolio KRD = sum of WEIGHTED KRDs for all bonds in the portfolio Portfolio Effective Duration = sum of portfolio KRDs I have some difficulty in understanding this: Effective Duration = sum of the KRDs Let’s say I have only one zero-coupon bond matured in 2.5 years, ED=2.5 How do the KRDs look like? The key rates are 3mo, 1 year, 3 years, 10 years.
If you only have one zero-coupon bond, then you only have one key rate duration. The question might provide more KRDs, but there is a zero weighting to those KRDs in the portfolio. 100% weighted to the one zero that you own.
Thanks. So, the KRDs values could depends on the number of key rates defined, and usually the KRDs around the maturity date have higher values. In other words, if I changes the number of key rates from 4 to 11, those related KRDs could change. It may have some yield curve “smoothing” also, I think. Overall, effective duration is an approximation, the same for KRDs.
KRDs around the maturity date will NOT have higher values. Think of a 1 year zero vs. a 30 yr zero: the 30 year is more volatile (moves more with int rates). I think you can forget about “changing the number of key rates.” Not sure what you’re saying. You have holdings in a portfolio that each have 1 key rate duration. If you have 10 holdings, then you have 10 krds. The eff duration is the weighted avg of the krds (weight the positions in the portfolio). Maybe I don’t understand the confusion…
I get confused again here. Effective duration is the simple sum of all KRDs, for either a single bond or the whole portfolio – No weight stuff here.
So suppose there are 3 bonds B1, B2 & B3 in a portfolio with weights wb1, wb2 & wb3. Say the key rates for our interest is 2y, 5y and 30y. Method 1: ======= wb1*krd(2y) + wb2*krd(2y) + wb3*krd(2y) + wb1*krd(5y) + wb2*krd(5y) + wb3*krd(5y) + wb1*krd(30y) + wb2*krd(30y) + wb3*krd(30y) = Portfolio effective duration. Method 2: ======= wb1*ED(2y) + wb2*ED(5y) + wb3*ED(30y) = Portfolio effective duration. Where ED(2y) = SUMMATION(krd(2y)) ED(5y) = SUMMATION(krd(5y)) ED(30y) = SUMMATION(krd(30y))
That’s exactly where my question came from. I think the weight is from the weight of the bond, not the weight of the KRD. Method 2: ======= wb1*ED1 + wb2*ED2 + wb3*ED3 = Portfolio effective duration Where ED1 = SUMMATION(krd(2y)+krd(5y)+krd(30y)) for bond 1 ED2 = SUMMATION(krd(2y)+krd(5y)+krd(30y)) for bond 2 ED3 = SUMMATION(krd(2y)+krd(5y)+krd(30y)) for bond 3 (Perhaps you mean ED(2y) = rate duration as shown in the schweser notes). The samples in CFAI and Schweser both use only zero-coupon bonds, so its formula looks like: Portflio ED = wb1*krd(2y) + wb2*krd(5y) + wb3*krd(30y). But for a general situation, “pacmandefense” posted a link for visual explanation: http://pic18.picturetrail.com:80/VOL894/4332674/9130502/360722643.jpg in the discussion: http://www.analystforum.com/phorums/read.php?12,931191,932620#msg-932620
This will be valid when you have only 1 bond in the portfolio with many key rates (in your case - 3 key rates - 2y, 5y and 30y). Then it’s correct to say this Portflio ED = wb1*krd(2y) + wb2*krd(5y) + wb3*krd(30y).
I can give up 
and believe we will get the same portfolio ED in the exam as long as only zero-coupn bonds are in the portfolio. For a portfolio with one and only one zero-coupon in it, and KRDs for 2y, 5y and 30y, Portflio ED = wb1*ED1= 1.00*(krd(2y) + krd(5y) + krd(30y)). The weight wb1 = (bond’s market value) / (portfolio market value). Not quite understand what wb2 means in your formula: Portflio ED = wb1*krd(2y) + wb2*krd(5y) + wb3*krd(30y).
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