Portfolio Duration

To calculate, you must find the sum of the individual security durations. I have seen one problem where the weights are the par values, and one problem where the weights are the market values. Which one is correct?

by weights i mean (security par value)/(total portfolio par value) vs. (security market value)/(total portfolio market value

i would think market values… where did you see them calc’d at par? we maybe should work one of these type q’s out here soon. this is very testable.

Where do you see the need to calculate portfolio durations other than key rate durations? Just did a quick once over and didn’t see that in the fixed-income section.

Just found this - it seems as though it’s weighted by face value and asssumed that all bonds are priced at par: Carol Stephens, CFA, manages a relatively small portfolio for one of her clients. Stephens feels that interest rates will change over the next year but is uncertain about the extent and direction. She is confident, however, that the yield curve will change in a nonparallel manner and that modified duration will not accurately measure her portfolio’s yield-curve risk exposure. To help her evaluate the risk of her clients’ portfolio, she has assembled the table of rate durations shown below. Issue Value (\$1,000’s) 3 mo 2 yr 5 yr 10 yr 15 yr 20 yr 25 yr 30 yr Bond 1 100 0.03 0.14 0.49 1.35 1.71 1.59 1.47 4.62 Bond 2 200 0.02 0.13 1.47 0.00 0.00 0.00 0.00 0.00 Bond 3 150 0.03 0.14 0.51 1.40 1.78 1.64 2.34 2.83 Bond 4 250 0.06 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Bond 5 300 0.00 0.88 0.00 0.00 1.83 0.00 0.00 0.00 Part 1) What is the value of the portfolio if only 3 rates change while the others remain constant? The 3-month rate increases by 20 basis points. The 5-year rate increases by 90 basis points. The 30-year rate decreases by 150 basis points. A) \$1,038,925.00. B) \$1,009,469.00. C) \$961,075.00. Your answer: A was incorrect. The correct answer was B) \$1,009,469.00. Key Rate Durations Issue Value (\$1,000’s) weight 3 mo 2 yr 5 yr 10 yr 15 yr 20 yr 25 yr 30 yr Effective Duration Bond 1 100 0.10 0.03 0.14 0.49 1.35 1.71 1.59 1.47 4.62 11.4 Bond 2 200 0.20 0.02 0.13 1.47 0.00 0.00 0.00 0.00 0.00 1.62 Bond 3 150 0.15 0.03 0.14 0.51 1.40 1.78 1.64 2.34 2.83 10.67 Bond 4 250 0.25 0.06 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.06 Bond 5 300 0.30 0.00 0.88 0.00 0.00 1.83 0.00 0.00 0.00 2.71 Total Portfolio 1.00 0.0265 0.325 0.4195 0.345 0.987 0.405 0.498 0.8865 3.8925 Change in Portfolio Value Change from 3-month key rate increase: (20 bp)(0.0265) = 0.0053% decrease Change from 5-year key rate increase: (90 bp)(0.4195) = 0.3776% decrease Change from 30-year key rate decrease: (150 bp)(0.8865) = 1.3298% increase Net change 0.9469% increase This means that the portfolio value after the yield curve shift is: 1,000,000(1 + 0.009469) = \$1,009,469.00 This question tested from Session 14, Reading 54, LOS a Part 2) If the entire yield curve undergoes a parallel shift such that the rate at all key maturities increases by 50 basis points, what will the value of the portfolio be? A) \$1,019,462.50. B) \$961,075.00. C) \$980,537.50. Your answer: C was correct! Key Rate Durations Issue Value (\$1,000’s) weight 3 mo 2 yr 5 yr 10 yr 15 yr 20 yr 25 yr 30 yr Effective Duration Bond 1 100 0.10 0.03 0.14 0.49 1.35 1.71 1.59 1.47 4.62 11.4 Bond 2 200 0.20 0.02 0.13 1.47 0.00 0.00 0.00 0.00 0.00 1.62 Bond 3 150 0.15 0.03 0.14 0.51 1.40 1.78 1.64 2.34 2.83 10.67 Bond 4 250 0.25 0.06 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.06 Bond 5 300 0.30 0.00 0.88 0.00 0.00 1.83 0.00 0.00 0.00 2.71 Total Portfolio 1.00 0.0265 0.325 0.4195 0.345 0.987 0.405 0.498 0.8865 3.8925 Since the yield curve underwent a parallel shift, the impact on portfolio value can be computed directly using the portfolio’s effective duration. There are two methods that can be used to calculate effective duration in this situation. Both methods use the market weight of the individual bonds in the portfolio. As shown in the third column of the table above, the market weight of each bond equals: Bond value/Portfolio value, where the portfolio value is \$1,000,000. Method 1) Effective duration of the portfolio is the sum of the weighted averages of the key rate durations for each issue. The 3-month key rate durations for the portfolio can be calculated as follows: (0.10)(0.03) + (0.20)(0.02) + (0.15)(0.03) + (0.25)(0.06) + (0.30)(0) = 0.0265 This method can be used to generate the rest of the key rate duration shown in the bottom row of the table above and summed to yield an effective duration = 3.8925. Method 2) Effective duration of the portfolio is the weighted average of the effective durations for each issue. The effective duration of each issue is the sum of the individual rate durations for that issue. These values are shown in the right-hand column of the table above. Using this approach, the effective duration of the portfolio can be computed as: (0.10)(11.4) + (0.20)(1.62) + (0.15)(10.67) + (0.25)(0.06) + (0.30)(2.71) = 3.8925 Using an effective duration of 3.8925, the value of the portfolio following a parallel 50 basis point shift in the yield curve is computed as follows: Percentage change = (50 basis points)(3.8925) = 1.9463% decrease This question tested from Session 14, Reading 54, LOS a Part 3) What is the value of Bond 4 if 3-month rates remain constant and all other rates increase by 135 basis points? A) \$250,000.00. B) \$229,750.00. C) \$243,375.00. Your answer: A was correct! Key Rate Durations Issue Value (\$1,000’s) weight 3 mo 2 yr 5 yr 10 yr 15 yr 20 yr 25 yr 30 yr Effective Duration Bond 1 100 0.10 0.03 0.14 0.49 1.35 1.71 1.59 1.47 4.62 11.4 Bond 2 200 0.20 0.02 0.13 1.47 0.00 0.00 0.00 0.00 0.00 1.62 Bond 3 150 0.15 0.03 0.14 0.51 1.40 1.78 1.64 2.34 2.83 10.67 Bond 4 250 0.25 0.06 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.06 Bond 5 300 0.30 0.00 0.88 0.00 0.00 1.83 0.00 0.00 0.00 2.71 Total Portfolio 1.00 0.0265 0.325 0.4195 0.345 0.987 0.405 0.498 0.8865 3.8925 Since the 3-month rate did not change, and all other key rate durations for Bond 4 are zero, a 135 basis points change will have no effect on the value of the bond. Hence, Bond 4 remains valued at \$250,000.00

So reading through that, it’s the market weight of the different bonds in the portfolio.

what qbank # is that? i want to review it tomorrow when i’m less tired.

I would NEVER post copyrighted material online - I made that question up myself. Email me if you’d like me to send it to you: skillionaire@87996.com All right, enough silliness, time to watch Slumdog Millionaire…g’night all.

i don’t think anyone cares if you post one q here and there. just not the whole qbank here fast and furious and possibly call it a lunch crunch. let me phrase this differently… what’s your favorite number?

I completely forgot about the KRD’s. Banni plz drop his fvt number on my G chat, I would like to know too.

The example I saw where the weights are market values was a vignette (q 8 8 4 3 5). Where it is done as a % of par value is below: Given the following information, which bond has the greater interest rate risk and what is the change in price if rates increase by 50 basis points? Par Market Price PVBP per \$1,000 par value Bond A 2,000,000 1,987,500 0.885 Bond B 7,000,000 8,588,250 1.025 A) Bond B, change in price = - \$88,500. B) Bond B, change in price = - \$358,750. C) Bond A, change in price = - \$358,750. Your answer: A was incorrect. The correct answer was B) Bond B, change in price = - \$358,750. PVBP (price value of a basis point) is the absolute value of the change in bond value for a 1 basis point change in yield. Change in price = -PVBP × change in basis point x par in thousands Bond A = -0.885 × 50 × 2,000 = -88,500 Bond B = -1.025 × 50 × 7,000 = -358,750

nevermind

Sorry if the joke didn’t come through last night, Qbank number is 87996.

i dont think the CFAI will make us decide between the two. if it does, then i’m going with par value.

Fully agreed, niraj_a.

Since most of the problems are conceptual anyway, I suspect that CFAI will probably test your knowledge of parallel vs. non-parallel shifts for a portfolio.

@skill: Thanks for the great set of questions. It really helps solidify the understanding of the concepts and the relationships between effective and key rate duration in the context of a single security as well as in the context of a portfolio. I.e. this helps you learn as opposed to just memorizing! Thumbs up to you!

As much as I’d love to take credit, that was a simple copy and paste. Thanks though.

what do you think about Slumdog Millionaire?

Freida Pinto is cheating on her husband with Dev Patel. I googled all of this one night after a poor study session with Mr. Schweser & Friends