Case 007Fixed income and creditWarm up

A fund holds Rs 40 crore of a 2-year government bond (duration 1.9), Rs 35 crore of a 5-year (4.4) and Rs 25 crore of a 10-year (7.6). Compute portfolio duration and DV01, show two ways to raise duration to 5.5, and the P&L of a 50 bp fall in yields.

PIMCOLos Angeles · 2026

The situation

Ketakivan Fixed Income runs a Rs 100 crore government bond portfolio: Rs 40 crore of a 2-year bond with modified duration 1.9, Rs 35 crore of a 5-year with duration 4.4 and Rs 25 crore of a 10-year with duration 7.6. The investment committee expects yields to fall and wants the portfolio's duration raised to 5.5.

Your task

What are the portfolio's duration and DV01 today, what are two ways to reach 5.5, and what does a 50 bp fall in yields earn before and after?

Quick check

What is the portfolio's duration today?

Worked solution

Try it on paper, then open one step at a time.

30-second answerThe answer to give first

Duration is 4.2 years and DV01 is Rs 4.2 lakh per basis point. A 50 bp fall earns about Rs 2.1 crore. To reach 5.5, either sell Rs 22.8 crore of 2-years and buy 10-years, or keep the bonds and buy 10-year bond futures worth about Rs 17.1 crore of notional. At 5.5 the same 50 bp fall earns about Rs 2.75 crore, and a 50 bp rise loses about as much.

Step 1How do you get portfolio duration from three bonds?

Weight each bond's modified durationThe percentage change in a bond price for a 1 percentage point change in its yield, with the sign flipped. A duration of 4 means a 1 point rise in yield cuts the price by about 4%. by its share of the money. Portfolio duration is the value-weighted average: 0.76 from the 2-year, 1.54 from the 5-year and 1.90 from the 10-year, which is 4.2. It works like the average age of a household: the result leans towards whoever there is most of. The 10-year is only a quarter of the money but contributes the most duration, 1.90 of the 4.2.

The relationship

D_p = \sum_i w_i D_i = 0.40(1.9) + 0.35(4.4) + 0.25(7.6) = 4.2 \qquad \text{DV01} = 100\text{ cr} \times 4.2 \times 0.0001 = \text{Rs } 4.2\text{ lakh}

w_i	share of portfolio value in bond i
D_i	modified duration of bond i
DV01	rupee change in value for a 1 basis point change in yields

What it says in wordsPortfolio duration is the value-weighted average of the bonds' durations, and DV01 is value times duration times one basis point.

Step 2What are the two ways to reach 5.5, and what does each cost?

You need 1.3 more years of duration, which on Rs 100 crore is Rs 1.3 lakh more DV01. The first way is to switch: each crore moved from the 2-year to the 10-year adds 5.7 years on 1% of the portfolio, so moving Rs 22.8 crore does it. The second is an overlay: keep every bond and buy 10-year bond futures. Treating the future as carrying the 10-year's duration of 7.6, you need about Rs 17.1 crore of notional. Confirm the contract size and the cheapest-to-deliver bond's duration on the exchange before sizing a real trade.

Portfolio duration of 4.2 is the sum of 0.76 from the 2-year, 1.54 from the 5-year and 1.90 from the 10-year; switching Rs 22.8 crore of 2-years into 10-years or adding Rs 17.1 crore of 10-year futures each lifts it to the 5.5 target.

The costs differ. The switch pays bid-offer on two bond trades, may realise gains or losses for tax and accounting, and gives up the 2-year's yield for the 10-year's. The futures overlay costs little to put on and is easy to reverse, but needs margin, must be rolled every contract month, and adds basis risk: the future tracks its cheapest-to-deliver bond, not exactly your 10-year. For a tactical view the committee may reverse in weeks, the overlay is usually the cleaner tool.

Step 3What does a 50 bp fall in yields earn, before and after?

Multiply DV01 by the move. Today, 50 bp times Rs 4.2 lakh is Rs 2.1 crore; at duration 5.5 it is Rs 2.75 crore. Convexity adds a little on top for a fall and takes a little less off for a rise, but at 50 bp the duration estimate is close. The honest half of the answer is the mirror image: raising duration to 5.5 also raises the loss from a 50 bp rise from about Rs 2.1 crore to about Rs 2.75 crore. The committee is not buying return, it is buying more exposure to being right or wrong about yields.

Position	Duration	DV01, Rs lakh	50 bp fall, Rs crore	50 bp rise, Rs crore
Today	4.2	4.2	+2.10	-2.10
At target	5.5	5.5	+2.75	-2.75

Raising duration from 4.2 to 5.5 lifts DV01 from Rs 4.2 lakh to Rs 5.5 lakh, so a 50 bp move in either direction is worth about Rs 2.75 crore instead of Rs 2.10 crore, ignoring convexity.

Where candidates lose it

The usual loss is averaging the three durations without weights, 4.6, which ignores that the portfolio holds most of its money in the shortest bond.

The second is presenting a higher duration only as more return when yields fall. The interviewer is asking what changes, and the answer is sensitivity in both directions, plus the cost of each way of getting there.

What the interviewer asks next

How would you raise duration while keeping the 2-year holding intact and not using futures?
The curve steepens rather than shifts. Which of the two routes to 5.5 does better?
What is the convexity adjustment for a 50 bp move on the 10-year, roughly?

Asked at PIMCO, Generalist, Los Angeles, 2026 (Wall Street Oasis): Given a portfolio of these 3 bonds (I forgot exactly what they were) explain how the portfolio changes if duration increases.

Company names and figures are illustrative.