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  1. 076A Rs 100 crore bond portfolio has a modified duration of 5. What is its DV01, and roughly what does a 25 basis point rise in yields cost?Bond mathsWarm upFixed incomeRisk management

    Try it first

    Say the DV01 before you work it through.

    Show the worked solution

    DV01 is Rs 5 lakh, so a 25 basis point rise costs about Rs 1.25 crore. Modified duration of 5 means the value moves about 5% for each percentage point of yield, or 0.05% per basis point. 0.05% of Rs 100 crore is Rs 5 lakh, and 25 basis points is 25 times that.

    Why turn duration into rupees at all?

    A shopkeeper who says the rent went up 4% has told you something; one who says it went up Rs 2,000 a month has told you what to do about it. Duration is the percentage version. DV01, the rupee change for a one basis point move, is the version a desk can add across positions, compare with a limit and put in a risk report. Two portfolios with the same duration but different sizes carry very different rupee risk, and only DV01 shows it.

    Duration becomes rupees one basis point at a timePortfolio valueRs 100 croreModified durationx 5One basis pointx 0.0001DV01Rs 5 lakhA 25 basis point rise, notch by notch: each notch is another Rs 5 lakh lost0 bp05 bpRs 25 lakh10 bpRs 50 lakh15 bpRs 75 lakh20 bpRs 1.00 crore25 bpRs 1.25 croreLoss at 25 bp: 25 x Rs 5 lakh = Rs 1.25 crore, about 1.25% of the portfolio
    Rs 100 crore times a modified duration of 5 times 0.0001 is Rs 5 lakh per basis point, so a 25 basis point rise in yields takes Rs 1.25 crore off the portfolio, one Rs 5 lakh notch at a time.
    The relationship
    DV01=V×Dmod×0.0001=100×5×0.0001=0.05 crore\text{DV01} = V \times D_{mod} \times 0.0001 = 100 \times 5 \times 0.0001 = 0.05 \text{ crore}
    Vportfolio value, Rs 100 crore
    D_modmodified duration, 5
    0.0001one basis point written as a decimal
    What it says in wordsThe rupee move for one basis point is the value times the duration times one hundredth of one per cent.

    Where does the straight-line answer stop being right?

    The modified durationThe percentage change in a bond price for a one percentage point change in its yield, taken at the current yield. estimate is a tangent: it treats the price and yield relationship as a straight line. For 25 basis points the straight line is close enough, but for a 200 basis point shock the curve bends away from it and the true loss is smaller than DV01 times 200. That bend is convexity. Mention it in one sentence; the interviewer will often ask for it next.

    Say also that DV01 assumes every yield in the portfolio moves by the same amount. If short rates rise and long rates stay still, a single DV01 number misses it, which is why desks also keep DV01 by maturity bucket.

    Where candidates lose it

    The common slip is out by a factor of 100: treating duration 5 as 5% per basis point and saying Rs 5 crore. The interviewer hears that you have not held a real rate position, where the size of one basis point is the first thing you learn.

    The second loss is stopping at the number. Say that DV01 is linear, so it overstates the loss for large rises, and that it assumes a parallel move.

    What the interviewer asks next

    • The portfolio doubles in size and duration falls to 2.5. What is DV01 now?
    • How would you cut DV01 by half without selling any bonds?
    • Why might a desk set a limit in DV01 rather than in duration?