Estimating market risk measures

Discussion in 'P2.T5. Market Risk (25%)' started by Imad, Jul 26, 2012.

  1. Imad

    Imad Member

    Hi David

    Hope you are well. Appreciate if you could explain below example taken from Qbank. I couldn't understand the relation btwn PVBP and VAR?

    Thanks
    Imad


    Question 11 - #29487
    The price value of a basis point (PVBP) of a $20 million bond portfolio is $25,000. Interest rate changes over the next one year are summarized below:
    Change in Interest rates
    Probability
    >+2.50%
    1%
    +2.00-2.49%
    4%
    0.00-1.99%
    50%
    -0.99-0.00%
    45%
    <-1.00%
    5%
    Compute VAR for the bond portfolio at 95 percent confidence level.
    A)
    $2,500,000.
    B)
    $2,750,000.
    C)
    $5,000,000.
    D)
    $12,500.
    The correct answer was C) $5,000,000.
    At 5% probability level change in interest rates is 2.00% or higher.Change in Portfolio value for 200 bps change in interest rate = 200*$25,000VAR = $5,000,000.
  2. Hi Imad,

    The question assumes that an adverse change to the value of the (long) bond portfolio is a increase in the interest rate (higher rate --> lower bond price), such that the worst expected 95/5% outcome is the +2% increase in the rate (e.g., the 99% worst would be the +2.5% increase). I find it easier to be flexible w.r.t 5% or 95% and just focus on: we want the adverse tail (causing a drop in value) and we can perceive the adverse tail as either 95% or 5%, which is here an (presumed!) increase in the rate (although notice a better question would specify the portfolio is long; if it were short, the worst expected 5%/95% would be a 1% rate drop.)

    I don't know why the probabilities don't appear to sum to 1.0 (part of the definition of a prob distribution is summation to 1.0)

    finally, PVBP (which is more commonly referred to as DV01 in the FRM, but they are the same) is the dollar increase associated with a one basis point decline (so it's approx equal to dollar decrease associated with a one basis point increase). There are 200 basis point in +2%. So answer is +2% * 100 bps/% * $25,000 change/bps. Thanks,
    • Agree Agree x 1
  3. Aleksander Hansen

    Aleksander Hansen Well-Known Member

    Just another example of why Bionic Turtle is superior in terms of practice questions:
    1) Correct answer
    2) More insightful and well thought through questions
    3) Rapid response, with an intuitive, easy-to-understand answer.
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