Questions on pure discount bond yield.?

Suppose you buy a 30-tear pure discount bond with a face value of 00 and a yield of 6% per year. A day later, market interest rates rise to 7% and so does the yield on your bond. What is the proportional change in the price of the bond?

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One Response to “Questions on pure discount bond yield.?”

  1. Aha! says:

    a 30 tear pure discount bond? Must be a very sad bond.

    There are a number of things I can do here depending on your level of study.
    Normally bonds are discounted on a semiannual basis. i.e. 60 periods in your case.
    although the question says it’s only a day later, so the effect on the day’s difference is tiny, fixed income analysts can be a bit picky about it as can say the new discounting period is 29 and 364/365 years.

    Presuming the question is asking you to discount on an annual basis i.e. 1 period per year, and the day’s change is negilible…
    at 6% yield, price is…1000/(1.06)^30 = 174.11
    at 7%: 1000/(1.07)^30 = 131.37
    proportional change: 131.37/174.11 = 75.45% i.e. the value of the bond has dropped by 24.55%, almost a quarter of its former value

    If it’s a semiannual basis and the day’s change is negilible…
    6% yield: 1000/1.03^60 = 169.733
    7%: 1000/1.035^60 = 126.934
    proportional change: 126.934/169.733 = 74.78% i.e. the value of the bond has dropped 25.22%, just over a quarter of its former value

    With the other 2 alternatives, you’re looking at a time period of 29.99726 if the discounting period is annual; 59.99452 if the discounting period is semiannual. Yield is 6 and 7% if annual; 3 and 3.5% if semiannual. However, I don’t think the person examining on this question will be that picky.

    Hope this helps

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