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Thread: need help with a Tbill question

  1. #1
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    need help with a Tbill question

    Here it says
    Price of stock is 100.
    The stock pays discrete dividend of 2 per quarter starting the next 3 months.
    Continuously compounded rate is 4%
    We want to create a 182 day of synthetic T bill with maturity value of 10000, with K = 95.

    We need to find how many shares of stock we need to buy.

    I dont quite follow the solution given. Any help?
    I used 10000/95 = 105.263
    105.263 - 2*exp(-0.04*3/12) - 2*exp(-0.04*6/12) - 2*exp(-0.04*9/12) - 2*exp(-0.04*12/12) and the result is different from the one given by the solution which is 100.99.

  2. #2
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    Quote Originally Posted by johnlu66 View Post
    Here it says
    Price of stock is 100.
    The stock pays discrete dividend of 2 per quarter starting the next 3 months.
    Continuously compounded rate is 4%
    We want to create a 182 day of synthetic T bill with maturity value of 10000, with K = 95.

    We need to find how many shares of stock we need to buy.

    I dont quite follow the solution given. Any help?
    I used 10000/95 = 105.263
    105.263 - 2*exp(-0.04*3/12) - 2*exp(-0.04*6/12) - 2*exp(-0.04*9/12) - 2*exp(-0.04*12/12) and the result is different from the one given by the solution which is 100.99.
    Wasn't your question answered here: http://www.actuarialoutpost.com/actuarial_discussion_forum/showthread.php?t=247403 ?

  3. #3
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    it didn't not explain thoroughly so....sighs....thought there would be a more constructive answer~

  4. #4
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    Quote Originally Posted by johnlu66 View Post
    it didn't not explain thoroughly so....sighs....thought there would be a more constructive answer~
    I'm confused by what you wrote down originally. You say it's a 182 T-Bill so why are you subtracting dividends at times t= 1/4, 1/2, 3/4 and 1?

  5. #5
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    Quote Originally Posted by NoMoreExams View Post
    I'm confused by what you wrote down originally. You say it's a 182 T-Bill so why are you subtracting dividends at times t= 1/4, 1/2, 3/4 and 1?
    I think you were right but if i use 105.263 - PV of div, i still get
    105.263-2 - 2*exp(-0.04*3/12) if i m not wrong this time, but i get 101.283 and still not 100.99 as my result.

    any help?!

  6. #6
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    Quote Originally Posted by johnlu66 View Post
    I think you were right but if i use 105.263 - PV of div, i still get
    105.263-2 - 2*exp(-0.04*3/12) if i m not wrong this time, but i get 101.283 and still not 100.99 as my result.

    any help?!
    I haven't checked your calcs. but why are you having dividends a time 0 and 1/4 now? You are told that the first dividend is paid 3 months from now.

  7. #7
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    you mean 105.263-2*exp(-0.04*3/6) - 2*exp(-0.04*6/6) ?

    it is still not 100.99

  8. #8
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    Quote Originally Posted by johnlu66 View Post
    you mean 105.263-2*exp(-0.04*3/6) - 2*exp(-0.04*6/6) ?

    it is still not 100.99
    That would be discounting at time 1/2 and time 1. You are told that you are standing at t = 0 and you have dividends coming at 3 months from now and every quarter. It's a 182 day t-bill so how many quarters do you have?

  9. #9
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    For 182 days there should be 2 quarters? I m just so confused now so. To discount the div for the 1st quarter is it 2*exp(-0.04*3/12)?

  10. #10
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    Yes. And for the 2nd quarter? You might want to review FM material for this kind of stuff, maybe that would help clear it up.

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