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# Thread: need help with a Tbill question

1. ## 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. Originally Posted by johnlu66
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.

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

4. Originally Posted by johnlu66
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. Originally Posted by NoMoreExams
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. Originally Posted by johnlu66
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. you mean 105.263-2*exp(-0.04*3/6) - 2*exp(-0.04*6/6) ?

it is still not 100.99

8. Originally Posted by johnlu66
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. 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. 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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