# Need some urgent help

#### Nakamura

##### Newbie
8 0
hi i am studying an ACI dealing certificate and I am stuck with one question I would very much appreciate any assistance.

The question is as follows:

You buy a US treasury bill 176 days before it matures when it was quoted at 7.0%/7.1% and sell it again when it is quoted at 6.6%/6.7% after holding it for 64 days. What yield have you achieved over the 64-day investment period, on a 365 day basis?

#### scose-no-doubt

##### Veteren member
4,630 954
you factor in capital gain?

#### Nakamura

8 0

##### Senior member
2,620 264
T-Bills are discount securities. Figure out the initial price and the sales price, then divide the difference by the former and annualize if that's what the problem requires.

#### Nakamura

##### Newbie
8 0
T-Bills are discount securities. Figure out the initial price and the sales price, then divide the difference by the former and annualize if that's what the problem requires.
I think you are supposed to figure out the yeild in a percentage by using only the information given so therefore I'm not sure there's any way to find out thr initial price or sales price it it wasn't given.

#### Jerry Westerby

##### Member
91 6
I think you are supposed to figure out the yeild in a percentage by using only the information given so therefore I'm not sure there's any way to find out thr initial price or sales price it it wasn't given.
quoted at 7.0/7.1

makes a t-bill price of

100 x 0.07 x 176/365 = 3.375%
true interest = 3.375/9100 - 3.375) = 3.493%
price = 100/103.493 * \$100 = \$96.62

similarly for 7.1% gives \$96.58

so price is \$96.58/62... and you bought, so paid the offer of \$96.62

i think

##### Senior member
2,620 264
I think you are supposed to figure out the yeild in a percentage by using only the information given so therefore I'm not sure there's any way to find out thr initial price or sales price it it wasn't given.
You have no choice but to derive the buy and sell prices from the information provided. That's the only way you can calculate your return.

#### Nakamura

##### Newbie
8 0
quoted at 7.0/7.1

makes a t-bill price of

100 x 0.07 x 176/365 = 3.375%
true interest = 3.375/9100 - 3.375) = 3.493%
price = 100/103.493 * \$100 = \$96.62

similarly for 7.1% gives \$96.58

so price is \$96.58/62... and you bought, so paid the offer of \$96.62

i think
That makes allot oF sense but how would u go from 96.58 dollers to a yeild of 7.90%

#### Jerry Westerby

##### Member
91 6
That makes allot oF sense but how would u go from 96.58 dollers to a yeild of 7.90%
the actual numbers I used are probably off a bit. Like t-bills use 360 day count, not 365. but that's the general idea.

use the quoted yields to find out the cash price, for both trades - buying them at the offer and selling them at the bid 64 days later. find out what return you got on your 64 day investment, and express that on a 365 basis.

#### Nakamura

##### Newbie
8 0
You have no choice but to derive the buy and sell prices from the information provided. That's the only way you can calculate your return.
That may be true but as far as I'm aware the formula to find the yeild for such a question is: discount rate/(1 - (discount rate x days/years))

And using that formula I am unable to get to 7.90%

##### Senior member
2,620 264
That's not the right formula for the return you're after.

As I said, first find the price of the Bill at the two points in time. Divide the bigger by the smaller to get the nominal return - something like 1.03. Take that number and annualize it by raising it to the power of (365/n) where n is the number of days held. Then subtract 1.

It would look like this: (P2/P1)^(365/n)-1

Where P1 and P2 are price at time 1 and 2 respectively.

#### Nakamura

##### Newbie
8 0
That's not the right formula for the return you're after.

As I said, first find the price of the Bill at the two points in time. Divide the bigger by the smaller to get the nominal return - something like 1.03. Take that number and annualize it by raising it to the power of (365/n) where n is the number of days held. Then subtract 1.

It would look like this: (P2/P1)^(365/n)-1

Where P1 and P2 are price at time 1 and 2 respectively.
Mate you are an complete legend thank you very much!! Well appriciated I was finally able to get the 7.90% answer:clap:

#### Nakamura

##### Newbie
8 0
That's not the right formula for the return you're after.

As I said, first find the price of the Bill at the two points in time. Divide the bigger by the smaller to get the nominal return - something like 1.03. Take that number and annualize it by raising it to the power of (365/n) where n is the number of days held. Then subtract 1.

It would look like this: (P2/P1)^(365/n)-1

Where P1 and P2 are price at time 1 and 2 respectively.
Actually I think that celebration may have been a little premature. Using the formula from above an driving the sale prices of the t-bills using 360 day basis and thne anualising it to a 365 basis I have come up have come up with the answer 7.636% which isn't a million miles away from 7.90% in real turn but mathamatically speaking its quite a way off so I am officially bamboozled because the examples of this sort of question in the study matieral are much more simple

For example one is as follows:

A UK tresury bill with remaining maturity of 70 days is quoted at a disxount rate of 7.1%. What is the equivalent yield. And the answer they have given is:

7.1%/(1 - (0.071 x 70/365)) = 7.198%.

So I am well an truely lost. Thank you for trying to help. As I'm sure by now your probably just as confused as I am, and appologise for being a pain in the preverbials!!

##### Senior member
2,620 264
Have you tried using the pricing/yield functions built into Excel?

And keep in mind that annualizing your rate of return isn't the same as pricing out (or deriving the yield of) a Bill.

#### Nakamura

##### Newbie
8 0
Have you tried using the pricing/yield functions built into Excel?

And keep in mind that annualizing your rate of return isn't the same as pricing out (or deriving the yield of) a Bill.
To be honest with you no I haven't tried the pricing/yeild function on excel mainly because because of the exam that will need to be taking for the aci dealing certificate I am going to have to learn how to do this with a calculator an a formula so as you can imagine I'm a little frustrated right now