Yield for Treasury Bill
- Thread starter Ludwma
- Start date
FS -
I am grateful for your business, we are delighted to be able to get paid for learning finance with you. But you don't need to re-push the question stack to me.
This is a forum and this forum is "best efforts" and I am not your personal concierge (we can agree that deserves a higher price than you've paid?). The vast majority of our customers are adults with manners and a general awareness who understand that I am also working on source content, and that, being, you know, human, I get to the questions as best I can.
I am aware of outstanding questions, I always do my best to address all of them; e.g., this weekend, while working both days in order to prep the T2 & T6 videos, I will be answering questions and, I hope, catching up on the backlog.
But your (you, you personally, repeated) efforts to add to my stress are not entirely appreciated.
Thank you for your understanding.
I am grateful for your business, we are delighted to be able to get paid for learning finance with you. But you don't need to re-push the question stack to me.
This is a forum and this forum is "best efforts" and I am not your personal concierge (we can agree that deserves a higher price than you've paid?). The vast majority of our customers are adults with manners and a general awareness who understand that I am also working on source content, and that, being, you know, human, I get to the questions as best I can.
I am aware of outstanding questions, I always do my best to address all of them; e.g., this weekend, while working both days in order to prep the T2 & T6 videos, I will be answering questions and, I hope, catching up on the backlog.
But your (you, you personally, repeated) efforts to add to my stress are not entirely appreciated.
Thank you for your understanding.
Hi FS,
169.4 is trick because it combines two steps. Money market instrument use so-called discount rates, which are not "true" rates of return. In this case, the quote of a Treasury is 9.0 and this means that the interest earned is 9.0% of the face value per 360 days. In the case of a 180-day T-bill, this QUOTE of 9.0 implies 9%*100*180/360 = $4.5 of interest earned per $100 face; 4.5% over 180 days = 9.0% over 360 days.
Since the T-bill will be redeemed at face of $100, the price is 95.50 (100 - 4.5); in this way, we can pay $95.50 today, in order to get back $100.00 in 180 days, for a return of 4.5% on the $100 face value; or 9.0% on an "annualized" basis. This is the convention.
However, if you pay 95.50 to earn $4.50, your "true" return (Hull's word choice) is your SIMPLE return = 4.50/95.50 = (100-95.50)/95.50 = 4.712% over the 180 days. So, the "true yield" is what we elsewhere call the simple return; i.e., the return without regard to compounding or period. My question reads "True (Effective)" but I'm not sure I like "Effective" on reflection. I think "simple return" may be a better synonym to Hull's "true."
That's the first step: the translation of a by-convention quote ("discount rate") of 9.0 into the "true" return of 4.712%.
The second step just performs converts this simple ACT/360 to continuously compounded ACT/365 per: R(continuous) = m*LN(1 + Rm/m), where m would be 2 if we weren't changing day counts; i.e., if act/360 were maintained, then R(continuous) = 2*LN(1+4.5/95.50) is the answer. Instead, to translate the day count, (m) is slightly above 2 = 365/180. I hope that explains it!
169.4 is trick because it combines two steps. Money market instrument use so-called discount rates, which are not "true" rates of return. In this case, the quote of a Treasury is 9.0 and this means that the interest earned is 9.0% of the face value per 360 days. In the case of a 180-day T-bill, this QUOTE of 9.0 implies 9%*100*180/360 = $4.5 of interest earned per $100 face; 4.5% over 180 days = 9.0% over 360 days.
Since the T-bill will be redeemed at face of $100, the price is 95.50 (100 - 4.5); in this way, we can pay $95.50 today, in order to get back $100.00 in 180 days, for a return of 4.5% on the $100 face value; or 9.0% on an "annualized" basis. This is the convention.
However, if you pay 95.50 to earn $4.50, your "true" return (Hull's word choice) is your SIMPLE return = 4.50/95.50 = (100-95.50)/95.50 = 4.712% over the 180 days. So, the "true yield" is what we elsewhere call the simple return; i.e., the return without regard to compounding or period. My question reads "True (Effective)" but I'm not sure I like "Effective" on reflection. I think "simple return" may be a better synonym to Hull's "true."
That's the first step: the translation of a by-convention quote ("discount rate") of 9.0 into the "true" return of 4.712%.
The second step just performs converts this simple ACT/360 to continuously compounded ACT/365 per: R(continuous) = m*LN(1 + Rm/m), where m would be 2 if we weren't changing day counts; i.e., if act/360 were maintained, then R(continuous) = 2*LN(1+4.5/95.50) is the answer. Instead, to translate the day count, (m) is slightly above 2 = 365/180. I hope that explains it!
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