What is true yield?
- Thread starter DTu
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Dr. Jayanthi Sankaran
Well-Known Member
Hi @DTu,
The prices of money market instruments are sometimes quoted using a discount rate. An example is the T-bills in the US. If the price of a 91-day T-bill is quoted as 8, this means that the rate of interest earned is 8% of the face value per 360 days. Suppose that the face value = $100. Interest of $2.0222 (= $100*0.08*91/360) is earned over the 91-day life. This corresponds to a true rate of interest of 2.0222/(100 - 2.0222) = 2.064% for the 91-day period.
As far as the true yield goes, I think it refers to the YTM.
Thanks
Jayanthi
The prices of money market instruments are sometimes quoted using a discount rate. An example is the T-bills in the US. If the price of a 91-day T-bill is quoted as 8, this means that the rate of interest earned is 8% of the face value per 360 days. Suppose that the face value = $100. Interest of $2.0222 (= $100*0.08*91/360) is earned over the 91-day life. This corresponds to a true rate of interest of 2.0222/(100 - 2.0222) = 2.064% for the 91-day period.
As far as the true yield goes, I think it refers to the YTM.
Thanks
Jayanthi
That's helpful. Thanks very muchHi @DTu,
The prices of money market instruments are sometimes quoted using a discount rate. An example is the T-bills in the US. If the price of a 91-day T-bill is quoted as 8, this means that the rate of interest earned is 8% of the face value per 360 days. Suppose that the face value = $100. Interest of $2.0222 (= $100*0.08*91/360) is earned over the 91-day life. This corresponds to a true rate of interest of 2.0222/(100 - 2.0222) = 2.064% for the 91-day period.
As far as the true yield goes, I think it refers to the YTM.
Thanks
Jayanthi
Hi @DTu and @Jayanthi Sankaran that's exactly correct, the "true yield" is the yield to maturity (aka, yield) of a so-called discount instrument. We don't normally see "true yield" in the context of bonds: it connotes the money market instruments which are short-term and don't have coupons. So to use Jayanthi's example (which is Hull's example) this 91-day T-bill has a quoted price of 8 but 8.00% is not the yield (yield to maturity) so Hull refers to the "true yield" in order to distinguish it from the "non-true" 8.0%.
The 2.064% might (really also) be called a simple interest rate, right? In this case, the cash price = $100.00 face value - 8*91/360 = $97.97778 such that the "simple" interest rate = $2.0222/$97.97778 = 2.064%; same as Jayanthi's answer. Strictly, if we annualized it, we could also say the "true annualizd yield" is 2.064%*360/91 = 8.16512%. And this is greater than 8.0%, hence the difference between the quoted yield of 8.0% (which is not really true and might better be called a discount yield) and the "true yield" of 8.16512%.
And, as a circular test of its nature as the true yield, we should be able to use it to discount from the face value to get the price: $100/(1+8.16512%*91/360) = $97.97778; this "demonstrates" that it a proper yield (yield to maturity), under the special case of only a single cash flow, and the 8.16512% is further a stated (aka, nominal) per annum interest rate with discrete (almost quarterly) compounding (i.e., it is not an effective annual rate, aka effective annual yield). The simple example is, I think, a useful meditation on the difference between stated interest rate (e.g., 8.16512% per annum) which is the true yield (yield to maturity), discount rate (8.0%; aka, 8 is quoted price) and effective annual rate (1+2.064%)^(360/91)-1. I hope that clarifies.
The 2.064% might (really also) be called a simple interest rate, right? In this case, the cash price = $100.00 face value - 8*91/360 = $97.97778 such that the "simple" interest rate = $2.0222/$97.97778 = 2.064%; same as Jayanthi's answer. Strictly, if we annualized it, we could also say the "true annualizd yield" is 2.064%*360/91 = 8.16512%. And this is greater than 8.0%, hence the difference between the quoted yield of 8.0% (which is not really true and might better be called a discount yield) and the "true yield" of 8.16512%.
And, as a circular test of its nature as the true yield, we should be able to use it to discount from the face value to get the price: $100/(1+8.16512%*91/360) = $97.97778; this "demonstrates" that it a proper yield (yield to maturity), under the special case of only a single cash flow, and the 8.16512% is further a stated (aka, nominal) per annum interest rate with discrete (almost quarterly) compounding (i.e., it is not an effective annual rate, aka effective annual yield). The simple example is, I think, a useful meditation on the difference between stated interest rate (e.g., 8.16512% per annum) which is the true yield (yield to maturity), discount rate (8.0%; aka, 8 is quoted price) and effective annual rate (1+2.064%)^(360/91)-1. I hope that clarifies.
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