Discount Rates and Money Market Yields for Treasury Bills
Summary
The document explains why Treasury bill prices differ depending on whether a quoted rate is interpreted as a discount rate or as a money market yield. Under the discount-rate convention, the discount is applied to face value to obtain the purchase price. Under a money market yield convention, the price is calculated by discounting face value using the yield over the relevant period. These conventions produce different prices even when their quoted rate is the same.
The answer distinguishes a bill’s issuance and secondary-market discount-rate convention from money market yield and bond equivalent yield, which are useful for comparing returns with other securities. It cautions that real-world yield calculations also depend on details such as the day-count basis and calendar conventions. The example is explicitly approximate and does not supply all of those market-specific assumptions, so its calculations should be read as an illustration of terminology rather than a complete pricing specification.
Key ideas
- A Treasury bill discount rate and a money market yield use different price conventions.
- Applying a discount rate to face value gives a different price from calculating price using a money market yield.
- Money market yield and bond equivalent yield help compare bills with other securities.
- Exact yield calculations depend on day-count and calendar conventions.
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# example regarding zero coupon bonds # example regarding zero coupon bonds This example is from Interest Rate Models: an Infinite Dimensional Stochastic Analysis Perspective by Carmona, René, Tehranchi, M R. I am wondering if the calculation is correct?, he says approximately, but I am wondering if you agree with me in that the calculation of the discount is to be calculated like this: ? $100000-100000/(1+r) = 100 000 *[1- 1/(1+0.06/4)]=1477.83$ And that he he pays at the start: $100000/(1+0,06/4)=98522.17$. Or shall the calculations be done as in the example? Here is the example: ## Answer by Alex C (score 1) https://quant.stackexchange.com/a/27852 You have to be very careful with terminology here. In particular "yield" is being thrown around carelessly by both of you. The textbook is correct if the (meaningless) phrase "at a 6% yield (rate)" is crossed out and replaced by "at a 6% discount rate". And this is how Tbill's are handled when they are issued (the press release by the US Treasury speaks of discount rate http://abcnews.go.com/Business/wireStory/rates-us-treasury-bills-fall-weekly-auction-40174524) and in the secondary market. The calculation you are doing is correct if you are assuming "a 6% money market yield" and then calculating the price from that. And money market yield (as well as "bond equivalent yield" a related measure) are useful measures that are closer to the everyday meaning of "yield", i.e. how much money you make per year. The MM yield and BE yield are what is used in analytical work (for example to compare tbills to other securities). The real world calculations of yields involve hair splitting details (such as 360 vs 365 day basis, leap vs non-leap years,...) that are best left out of a general textbook and so just consider this an an approximate example without sweating the details.
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