Why Money Market Yield Is Computed from T-Bill Purchase Price
Summary
The exchange explains how to calculate a US Treasury bill’s money market yield directly from its purchase price and face value. It gives the formula as the price gain divided by the purchase price, annualized on a 360-day basis for the holding period. This addresses the question of why money market yield is considered more representative of an investor’s return than bank discount yield, which uses face value as its base.
The answer says that converting bank discount yield into money market yield is unnecessary if the purchase price is available. It characterizes bank discount yield as a weak return measure, but gives no numerical comparison or worked example. The discussion is limited to these quoted yield conventions; it does not address alternative day-count conventions, compounding adjustments, or how to compare bills across different maturities.
Key ideas
- Money market yield can be calculated from the purchase price and face value directly.
- The calculation annualizes the price gain relative to the purchase price over a 360-day year.
- Bank discount yield uses face value as its base, so it does not directly express the investor’s return on invested cash.
- Converting bank discount yield to money market yield is unnecessary when the purchase price is known.
Tags
Full text
# Bank discount yield and money market yield
# Bank discount yield and money market yield
I have a question regarding `Bank Discount Yield` and `Money Market Yield` for US TBill.
Some books mentioned that `Bank Discount Yield` is not a meaningful measure of the return for the TBill because:
- The yield is calculated based on face value, not purchase price.
- The yield is annualized into 360 days, not 365 days.
- The yield is based on simple interest and ignores compouding.
The book also suggests that `Money Market Yield` is superior to the `Bank Discount Yield` because it is computed relative to the purchase price, not the face value.
I don't understand this because the equation of calculating `Money Market Yield` is:
```
(360 x R) / (360 - t x R)
```
where `R` is the `Bank Discount Yield`, `t` is the holding period.
I think the `Money Market Yield` is solely calculated from `Bank Discount Yield`. It is not calculated from the actual purchase price.
If `Bank Discount Yield` cannot be used to measure the return, why the `Money Market Yield` can?
## Answer by Alex C (score 1)
https://quant.stackexchange.com/a/23142
The money market yield can be computed directly from the purchase price as $Y_{mm}= \frac{100-P_0}{P_0}\frac{360}{t}$
See for example equation 9.3 here http://www.icmagroup.org/assets/documents/Media/Bondmarketsbook/Bond%20markets_structures%20and%20yield%20calculations.pdf
The calculation of the BDY first and then conversion to MMY with your conversion formula is not necessary. The BDY, as your textbook indicates, is fairly useless in any case. Might as well calculate MMY directly.Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.