APY - annual percentage yield - the percentage increase in an investment value including reinvestments after holding one year.
This is a standard figure that is supposed to make comparing products easy.
It is simple enough for bank accounts. They calculate it for you based on the rate (APR) and frequency of compounding (daily, monthly). But it is not so simple for MMFs or T-bills. Rather than calculate compounded yield over a year as a bank does, the figures you see with MMFs and T-bills use simple interest to annualize.
The MMF 7 day SEC yield is just a daily yield multiplied by 365 (or 366), i.e. simple interest.
For a MMF, to get the effective annual yield (APY), the formula is:
APY = (1 + 7 day SEC yield/365) ^ 365 - 1 (use 366 as needed)
Fidelity shows the effective yields for its MMFs on the funds' "performance and risk" page.
The annualized yield quoted for a T-bill is just the total return of the T-bill to maturity multiplied out to a year (simple interest). For example, with an 8 week T-bill (56 days), the total return of the T-bill is multiplied out by 365/56.
To compound interest, we reinvest the T-bill (including interest) at maturity, repeating until we've covered a whole year. That might result in a fractional number of reinvestments. For example, an 8 week (56 day) T-bill would get invested a total of 365/56 times, or roughly 6.5 times. No matter, the formula handles this.
T-bill total return = ($100 - purchase price)/ purchase price
APY = ((1 + T-bill total return)/T-bill days) ^ (365/T-bill days) - 1
Consider
this 8 week (56 day) T-bill. Purchase price was $99.216.
T-bill rate = ($100 - $99.216)/ $99.216 = 0.7901951%
APY = (1 + 0.7901951) ^ (365/56) - 1 = 5.264%
The stated annualized yield (using simple interest) is 5.150378%.
A bank account with an APY of 5.0% looks better than SPAXX (current 7 day yield 4.94%), but SPAXX returns more (5.06%) with compounding. Similarly, between a T-bill and a bank account with the same rate, the T-bill is better. Its quoted rate doesn't include the effect of compounding.
Comments
T-Bill return is WYSIWYG, it's the effective TR. If anything, the theoretical nominal rate during the T-Bill holding period would be lower (not higher) than the WYSIWYG TR. Most insurance companies also quote effective rates (TIAA Traditional, etc), not the nominal rates (as is typical by banks). At one time, banks were playing games with this, so now they are required to disclose the nominal rate, but may also show the effective (compounded) rate.
General caution - be consistent in comparison. I have seen some comparing compounded m-mkt rates (when available) with the 30-day SEC yield (when compounded rate isn't available).
One is interest rate (not yield) assuming daily compounding. The other is total annual return. The former is indeed lower than the stated rate of a T-bill, though the latter is higher than the T-bill's stated rate.
Consider bank accounts at two banks. One bank compounds interest monthly, one compounds daily. For simplicity I'll work with 30 day months and 360 day years. It doesn't change the reasoning, it just makes the numbers easier to follow.
The monthly one says that it has an APR (not compounded yield) of 6%. Each month, it pays 1/2% interest. Its APY (compounding 12 times) is 6.17%.
The daily one says that it has an APR of 5.9855%. Each day, it pays 0.001663% (1/360th of the APR). With daily compounding that comes out to 1/2% each month and an APY of 6.17%. Same as the other bank.
Now instead of bank accounts, think of a T-bill with a one month maturity. (It's hypothetical, real T-bills mature in 4 weeks.) Let's say that like these banks, at maturity (in one month) you get back 1/2% more than you invested.
The stated yield on the T-bill would be 1/2% annualized, i.e. 12 x 1/2% = 6%. Assuming you reinvest each month in a T-bill with the same terms, you'd have 6.17% more than you started with at the end of the year because of monthly compounding. That's higher than the stated yield.
But if we hypothesize that the T-bill is actually compounding on a daily basis for a month, then it would be like the bank that compounds daily. Its daily APR would be 5.9855%. That's lower than the stated yield of 6% and lower still than the 6.17% you would get by reinvesting these T-bills for a year.
This is how one can come up with both a lower rate (assuming daily compounding) and a higher total return (by reinvesting over the course of a year) than the stated rate of a T-bill.