Saturday, October 28, 2006

Comparing 7-day yield and APY

Money market mutual funds typically quote a 7-day yield, but bank accounts typically quote an APY. Alas, they are not the same.

The 7-day yield is the simple annual rate (actually an annualized simple daily rate), which varies from day to day, but is averaged over a 7-day window. There is no compounding in that rate, so it actually doesn't tell you how much you will earn if the rate remained unchanged for a year. Note: the actual calculation of the 7-day yield is rather more complicated, but the point is that the number is an annualized simple rate. The fund expenses are taken out of the underlying earnings when the 7-day yield is calculated.

Bank APY or annual percentage yield is the effective rate when a simple rate is compounded, typically on a monthly basis.

So, to compare a 7-day yield and an APY we simply need to add in the compounding to the 7-day yield or take it out from the APY.

In Excel, the formula I use to calculate APY from 7-day yield is:


The formula I use to calculate the 7-day yield (or simple annualized interest rate) is:


Note: the yield would be expressed as a decimal fraction, so 5.05% would be expressed as 0.0505.

The assumption is that compounding is on a monthly basis, which is how my brokerage and bank accounts credit interest.

Here are some sample yields that I have recently run across:

  • 2.96% 7-day yield = 3.00% APY
  • 3.00% 7-day yield = 3.04% APY
  • 3.45% 7-day yield = 3.50% APY
  • 3.50% 7-day yield = 3.56% APY
  • 3.93% 7-day yield = 4.00% APY
  • 4.00% 7-day yield = 4.07% APY
  • 4.44% 7-day yield = 4.53% APY
  • 4.45% 7-day yield = 4.54% APY
  • 4.50% 7-day yield = 4.59% APY
  • 4.75% 7-day yield = 4.85% APY
  • 4.89% 7-day yield = 5.00% APY
  • 4.90% 7-day yield = 5.01% APY
  • 4.94% 7-day yield = 5.05% APY
  • 4.97% 7-day yield = 5.08% APY
  • 5.00% 7-day yield = 5.12% APY
  • 5.02% 7-day yield = 5.14% APY
  • 5.03% 7-day yield = 5.15% APY
  • 5.05% 7-day yield = 5.17% APY
  • 5.07% 7-day yield = 5.19% APY
  • 5.09% 7-day yield = 5.21% APY
  • 5.10% 7-day yield = 5.22% APY
  • 5.15% 7-day yield = 5.27% APY
  • 5.20% 7-day yield = 5.33% APY
  • 5.25% 7-day yield = 5.38% APY

Final note: You cannot simply compare two investments based on the quoted yields since the terms of the investment may be different. For example, a money market mutual fund will tend to vary from month to month (or even day to day), but a CD will be fixed for the full term of the CD. CDs are also notorious for introductory "teaser" rates which then fall significantly to "normal" rates for subsequent investments. Or, the bank may require you to have a minimum balance in checking and savings account which pay very low rates before they'll offer you the CD at the higher rate.

I just transferred some cash from my bank account to PayPal which has a 7-day yield of 5.03%, which is equivalent to an APY of 5.15%.

-- Jack Krupansky

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At 11:45 AM EDT , Anonymous Anonymous said...

The discussion helped with some comparison issues I have been having. However, could you extend your discussion to make a money market comparison to short term CD’s. These are available within a brokerage account and appear to provide the opportunity to move about 20 basis point’s above the money market. The certificate of deposits pay interest at the end of the 60 or 90 days, so no compounding vs. the money market fund monthly compounding. c

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