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For a savings account that is returning 2.0 APR, on $10,000, $200 in interest will be earned in one year.

If I have a return of 9% on a stock trade with a holding period of 3 months, is the annualized return 4 x 9% = 36%?

Doesn't that assume I will make 9% on three additional trades? What if those three trades are all negative? Now the annualized return isn't even 9% anymore.

If the above is incorrect, what is considered the annualized return on the stock trade?

9

Doesn't that assume I will make 9% on three additional trades?

No (well, sort of, but not really). "annualized" doesn't mean "what will my return be in one year". It means "what's the equivalent annual return of this non-annual investment". So yes, to get 36% over one year you're assuming that the return is replicable (meaning that IF you earned 9% each quarter, then your return over one year would be 36%), but you're not really assuming that it WILL return that over the next 9 months.

Also, to be technical, if you earned 9% each quarter and the returns compounded (meaning you earn 9% on top of the 9% you earned last quarter), then your annualized return would be

(1.09 * 1.09 * 1.09 * 1.09) = 1.41 = 41% annual return

So the compounding period can make a difference in the calculation as well.

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    Can you elaborate on this? It seems contradictory: "you're assuming that the return is replicable, but you're not really assuming that it WILL return that over the next 9 months." – 4thSpace Jun 11 '18 at 14:15
  • I added a bit, what I meant was that IF the investment earned another 9% each quarter, not that you are assuming that it WILL (meaning you cannot EXPECT it to replicate the return from the first quarter). In other words, the calculation assumes that it will, but just to make the result equivalent, not to imply that past results imply future results. – D Stanley Jun 11 '18 at 14:27
  • Right - that's my point: Depending on what happens with returns over the next 3 quarters, it could be anywhere from negative to higher than 36%. That's meaningless. To much assumption going on. Reproducing 9% four times in a row is quite a feat. Guess I still don't understand. – 4thSpace Jun 11 '18 at 14:30
  • Think about it this way - it's correct to say "my annualized return over the last three months is 36%". It's wrong to say "in one year I WILL have a 36% return". Yes your return might be different over an entire year, but in order to compare the return to investments over different time periods, annualization puts everything in the same context. – D Stanley Jun 11 '18 at 14:32
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    @4thSpace: Think of it this way: suppose that right now you are traveling at 100 kilometers per hour. This does not necessarily mean that you will be 100 km away one hour from now; it merely means that if you continued at the same rate, you would be 100 km away. Just because it's a hypothetical situation about the future doesn't mean that "100 km/h" isn't a useful number about how fast you're going. Similarly, just because your rate of return won't necessarily hold up over an entire year doesn't mean that the annualized rate is a meaningless number. – Michael Seifert Jun 11 '18 at 19:57

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