How to Annualize a Rate of Return

According to the Vanguard website, the Vanguard S&P 500 Index Fund is down 12.07% YTD as of yesterday’s close. To get an idea of what that return would look like if it were to continue for an entire year, you can annualize the YTD return.

It’s a fairly simple calculation to perform as long as you have the following information:

1. Number of days that have elapsed so far this year. This is easy to calculate if you have access to Excel.

2. The YTD return of the investment that you want to annualize.

The formula for annualizing a ROR is pretty straight forward:

[(1 + YTD ROR)1/(#of days/365)] – 1

The YTD ROR should be expressed as a decimal. Plugging in the Vanguard S&P 500 Index Fund information from above, the equation looks like this:

[(1 – .1207)1/(204/365)] – 1

[.87931/(0.55890411)] – 1

[.87931.7892] – 1

0.7944 – 1

-.2056 or -20.56%

So, a 12.07% loss for the first 204 days of the year equates to a 20.56% loss on an annualized basis.

Now let’s say you are down 12.07% but you purchased this fund on December 31, 2006. How do you annualize that return? The only input that changes in the above formula is the number of days, which is now 570.

[(1 – .1207)1/(570/365)] – 1

[.87931/1.5616] – 1

[.87930.640350877] – 1

0.9209 – 1

-.0791 or -7.91%

Had you purchased an investment on December 31, 2006 that is currently down 12.07% since the time of purchase, your annualized rate of return on that investment would be -7.91%. Not much of a return is it? Anyway, now you know how to annualize your returns. Fun stuff!

9 thoughts on “How to Annualize a Rate of Return”

1. Wilson says:

First am I:)
This makes me scratch my head, despite tons of mathematical formulas in that skull. The rule is just too complicated for joe6packs. My rules are much better: A) do I make money at the end of the day? B) Is my positive return, if any, greater than that of a CD account? That’s all I want to know.
Just make money, simple.
The formulas illustrated hereinabove, I guess, are used by financial advisers to justify the negative or poor return, just like mortgage/financial companies use off-balance-sheets, level-3 assets, etc, to present their nice performance to share holders:)

2. Wilson,

Actually, most financial advisors would be wanting to keep their clients from knowing how to annualize negative returns since it makes the numbers look worse.

3. ebow says:

I can follow the formula well enough but don’t really see the point. If I’ve held a security for more than a year, and it’s down 12.07% since I bought it, why do I care what the equivalent rate of return over a year would be? I’m still down 12.07%. Another blogger wrote about some kind of stock buy-back he got in on, and expressed his gains in terms of an annualized rate. The transaction’s over and he can’t make any more money on it, so what is the annualized rate good for?

4. ebow,

An annualized ROR is good for comparing your performance (or your advisor’s or mutual fund’s performance) with a benchmark.

5. Taylor says:

You should care about annualized rate of returns because that’s how financial numbers are typically reported. It’s especially important in merger arbitrage opportunities where you may only be holding a stock for as little as a month just to pick up a percent or two. That 1-2% gain doesn’t look like much, but on a risk/reward basis it’s actually very desirable. Annualizing that 1-2% allows you to compare your performance to major financial indexes historical returns (which are all based on annual returns). It’s not a complex formula, and it will give you a better idea of how an investing strategy should perform over longer periods of time.

6. david says:

Thanks for the formula. I think the second step would be clearer written as (1 + -0.1207)

7. Leon Goekjian says:

I have tried to solve the above equation if you divide 1/0.55890411 I got 1.789215685 and not 1.7805 like you got in your example. I used Excel. Please advise. Why?

1. Leon,

You’re right. I corrected the numbers. Not sure how that happened. Thanks for the catch.