Annualising a short return: 2% in a month is not 24%

A number that sounds better than it is

Imagine a headline: "Fund gains 2% in a month." Multiply by 12 and you get 24% a year. It feels natural. It is also a forecast dressed as a fact.

Three things are wrong with it. The first is the arithmetic, which depends on the method. The second is that one month is a tiny sample. The third is that the same method works just as well on falls, where it produces alarming numbers nobody should quote.

Two ways to annualise

Simple annualising multiplies the period's return by the number of periods in a year. 2% × 12 = 24%.

Compounded annualising assumes you repeat the gain every period and it builds on itself. The 2% month repeated twelve times is 1.02 to the power of 12, about 1.268, or 26.8%.

Neither is the fund's return. They are what the fund would earn if the month repeated twelve times, and that has no reason to happen. See CAGR versus absolute return for how returns over a real period are expressed.

More examples

Look at the first row. Half a percent in a week, which is ordinary noise, becomes almost 30% a year. The shorter the period, the wilder the headline, which is why short windows are so tempting to quote.

The same trick works on losses

Apply the method to a bad month. A fall of 5% in a month, compounded over twelve months, is 0.95 to the power of 12, about 0.54, or a fall of roughly 46% a year.

No sensible person would claim a fund is "falling 46% a year" because of one month. Yet the identical logic produces "earning 27% a year" from a good one. If the first sounds silly, the second should too.

Why a short window tells you little

• Sample size. A month holds about 21 trading days. A few big days can decide the result.
• Mean reversion and noise. Markets fall back and rebound. A strong month is often followed by a weaker one, and the reverse.
• Start and end dates. A window that starts after a drop and ends after a rally flatters any fund. Move the dates a week and the number changes.

This is also why rolling and calendar views help more than a single snapshot. Compare how a fund's category performed over a quarter with how the same funds did over years.

What to do instead

1. Compare equal periods. Read 1-year, 3-year and 5-year returns side by side, on the same end date.
2. Treat anything under a year as an absolute return. A 2% month is simply a 2% month.
3. Use CAGR for 3 years and more. It is already a per-year figure, so no further adjustment is needed.
4. Be wary of advertised "annualised" short returns, especially in debt and arbitrage funds, where small differences get inflated. Money market fund returns show the kind of ranges that are normal.
5. Match the window to your goal. A goal five years away is judged on five-year records, not on last month.

The takeaway

Annualising is arithmetic, not evidence. Compounding a month into a year tells you what would happen if conditions repeated twelve times, and conditions rarely repeat. Quote short returns as short returns, and leave the big annual numbers to periods that earned them.

This post is educational, not financial advice. All figures are arithmetic illustrations, not any fund's results or forecasts.