# Annualised Rate of Return

### The average annual return an investor sees over a set period of time.

The annualised rate of return is the average return an investor sees over a set number of years. It is nearly always expressed as a percentage.

Calculating this may seem like a simple thing to do but it does require some creative mathematics.

Let’s say you invested £1000 in a particular stock. After 5 years, the stock is worth £1,250.

Over that 5 year period, your stock has increased by 25 per cent in value.

A common mistake that people make is to simply divide this percentage by the number of years they are examining - in this case 5 - and say that the result is the annualised rate of return.

This is wrong because it doesn’t take into account compound interest. If you don’t believe us, try it on your calculator and you’ll see what we mean!

### How to calculate the annualised rate of return

To get the annualised rate of return you just have to follow this formula - here is where that creative mathematics comes into play.

AR = annualised rate of return

I = initial investment

GL = Gains/losses

N = number of years

AR = ((I+GL) ÷ I) ^ (1/N) - 1

If we go back into our example and put the numbers in, our formula will look like this;

AR = ((1000+250) ÷ 1000) ^ (1/5) - 1

Now let’s run through it 🙂

AR = (1,250 ÷ 1000) ^ (1/5) - 1

AR = 1.25 ^ (1/5) - 1

AR = 0.0456

AR = 4.56%

### ‍Damn statistics!‍

Investors are big fans of statistics as they can use them to understand how their portfolio or prospective investments have performed over a certain period of time.

The annualised rate of return is one such statistic. The danger with it is that, like all statistics, it can be misleading.

In the example we gave, 4.56 per cent may have been the average growth that our stock experienced over a five-year period - but it doesn’t tell the full story.

For instance, the stock in our example could have;

Gained 10 per cent in its first year
Lost 20 per cent in the second
Gained 15 per cent in the third year
Lost 5  per cent in the fourth year
Gained 30 per cent in the fifth year

All of this and it would still be worth £1,250.

So remember, statistics can be misleading!

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