What return actually means
Return is what you earn relative to what you put in, over a certain time. With any return figure, three follow up questions are worth asking: per year or in total, before or after costs, before or after inflation.
Learning objective: After this lesson you can judge a return figure correctly by its time frame, costs and inflation.
When someone tells you they made fifty percent, three details are missing. Over what time? After what costs? And has inflation already been taken off?
The time frame matters
Fifty percent in one year is exceptional. Fifty percent over ten years is just over four percent a year, which is fairly normal. Without a time frame the number tells you nothing.
Counting per year
So always work per year. That's the only way to compare two investments. And take off what really goes out: fees, taxes and inflation. What's left afterwards is what you actually earned.
Careful with averages
Be careful with averages. If Nina loses 50 percent in the first year and gains 50 percent in the second, the average is zero. But only €750 of her €1,000 is left. With investments that swing a lot, the simple average always looks better than what really ends up in your account.
The gap in Nina's example has a name. The simple average of yearly returns is called the arithmetic mean. The rate at which your money actually grew over the whole period is called the geometric mean or annualised return. You get it by dividing the end value by the start value, taking the nth root (n being the number of years) and subtracting 1. As soon as an investment fluctuates, it's lower than the simple average.
The gap between averages
How big the gap is depends on the volatility. As a rule of thumb, subtract the squared standard deviation divided by two. An investment expected to return 8 percent a year on average that swings by 20 percent grows at more like 6 percent over the years. So volatility isn't just unpleasant. It costs you real money.
Time-weighted returns
If you pay in or take out money regularly, there's one more distinction. The time weighted return shows how well the investment itself did, regardless of when you paid in or out. Funds are compared with it. The money weighted return shows what you personally earned. If someone bought a lot more after a strong rise and the price then fell, their own return can be clearly worse than the fund's.
Summary
- A return figure without a time frame means nothing.
- The geometric mean counts, not the simple average.
- Volatility reduces what's actually left at the end.
Did you get it?
Minus 50 percent, then plus 50 percent. Where are you?
At 75 percent of what you started with. The simple average of zero is wrong.
Which calculation describes your actual result over several years?
The geometric mean, in other words the annualised return.
Why does volatility cost money?
Because the more an investment swings, the further the growth rate you actually achieve falls below the expected one.
Check your understanding
Your task
$5,000 grows to $6,655 in three years. Calculate the return per year by dividing the end value by the start value, taking the cube root, and subtracting 1. Then subtract 0.5 percentage points for fees and 2 percent for inflation and write down what you really earned per year.
Related
- Currency riskStage 2
- Why saving in a bank account means losing moneyStage 1
- Risk and return are linkedStage 1
- Matching questions for this stageQuestions