The numerical difference between a forecasted quantity and the actual result is known as absolute error. If you predict that you'll run a mile in eight minutes and you run it in nine, your absolute error is one minute.
In investing, absolute errors are expressed in dollars. For example, at the beginning of 2015, Amazon.com stock was trading for about $313 per share. Let's say you forecast that Amazon would be trading for $500 by Dec. 1. Well, on Dec. 1, Amazon opened at approximately $674. So your forecast's absolute error would be $174.
This is the formula:
It's also worth noting that you don't need to worry about positive and negatives when stating absolute error. If you predict a stock's value to be $100, whether it becomes $105 or $95, you were "off by $5" either way.
Expressed as a percentage, relative error takes the price of the investment (or other quantity) into consideration when expressing the difference between a forecasted value and actual value.
For example, consider the following hypothetical situations:
- You predict that Amazon's share price will be $650 on the last trading day of 2015, and the actual price turns out to be $655.
- You predict that Microsoft's share price will be $60 on the last trading day of 2015, and the actual price turns out to be $55.
In both examples, your prediction was $5 off from the actual price, so your absolute error is the same in each case. However, your Amazon prediction was far more accurate since you're trying to predict the value of a much more expensive stock.
Relative error takes the different share prices into account and expresses the error as a percentage of the actual value:
In the Amazon example, your relative error would be:
In the case of your Microsoft prediction, your relative error would be:
What this means is that even though both predictions were just $5 off from the actual price, the Amazon prediction was much more accurate, because it was closer to the actual price when considering the price of the stock.
For comparisons, it's all relative
While both ways of expressing error can be useful when evaluating investment forecasts, relative error is by far the best way to compare forecasts of different stocks' prices and their accuracy.
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