# Why Diversification Works

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It is unfortunate, but to understand why diversification works, we must understand a little math. And here it is:

If we take a series of returns (say +4%, -5%, +9%, -1%), we can simply add them up to get what our total return would be (+7%). In math, they call this a *linear relationship.*

To gauge the risk of this series is a bit more complicated. We must take the average of the series and then calculate the difference between each point and the average. This tells us how far, on average, each period’s return deviates from the average. Math folks call this the *standard deviation*, which is what we think of as risk – it’s the ups and downs as an investment goes through time.

###### Where the Magic Happens

When we take two or more series and combine them together, a little magic happens! The standard deviation is smaller than adding the two standard deviations individually. This is a *non-linear relationship.*

Because returns are *linear* and risk is *nonlinear*, we can get to the same returns with less risk by combining two investments that have different returns in each period but end up with the same return over the long run. Think of this as combining two waves. When we put two waves together, they cancel each other out and we are left with a straight line.

And this is why diversification works: we get the sum of the returns with less than the sum of the risk.

Now, in the real world, we can never find two investments that exactly cancel each other out, but if we look over time at how various groups of investments behave, we can structure a portfolio that promises the smoothest path to where we want to go.

This mathematical magic is the key to constructing a portfolio that your well-thought-out financial plan deserves: a beautifully *diversified* investment strategy!