Another critically important concept related to risk reduction is that of diversification. By mixing our investments among asset classes that are not related to each other—i.e. diversifying our investments—we can both increase overall return while decreasing risk.

A coin toss example

A great example of this principle is borrowed from William Bernstein’s book, “The intelligent asset allocator”.

Imagine someone offers you two investment options.

  • Option 1 involves flipping a coin at the end of each year. Heads—your total savings are increased by 30%; Tails—your savings are decreased by 10%.

  • Option 2 splits your balance in half at the end of each year, and then applies the same coin toss transaction individually to each half.

Would you say Option 2 is better or worse than Option 1? It might seem they would be the same.

Without going into the math, the annualized return, over time, of Option 1 is 8.2%, and the risk—the standard deviation—is 20%. The annualized return of Option 2 is 9.1%, an increase of nearly 1% over Option 1, and the risk is only 14%.

By simply going with two coin tosses, we increase return and reduce risk. That’s the benefit of diversification!


The diversification benefits provided by Option 2 come from the fact that the two coin tosses are unrelated, or uncorrelated—i.e. the chance of getting heads on coin toss 2, is unrelated to what happened with coin toss 1.

This important concept has a number of implications. For example:

  • Buying the shares of 1000 companies in the stocks asset class provides more diversification benefit than buying shares of a single company.

  • Splitting your investments across relatively uncorrelated asset classes like stocks and bonds provides more diversification than splitting them among stocks of large companies and stocks of small companies.

In this guide, we recommend distributing your investments across multiple asset classes that are as uncorrelated as possible, in order to achieve diversification benefits.

An interesting—and perhaps paradoxical—consequence is that, at all times, some of your investments should be doing good while others should be doing bad, and that behavior is actually beneficial in the long run!