Why Does Diversification Work?

In my previous post I showed how over time an investment with a given expected return is likely to have a lower actual return due to volatility. The more volatile an investment is, the bigger the difference between the expected return and the actual returns you get. This explains the inconsistency among various reports of average stock market returns.

One way to reduce volatility and increase the actual return from investments is diversification. To diversify means to spread your money among multiple investments. This is the “don’t put all your eggs in one basket” advice that we often hear.

Let’s go back to the example in the previous post where we have an investment that each month either doubles or loses 60% with equal probability. This kind of extreme case is unrealistic, but makes it easier to understand how diversification helps. We saw before that the most likely outcome was that this investment would lose almost everything over 3 years, even though the average outcome is that $10,000 grows to $7 million.

Suppose now that we have two independent versions of this investment (A and B). There are now 4 equally likely outcomes each month: both up, only A up, only B up, and both down. Let’s look at three different investment approaches:

1. Put $10,000 into investment A and let it ride for 3 years.
2. Put the $10,000 in investment B.
3. Use a combined (or diversified) strategy where we put $5000 into each investment, and after each month pool the money and split it up evenly between the two investments again.

Here is a typical outcome after 3 years:


Incredibly, both investments A and B on their own dropped down to $180, but the diversified approach grew to $36,000! Even more amazingly, look at what happens when the money is split evenly among 100 different independent instances of this type of investment:


In this case, the money grew fairly steadily all the way up to almost the $7 million expected return that we calculated earlier. Diversification among identical independent investments doesn’t change the expected return, but it does reduce volatility which drives the most likely outcome closer to the expected return.

This may seem too good to be true. That’s because it is. In the real world there aren’t investments that offer such high returns. Also, investments are not completely independent. For example, spreading money among a number of good stocks reduces volatility, but only up to a point. The stock market as a whole still has volatility because the returns of all stocks are correlated.

This idea of correlation is important for mutual fund investors. An investor may feel better owning 20 different mutual funds, but if the funds own all the same stocks, then the funds are highly correlated. This means that they all tend to go up and down together, and the investors have not reduced the volatility of their returns much.

In the examples used here, we saw the benefit of diversifying among investments with identical attributes. There would be no benefit if you diversified into a poor investment. For example, if you own 3 good stocks and you diversify into lottery tickets, your expected return and your most likely return will both go down.

Diversification is good for your investment returns, but only if each individual investment has a good expected return.