Smart people who analyze different investment strategies often talk about correlations. Investments have correlations that are high, low, positive, or negative. This can all sound impressive, but as I’ll show, any conclusions we draw based on correlations can be suspect. In the investment world, correlation is a measure of how asset returns move together. A positive correlation means two assets tend to give good returns together and bad returns together. A negative correlation means they tend to move in opposite directions. A zero correlation means the direction of one investment doesn’t tell you anything about the direction of the other investment. It’s impossible to know the correlation of two investments exactly. All you can do is measure their correlation over a period of time. We then just assume the correlation will remain the same into the future. To show the problem with this approach, I simulated two streams of monthly investment returns. The distributions I chos...

Most of us have heard that it is good to hold asset classes with low or negative correlation. The informal explanation for this is that risk is lower because when one asset class, such as stocks, is going down, another asset class, such as bonds, is going up. However, this explanation is misleading. It is possible for two investments to both be going up over a period of time, but have negative correlation. Consider the following example: Investment A earns either 2% or 20% each year based on a 50/50 coin toss. Investments B, C, and D do the same. Investment B's return is based on the same coin as A uses. Investment C uses its own independent coin. Investment D does the opposite of A's coin. All 4 investments have an expected compound return of 10.63% (for math geeks, this is 1 less than the square root of 1.02 x 1.20). Even though the investments all look the same based on their returns, their correlations are different: A and B are +100% correlated (perfect cor...

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 ...