This interaction is measured by correlation. Technically speaking, correlation is a scaled version of covariance. Covariance measures how two variables change in relationship to one another. Correlation normalizes covariance to a scale ranging from -1.0 to +1.0.
Calculating how much return the various investments contribute to a portfolio return is quite straightforward. It is simply the weighted average of the returns of each individual investment. The generalized formula looks like this:
But for simplicity’s sake let’s assume a two-asset portfolio, in which case the formula is this:
Pretty simple, right? The weight of one asset (), multiplied by its return () plus the weight of the other asset (), multiplied by its return ().
The formula for calculating an investment’s contribution of risk to a portfolio is more complicated, but that’s actually a good thing. Correlation is the “X-factor” that has the potential to lower a portfolio’s overall volatility. As before, “w” is the weight and the new terms “σ” and “ρ” signify the standard deviation and covariance, respectively. The formula for a portfolio’s variance is:
Again, the generalized formula looks intimidating, but breaking it out in to a simple two-asset portfolio makes it easier to understand.
The first two terms in the equation represent the stand-alone contribution of the risk of assets A and B to the portfolio. Because the weights will be represented by a decimal and because they are being squared, the impact of the standalone risk will always be less than the weight. For example, an 80% weight squares out to .64, and a 40% weight squared would be .16.
This makes the third term, the combined risk of assets A and B, pretty important. The symbol for correlation is highlighted in red.