Exercise

# Driver 3: The correlation between the asset returns

The third driver of portfolio performance is the correlation between asset returns. Generally speaking, the correlation tells you how two asset returns tend to move together.

The correlation of assets has important consequences in overall portfolio performance. This correlation is important because it can reduce volatility through diversification, or reducing overall correlation. In fact, the lower the correlation, the more successful the portfolio tends to be in regards to partially offsetting large losses in one asset with only a minor loss, or even a gain, in another asset.

In the extreme case of two identical asset returns, the correlation will be 1, and there is no diversification potential. In the other extreme case where, if one asset return is above average, and the other is almost always below average, the correlation is negative. The correlation is 0 when the asset returns are linearly independent of each other. Note that interdependency can still exist on a non-linear level even when the correlation is 0.

As an exercise, suppose you have an equally weighted portfolio of two assets. Their correlation jumps from 0 to 0.5. What happens with the variance?

To help you answer this question, we created a function `pf_var(x)`

that calculates the portfolio variance for the equally weighted portfolio of equities and bonds, when their correlation is assumed to be equal to `x`

. Play with correlation values and see how the portfolio variance changes when the correlation increases from 0 to 0.5.