Uncorrelated Portfolio Holdings

The portfolio standard deviation, or risk, is not simply the addition of the risk of each portfolio holdings. The way in which the portfolio holdings interact contributes to the overall portfolio risk.

Correlation

Correlation is a statistical measure of the relationship between two series. The series need not pertain to financial assets, but within a portfolio context, the series will consist of the historic returns of two potential portfolio constituents.

When the returns move in “lockstep” with one another, they are said to be perfectly correlated and have a correlation coefficient of +1. The converse implies a correlation coefficient of -1.

By combining portfolio holdings with correlation coefficients that are less than +1, and not even necessarily a negative correlation, the overall risk of the portfolio is reduced. Uncorrelated portfolio holdings diversify the risk of the portfolio providing a less volatile portfolio return as different underlying assets contribute to the return of the portfolio at different times.

Question

Given the following correlation coefficients, which two-asset portfolio combination is likely to exhibit the lowest risk?

  • Asset A – Asset B correlation = 0.7
  • Asset A – Asset C correlation = 0.3
  • Asset B – Asset C correlation = 0.5

A. Portfolio AB

B. Portfolio AC

C. Portfolio BC

Solution

The correct answer is B.

The portfolio with the lowest correlation between underlying assets is likely to have the lowest portfolio risk. An understanding of the standard deviations of the underlying assets, as well as the allocation to those assets, would be required to give a definite answer.

Reading 39 LOS 39f:

Describe the effect on a portfolio’s risk of investing in assets that are less than perfectly correlated

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