# Uncorrelated Portfolio Holdings

The portfolio standard deviation, or risk, is not simply the addition of the risk of each portfolio holding. The interaction between portfolio holdings 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. In the context of a portfolio, the series will consist of the historical 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.

When you put assets together in a portfolio with correlation coefficients less than +1 (they don’t have to be negatively correlated), it reduces the overall risk of the portfolio. Having uncorrelated assets means they don’t move together in the same direction all the time. This risk diversification leads to a portfolio with less volatility, and different assets contribute to the portfolio’s return at various 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 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.

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