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.

Correlation plays a crucial role in risk diversification. Assets with negative correlations, like Beachwear and DVD rental, move in opposite directions, providing a hedge against risk. Lower correlations generally mean lower risk, but finding assets with significantly low correlations can be challenging.

Historical returns may not always predict future returns accurately, but historical risk tends to remain relatively stable. Correlations among assets within the same country are consistent, while intercountry correlations have risen due to globalization.

Diversification across asset classes, countries, and industries is key to mitigating risk. Index funds offer a cost-effective way to diversify, especially for small portfolios. Investing in foreign countries and avoiding over-investment in one’s employer’s stock are also recommended diversification strategies.

Insurance and investments with negative correlations, like gold, can further reduce portfolio risk. Options such as put options provide protection against significant losses, albeit with associated costs. Overall, diversification is vital for a resilient portfolio that can weather market fluctuations.

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.