Sequel to our last article on portfolio diversification, which was an introduction to portfolio diversification. This week, we take it a step further as we look more in-depth into the math behind portfolio diversification, i.e., using correlation to achieve the objective of portfolio diversification which reduction of systematic risk.

**How to Check the Correlation between Asset Classes**

The basis of diversification is that different classes of assets respond differently to certain macroeconomic variables or economic conditions. For instance, prices of financial assets (like stocks and bonds) and physical assets (like gold), may move in opposite directions due to inflation. High inflation may lead to a rise in gold prices, whereas it may lead to a fall in prices of financial assets.

Most Portfolio or hedge fund managers make use of statistical measures such as covariance and correlation to determine the relationship between two different asset classes before placing it in a portfolio. Correlation is a statistical tool that measures the degree to which two securities move in relation to each other. Correlation shows the strength of a relationship between two securities and is computed as the correlation coefficient which has a value that must fall between -1.0 and +1.0.For instance, if two investments tend to be up or down during the same time periods, then they have positive correlation, while, if one investment tends to be up and the other is down, then they have negative correlation. If there is no pattern to the up and down of one investment compared to another, then the two investments have no correlation. To calculate correlation, one must first determine the covariance of the two securities. Next, one must calculate each security’s standard deviation which measure the market volatility of each security. For example, to determine the relationship between different asset classes, investors make use of historical average price movement of one investment in relation to another investment during different economic conditions. Based on this trend investors can determine the degree of relationship or price volatility between two securities using correlation coefficient.

In actual practice, it’s difficult to find a pair of assets that have a perfect positive correlation of +1.0, a perfect negative correlation of -1.0 or even a perfect neutral correlation of 0. A correlation between different pairs of assets could be any one of the numerous possibilities lying between +1.0 and -1.0 (for example, +0.62 or -0.30). Each number thus tells you how far or how close you are from that perfect 0 where two variables are uncorrelated. So, if the correlation between Asset A and Asset B is 0.35 and the correlation between Asset A and Asset C is 0.25, then you can say that Asset A is more correlated with Asset B than it is with Asset C. If two pairs of assets offer the same return at the same risk, choosing the pair that is less correlated decreases the overall risk of the portfolio.

**Uncontrollable Event that affect uncorrelated Assets **

There are instances when non-correlated assets suddenly become highly correlated, although they rarely happen. That’s why it is important to measure your level of risk exposure and how much risk is acceptable in your portfolio. The most diversified portfolio consists of securities with the greatest negative correlation. A diversified portfolio can also be achieved by investing in uncorrelated assets, but there will be times when the investments will be both up or down, and thus, a portfolio of uncorrelated assets will have a greater degree of risk, but it is still significantly less than positively correlated investment. However, even positively correlated investments will be less risky than single assets or investments that are perfectly positively correlated. However, there is no reduction in risk by combining assets that are perfectly correlated.