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September 2023 · 5 min read

### Correlation within your Stock Portfolio

Research
Educational
Intermediate

In a previous post, we discussed the risk budget that an investor has and the need to allocate that budget between competing investments. This budget choice could be on a cash basis or on a volatility basis, where a certain percentage of their target volatility is allocated to an investment. Correlation and the risk budget are linked as the risk budget is a choice between investing a proportion of your wealth in different investments, each with a varying degree of risk. This is why the correlation amongst those investment choices is an important input.

##### First, let us define correlation

Correlation is a simple measure that explains the relationship between two variables. It normalises the covariance of the two variables, i.e how they move together, by scaling using the standard deviation of the variables.

If your portfolio consists of two stocks which have a negative correlation, then your overall portfolio volatility will be lower than the weighted average of their volatilities. When one stock rises in price, most likely the other will fall and in aggregate your portfolio volatility will be reduced. Correlation has the following properties

• bounded between -1 and 1 and can never be outside that range
• represents how strong the relationship is between two sets of data
• can and does change through time and depends on the window used for the correlation calculation

#### Why is correlation so important ?

Correlation is a critical component when you consider two or more stocks in your portfolio. Diversification of a stock portfolio only benefits the investor when there is less than perfect correlation between the stocks. We saw this in our post on the efficient frontier where we illustrated the risk versus return benefit of combining stocks with less than perfect correlation.

When it comes to portfolio management and multiple strategies competing for a risk budget, i.e inclusion in the overall portfolio, then the importance of correlation shifts from the stock level to the strategy level. We will illustrate these concepts in the following sections.

##### Correlation moves from stocks to strategies

We have seen the power of modifying correlation between stock A versus stock B. Changing correlation can either reduce the portfolio risk whilst generating the same amount of return or the correlation change improves the returns for the same amount of risk - both methods increase the risk-adjusted returns of the portfolio. We now shift that logic to the strategy level instead of the stock level. We are considering the impact of strategy correlation when combining two strategies together into one final portfolio.

An investor has thousands of stocks to choose from to form their portfolio and can choose from various investment strategies, each of which generates a set of stocks to invest in. The set of stocks investors can choose from is normally called the universe of stocks. In quantitative terminology, when we consider all stocks and want to rank all stocks against each other we refer to this as the cross-section of stocks.

In this cross-sectional world where we are attempting to come up with quantitative equity trading signals, we must move away from any toy examples on a small set of 3-5 stocks and instead think about ranking between thousands of stocks. Therefore, our effort is focused on developing strategies that are based on sound mathematical and financial concepts that are applicable across all stocks so we can generate a final score (ranking) for each stock, which represents a stocks future forecasted return or alpha.

Imagine we develop two investment strategies, call them strategy A and strategy B. Strategy A is a value strategy where it focuses on a mathematical rules-based method to identify the top 50 value stocks. Strategy B is a momentum strategy that focuses on identifying the top 50 stocks based on some new momentum metrics. The correlation concept we applied to stock A and stock B can likewise be applied at the strategy level so our goal here is to hopefully identify low or even negative correlation between momentum and value and therefore combine the two strategies into a final portfolio. This final portfolio would then provide higher risk-adjusted returns to an end investor, rather than investment in purely strategy A or strategy B independently.

##### Style Factor Correlation Examples

To illustrate the strategy correlation concept we mention above, we can look at equity style factors and their correlation. Equity style factors in general have some overall correlation principles but the correlation is time-varying and does move around over short time horizons. Two factors that have historically tended to have negative correlation are value and quality and value and momentum. Rolling 2-year correlation of the value factor to momentum, size and quality factors

Therefore an end investor if they wanted to increase their risk-adjusted returns could consider investing in two strategies, say for example value and momentum, to really benefit from this negative correlation to increase their overall risk-adjusted returns of their final portfolio.

##### Decrease portfolio volatility by equal-weighting value and momentum

An investor if they wished to reduce overall portfolio volatility could allocate 50% of their investment to value and 50% to momentum and

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