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The Difference Between Correlation and Beta


In the above reasoning, which the majority of the public swallowed without flinching, there is a lot wrong with it. Such logic is clumsy, dangerous and shows that the information carried by the correlation is misunderstood. The objective here is in no way to comment on the assumptions of the reasoning or whether, in the future, the correlation between bitcoin and the Nasdaq100 will fade. The purpose of this paper is rather to explain to you, in an educational way, what information is contained in the correlation factor and the Beta so that you can make the difference between the two and no longer confuse them. I spoil you a little: it is quite possible that bitcoin and the Nasdaq100 remain very strongly correlated even if the first falls towards 0 while the second simply reaches the bottom of its range.

What information do correlation and Beta provide the analyst?

Beta and correlation (from Pearson) are two tools that are generally used for the purpose of diversification. When we are interested in a new title, we wonder if it will really bring something new to our portfolio or if it will bring more or less the same thing.

Mathematically (and in the context of finance), correlation reflects the tendency of two series of returns to deviate jointly from the average of their variations. The mathematical expression in question is not so simple to understand and even the previous sentence may not be obvious to everyone. What is extremely important to understand is that correlation only gives a partial description of how two assets move together. It measures the tendency that two investments have to move in the same direction, but it absolutely does not take into account the relative amplitude of the movements.

The Beta meanwhile gives both information! Direction and relative volatility. In other words: what is the variation of such an instrument when another instrument (often the benchmark) varies by 1%. This second tool is therefore much more relevant when it comes to comparing the returns of two investments.

Let’s see this with a very simple example (the data is fictitious):

Educational visual. Two perfectly correlated assets can evolve at different rates. Source: Zonebourse

The lower graph and the correlation matrix show you that the returns of certain assets can be perfectly correlated without them evolving at the same rate.

As you will have understood, the correlation gives interesting information, however, when it is used alone, it does not make it possible to judge the relative risk of two investments. The Beta calculation incorporates both the correlation and the relative risk between the two investments.

What is the logic behind adding new value for the purpose of diversification?

The educational work of Byron Monoghan, director at Mackenzie Investments, allows me to enlighten you on the theory of diversification. Be careful though, this is only theory, which is also based on the work of Markowitz dating from 1950 (widely questioned today). Let’s go back to the last sentence of the previous paragraph: “The Beta calculation integrates both the correlation and the relative risk between the two investments.”

This statement amounts to writing:

Beta formula simplified

Following the logic of modern portfolio theory, the job of an analyst who wants to diversify is to verify the inequality below. Without realizing it, it’s usually a translation of what you naturally check.

Logic of diversification

By using the first equation to simplify the second, we are able to understand the interest that Beta represents for the analyst who wonders about the relevance of adding the new investment to his portfolio.

Place of Beta in the logic of diversification

The analyst must therefore verify that the expected return of the new investment is higher than the expected return of his current portfolio multiplied by the Beta between the new investment and the current portfolio. When we look at inequality with hindsight, we notice that the notion of risk is contained in Beta.

Conclusion

On the first part of this article, I hope to have enlightened you on the differences that exist between the notions of correlation and Beta. Correlation measures the tendency that two investments have to move in the same direction, but it does not take into account the relative magnitude of the movements. The Beta meanwhile gives both information! Direction and relative volatility. If you want to continue reading and not stop there, feel free to continue by clicking on this link.

The principle of the second part was simply to present the approach underlying the objective of diversification, to allow you to understand the place of Beta in this reflection.


Main source: Mackenzie Investments



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