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RESEARCH

Man versus Machine:
Visualising Correlations

Frederiek Van Holle, PhD – Quant Solutions
Joeri Willems, CFA – Quant Solutions

wit-pijl

Cluster analysis via unsupervised machine learning

For an investor, determining how much to invest in stocks and bonds can be something of a challenge. The theory tells you to put a numeric value on your risk aversion, estimate the volatilities of the assets and the correlations between them, express your “utility function”, i.e. how afraid you are of risk and how much return you wish to obtain and, finally, put all this information in a well-constructed optimiser to get the answer.

Reality is often far removed from theory, and less sophisticated investors select portfolios based on predetermined risk profiles such as “defensive”, “balanced” and “dynamic”, assuming that the providers of these risk profiles have done the necessary homework for them. The story becomes even more complicated when you want to combine different equity strategies, different types of funds and alternative strategies such as hedge funds. A diversified portfolio should take into account all the linkages between these different assets in the portfolio because combining similar strategies is not a sensible thing to do as it will lead to a concentration of risk in the portfolio.

The linkages between the different assets in a portfolio are summarised in a so-called covariance matrix. The raw material of this matrix consists of the volatilities of the different assets in the portfolio and all their pairwise correlations. Although this covariance matrix contains a wealth of information, for the ordinary mortal this matrix is just a collection of numbers (and a lot of them at that).

In this article, we present a way to visualise the correlation matrix in an attractive and didactic manner. This will help both to understand the dynamics within an investment portfolio better and to determine whether adding a certain asset class or strategy to the portfolio makes sense from a diversification perspective.

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