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The Actuary The magazine of the Institute & Faculty of Actuaries
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Book review: Anticipating Correlations

Professor Robert Engle’s book, based on a series of lectures to the Econometric Institute at Erasmus University, forms a cogent survey of a range of ways in which financial mathematicians have tried to model correlations between financial factors.

Many factors exhibit correlations with others. For instance, currencies show alignment, as do stocks in similar sectors. However, at times, stocks and bonds show very varied levels of correlation, alternatively positive and negative. Predicting how these change over time and anticipating what the market might be doing next is a trick which, if successful, carries huge market advantage. Hence the efforts put into such prediction.

Engle looks first at the economics underlying the correlations, peppering his papers with references to books and papers (a huge number by himself) in recent years. Classes of function are briefly introduced before the meat of the book delivers an analysis of the models that are in use and their suitability. His own ‘Dynamic Conditional Correlation’, which attempts to produce moving correlations based on developments in the recent — but not too recent — past, is shown to be the best by a number of measures. As with all modelling, one is given to wonder whether any advantage demonstrated by back-testing will in fact be eroded by use and its impact on future market behaviours.

The scale of some systems is such that the matrix inversion required becomes too voluminous for practice. Pairwise estimation is treated as a means to a solution, which he names the MacGyver method, after the popular US TV show. This and other techniques are introduced in later chapters to assist those who are thinking of implementing such approaches.

Professor Engle recognises that the key to success is in methods that anticipate future trends correctly and admits that much more research and investigation is needed in this area. Examples of behaviours from 2007 are given to demonstrate the difficulties and some of the ways to solution. The responses of markets in credit derivatives are given some interesting treatment, in the light of what has been happening so recently.

No doubt much more literature will develop in this area. Professor Engle has done a service by laying out how his mind is moving and thinking at the current time.

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