I have thought about doing an introductory post on Bayesian Analysis for a a while now. There were several real-world applications that I considered – finance, machine-learning, election-forecasting etc.
Among these, the topic I can deal with most thoroughly, without inadvertently misleading the reader (or myself!), is probably finance. And one of the most accessible areas of mathematical finance is portfolio theory.
Beginning with a crash course in elementary statistical concepts, I hope to introduce what portfolio theory is about – the basics of the Capital Asset Pricing Model (CAPM) – where it works and where it fails – both in terms of theory and, more importantly, in terms of application to real-world scenarios.
An introduction to basic Bayesian reasoning will then follow. I do intend to use some concepts from probability and statistics to explain the ideas – but will focus more on the intuition than the mathematics.
I will then introduce a Bayesian take on portfolio allocation – the Black-Litterman model. The emphasis will be on the inherent intuitiveness of the model and how the allocations made using it are more robust than those suggested by CAPM.
Hopefully, this series of posts will be helpful to people who want to design portfolio-allocation frameworks of their own to manage investments (whether as a hobby or in a professional capacity).
So, stay tuned for the next part – where I will introduce some basic statistics and how it can help characterize the various attributes of a financial portfolio.
An Aside on Mathematical Prerequisites
I will use as little mathematics as possible to explain the concepts (referring to more rigorous articles, when necessary). I will also supplement the analysis with Python/R code to help the reader grasp these ideas (because nothing aids the understanding of a concept than writing code that implements it).
As a prerequisite, some familiarity with matrix algebra would be very helpful – as it helps make the notation very succinct and the concepts easier to follow (nothing too advanced, if you know how to multiply matrices together, then you know enough). Some basic calculus and algebra would be useful as well.
I do wish to point out, however, that there is no substitute to actually doing the math to really understand any conceptual model and the assumptions behind it. Intuition helps, but it can only get you so far. My intent here is to ignite your interest in these areas without being daunted and discouraged by the mathematical aspects of the theory at the outset.
It would be a great outcome if you would be willing to explore these areas further in a mathematically rigorous fashion as a result of reading these posts. It might be a bit cumbersome – but I assure you, the rewards, intellectual and otherwise, are worth it.