Customer Reviews

Mean-Variance Analysis in Portfolio Choice and Capital Markets

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The bible on mean-variance optimization for portfolio selection. If you need to know the nuts and bolts of how to do MVO, this book has it. But be prepared to wade through some fairly advanced math. Theoretically, anyone with college Calculus and Matrix Operations should be able to make it through the math. But I can tell you from personal experience, it's pretty rough going. The text is written for mathematicians, so unless one is very comfortable with some fairly advanced matrix work, it can be very hard to follow what's going on.

Peter Todd provides an implementation of Dr. Markowitz's algorithm in VBA. If you are a programmer, be prepared: The code was also written by a mathematician for mathematicians. If you don't understand the math behind the algorithm, you probably won't be able to decipher the code. And the code is complex enough that I doubt it could be copied by rote.

With all that said, this really is an incredible book. It is ideal for a team comprised of a mathematician and a programmer who need to write an application to do MVO. We are using it as our primary reference in creating an 'efficient frontier' optimizer for use in investment software.

The authors of this book essentially present a generalization of the simple mean variance approach to portfolio analysis.Risk is measured by an n x n variance -covariance matrix(as opposed to the simple case of measuring risk by the standard deviation,sigma).This approach is built upon the assumption of normality(joint normal,bivariate normal,multivariate normal,cumulative normal,log normal.The Central Limit Theorem is simply assumed to always be the case so that the distribution of the sample means will always approximate a normal distribution.J M Keynes expressed this conclusion by the statement that w,the weight of the evidence,equalled 1,where w was defined on the unit interval [0,1]).This essentially rules out the use of different probability distributions.The techniques illustrated in the analysis in this book do not have any application under conditions where any type of discontinuity and/or dependence of the data points shows up in the time series data.This is precisely what J M. Keynes argued in his 1939-40 dispute over the application of the use of multiple regression and correlation analysis to time series data concerning investment in plant,equipment,and inventories with Jan Tinbergen in the pages of the Economic Journal and what Benoit Mandelbrot has discovered time and again for over 50 years in his goodness of fit studies of financial market pricing data.It turns out the the Cauchy,Frechet,and power law distributions,like the Pareto distribution,are far more accurate representations of the time series data then the normal distribution,which is a special case of the Cauchy.This book presents an analysis of sound techniques only when the normal distribution is applicable.