Wednesday 30 October 2019

Markowitz 1952, what it does and does not do

Portfolio Selection, the original paper, introduces mean variance optimisation, it sets quantities as weights, it prioritises risk as variance, it operationally defines risk as variance as opposed to e.g. semi-variance, it gives geometric demonstrations for portfolios of up to four securities.  It comes from an intellectual statistical pedigree which is pro Bayesian (Savage).  It briefly connects E-V portfolios with Von Neumann Morgenstern utility functions.  It deals with expected returns, expected correlations.  It is neutral on management fees, transaction costs, if you would like it to be, since you can adjust your raw expected returns to factor in expected costs.

It doesn't give a mathematical proof in $n$ securities.  It doesn't generalise to dynamic expectations models $E[r_{i,t}]$ but assumes static probability distributions $E[r_i]$.  It doesn't introduce the tangent portfolio (a.k.a. the market portfolio).  It doesn't treat cash as a distinguished and separate asset class to be bolted on at the end of a 'risky assets only' E-V analysis.  It doesn't postulate what would happen if everyone performed mean-variance optimisation in the same way, i.e. it doesn't perform an equilibrium analysis.  It doesn't draw the risk-free to tangent 'capital allocation line' as a mechanism for leverage.  It doesn't assume unlimited borrowing.  It doesn't allow short positions.   It doesn't give techniques for solving the optimisation problem.  It doesn't talk about betas.  It doesn't prove which sets of utility functions in the Von Neumann-Morgenstern space are in fact economically believable and compatible with the E-V efficiency.  It doesn't just assume you look at history to derive returns and correlations and your're done.

Taking Sharpe and Markowitz as canonical, I notice that Shape seems less enamoured with Bayesian approaches (he critiques some Robo-advisors who modify their MPT approach with Black-Littterman Bayesian hooks.  For seemingly different reasons, they both end up not embracing the market portfolio/tangential portfolio idea; in Markowitz's case it is because he doesn't agree with the CAPM model assumptions which theoretically get you to the market portfolio in the first place, and with Sharpe, it is because he moved his focus from the domain he considers as having been converted already to pro-CAPM approaches, namely the professional investment community focused on accumulation of wealth, towards the individual circumstances surrounding retirees, in the decumulation stage.  However, I think, if you strip away why he's allowing more realism and individuality into the investment decisions of retirees, it boils down to Markowitz's point also.  Namely that realistic model assumptions kind of kill many flavours of pure CAPM.


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