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.

Markowitz v shareholder value

Isn't it strange that Markowitz taught us that when it came to returns, maximising value is a stupid idea, whereas when it comes to evaluating the behaviour of managers in firms, maximising value stands still alone as a universal goal in US/UK models of capitalism.

Or, spelled out a little, companies are allowed to act as though they have permission exclusively to increase the share price (and hence increase the period return on the share price) as their operational definition of the goal of maximising shareholder value as opposed, for example, to maximising risk adjusted expected returns.

If risk adjusted returns are the goal for investors in portfolios of stocks, then why aren't they also the goal for owners of individual stocks.

Shiller advice to Oil heavy central banks

By the way, in the same video, did Robert Shiller really advise Norway and Mexico to take up massive short oil futures positions just to get them on to the efficient frontier?  He forgets to mention here that in doing so in such a size, you're bound to impact the underlying oil market, adversely, so that cost needs to be written against the benefit you'd have in moving closer to a more efficient national portfolio.  Another cost would be the cost of all those short futures would increase the basis between oil futures and oil itself.  You'd be paying that price on an ongoing basis as each future rolled.   Thirdly there's the mark to market issue.  Fourth there's the issue of which magnitude to short, the extracted oil only?  The total resource in the country?  Not at all quite as clear cut advice as he makes it sound here.

portfolios of asset types can contain hidden correlation

The risk of creating portfolios with asset classes is that there is hidden correlation.  For example, Shiller in this lecture, around the 55 minute mark in explaining the virtues of efficient portfolios, claims that having stocks, bonds and oil in your portfolio in some combination is a good thing, since it reduces correlation.

Well, to carry that point of efficient E-V further, you end up wanting to dis-articulate stocks into factors, since some stocks are more heavily oil sensitive than others, some stocks, with stable and predicable dividends, are more like bonds than others.  Just leaving the object set of the portfolio at assets leaves some hidden correlation off the table.  

In a sense, then, factor models are ways of taking x-rays of a security to see how correlated they are to fundamental economic elements (oil, carry, momentum, etc.)

In the limit, I think a good model needs also an element on the cyclicity of factors.  The most stable, that is, acyclic, factors are already found and have reasonable stories which persist through business cycles.  But this doesn't mean the rest of the factor zoo is for the dump.  If they can be attached to a meaningful theory of the business or credit cycle, then a factors carousel can be created.   Not all correlations are linear and constant.  Some can by cyclic, so perhaps linear regression isn't the ideal form for producing and measuring these correlations.

But getting a nowcast or forecast of economic conditions is not easy, nor do I think it properly interacts with factor models.

Portfolios of what?

Markowitz clearly had portfolios of stocks in mind.  It is also possible to see cash as another asset in the mix there, and government bonds.  But why not strategies or asset classes or even factors.  I really like the idea of strategies-and-factors.  To make this clear, imagine there was a well represented tradable ETF for each of the major strategies, being macro economic, convertible arbitrage, credit, volatility, distressed, m&a, and equity long short, commodities, carry trade.  Furthermore imagine that the equity long/short was itself a portfolio of factors, perhaps even itself an ETF.

A portfolio of factors from the factor zoo makes for an interesting though experiment.  I realise just how important it is to understand the correlation between factors.

Also, in the limit, imagine a long stock and a short call option on the same stock.  Can delta be recovered here using the linear programming (or quadratic programming) approach?  Unlikely.  But it highlights one of the main difficulties of the portfolio approach of Markowitz - just how accurate (and stable) can our a priori expected returns and expected covariances be?  

Imagine a system whose expected returns and expected covariances are radically random on a moment by moment basis.  The meaning and informational content of the resulting linearly deduced $x_i$s must be extremely low.  There has to be a temporal stability in there for the $x_i$s to be telling me something.  Another way of phrasing that temporal stability is: the past is (at least a little bit) like the expected future.  Or perhaps, to be more specific, imagine a maximum entropy process producing a high variance uniformly distributed set of returns; the E-V efficient portfolio isn't going to be doing much better than randomly chosen portfolios.

Also, surely there ought to be a pre-filtering step in here, regardless of whether the portfolio element is a security or a factor or an ETF representing a strategy, or perhaps even an explicit factor which is based not on and ETF but on the hard groundwork of approximating a strategy.  The pre filtering strategy would look to classify the zoo in terms of the relatedness of the strategies, on an ongoing basis, as a way of identifying, today, a candidate subset of portfolio candidates for the next period or set of periods.  Index trackers (and ETFs generally) already do this internally, but it ought to be a step in any portfolio analysis.  The key question you're answering here is: find me the cheapest and most minimal way of replicating the desired returns series such that it is within an acceptable tracking error.