In 1990 Markowitz was awarded the Nobel prize, so I had a read of his short acceptance speech, which quite clearly sets the scene for his work. He describes microeconomics as populated by three types of actor - the firm, the consumer and the investor (that last one being the actor he focuses on). He then also interestingly creates binary divisions on work in on each of these three actors. First, the individual and then the generalised aspect of their ideal behaviour. How ought a firm best act? A consumer? An investor. After having answered these questions, the generalisation is, how would the economy look if every firm, every consumer and every investor acted in the same way.
It is worth pausing on just this point about generalisation alone. Clearly the question of uncertainty must raise its head to our modern ear. Can one model all firms as following he same basic template, a so-called rational template? If we can, then we may identify an economic equilibrium state. Likewise, with consumers, how does an economy look if everybody is consuming according to the same basic utility function. In both of these cases, whilst uncertainty is present, and known about by economic modellers, it is given a back seat. Markowitz accepts this, but shows how it is literally impossible to background when it comes to the actions of the rational investor, since doing so leads to a model where every investor picks the single security with the largest expected return. This does not happen, so any model which treats risk/uncertainty poorly is insufficient.
I think it is probably widely agreed that today, models of the firm's behaviour and of consumers' behaviour is best done with uncertainty built into the model. The old linear optimisation models accepted that variability in firms, or consumers could be averaged away. That is, that it was a valid approach to assume minimal uncertainty and see how, under those simplifying model assumptions, equilibrium models of the economy might be produced.
But fundamentally, portfolio investing in the absence of risk makes no sense at all. In this case, in the limit, we find the portfolio with the best expected return, and put all our money in this. However, not many people actually do that. So, in the sense that the micro-economic models of the investor make claims to model actual behaviour, then uncertainty must play a more prominent role.
Markowitz also hands off on 'the equilibrium model of the investor' to Sharpe and Lintner's CAPM. He is happy to see basic portfolio theory as the element which attempts to model how people actually act (hence, a normative model) and leaves positive elements to Sharpe's theory, which I think he does so with only partial success. But certainly I see how he's keen to do so, especially since his mean variance functions are not in themselves utility functions, and in that sense don't touch base with economic theory as well as Arrow-Pratt.
Rather, looking back on his achievement, he makes a contrast between Arrow-Pratt and his own, perhaps more lowly contribution and praises his approach as computationally simpler. This may be true, but it isn't a theoretically powerful defence. However, I like Markowitz, I like his lineage, Hume, Jimmy Savage and the Bayesian statistical approach. I'm happy to go along with his approach.
I notice how Markowitz gently chides John Burr Williams for describing the value of an equity as the present value of its future dividends, instead of describing it as the present value of its expected future dividends, that is to say, Markowitz draws out that these dividends ought to be modelled as a probability distribution, with a mean and with a variance.
Markowitz also highlights early on in his career that he reckons that downside semi-variance would be a better model of risk in the win-lose sense, but he notes that he's never seen any research which shows semi-variance captures a better model than variance. This is a rather passive backing off of his original insight into semi-variance. Did he not consider doing any real work on this? Is it enough for him to note that he hasn't seen any papers on this? However, it is certainly true that there isn't a huge numerical difference in equity index returns, usually, so I could well believe this doesn't matter as much as it sounds, though it would be good to know if someone has confirmed it isn't an important enough distinction.
What Markowitz in effect did was replace expected utility maximisation with an approximation function, which is a function of portfolio mean and portfolio variance, and then he, and others later, try to reverse this back in to particular shapes of utility function. This is where the computer science algorithm of simplex, together with the ad hoc objective function involving maximising returns and minimising variance attempt to meet top quality economic theory, as expressed in Morgenstern and Von Neumann.
Markowitz then spends the rest of his lecture showing how strongly correlated mean-variance optimisation is with believable utility functions.
He wraps up, as I'm sure many good Nobel laureates do, by talking about new lines of research. Here, he lists three: applying mean variance analysis to data other than just returns. He refers to these as state variables. They too could have a mean-variance analysis applied to them. Semi-variance, as mentioned already, is another possible new line of development, and finally he mulls over the seemingly arbitrary connection between certain utility functions and his beloved mean-variance approach. The slightly point here is that all three of these potential lines of investigation were already candidates back in 1959, yet clearly here is Markowitz in 1990 repeating them as issues still.
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