Markowitz’s European tour
Portfolio theory is alive, flourishing and set for another 50 years at least – that was the message from Nobel prize winner Professor Harry Markowitz, when talking to the PGGM ‘Beyond the year 2000’ conference held in The Hague recently.
Markowitz reviewed the development of the theory since the early 1950s, when it first emerged and examined how portfolio theory itself encouraged globalisation of investment. “This happened by at least three paths,” Markowitz explained. “The first of these were academic studies, which said that if you diversified globally you would have less risk and volatility for given return. That actually happened and that encouraged global accounts.
“Another type of academic study was concerned with the question: ‘Why is it that people invest more in their own countries than these optimum calculations would indicate?’ The studies came up with various explanations, but these do not fully explain the strong home bias and that people ought to be investing more internationally,” said Markowitz.
“The third avenue, at least in the US, were the consultants, particularly George Russell of Frank Russell Co, who said: ‘We keep investing the pension funds we advise in US securities. They are highly correlated. Portfolio theory tells us to find investments which are not going to go up and down together. So our clients would do well to spread their investments more globally.’ This was a major force in increasing the globalisation of US pension funds.”
He then went on to answer his question: “How did globalisation affect portfolio theory? The basic maths I published in 1952 and 1959 does not change. It is still true that the expected return on the portfolio is related in a certain way to the expected returns on the components and the variance of the portfolio is related to the variances of these correlations.
“But if you are going to apply portfolio theory to global portfolios, somehow someone has to come up with expected returns and variances and correlations for global asset classes and securities. So, for example, we have the JP Morgan risk co-variance matrix, where the company has made its estimates of variance and correlations for various classes of securities.
“As far as expected returns go, Fischer Black and Bob Litterman at Goldman Sachs came up with certain methodology for estimating expected returns for currencies and so on. They said the problem with applied portfolio theory is that you have to come up with estimates of expected returns for each currency and each asset class globally and said: ‘Maybe you, Mr Banker, have some estimates you wish to make for the franc and mark, but not for the peso. But where you do not want to make estimates, we will use equilibrium beliefs.’ But where do these ‘beliefs’ come from? They came from the capital asset pricing model, that came from portfolio theory. ‘But where you do have beliefs we will use these and they will become an input for the PT calculations.’ ”
Markowitz then turned his attention to the future of portfolio theory. “There are two questions that can be asked: ‘Will the theory continue to be used?’ and ‘Will some of its internal details change and if so, how?’
“I do believe that portfolio theory will continue to be used in the next 50 years, and increasingly. Uncertainty is something that is intrinsic in markets; it is part of the world, part of competition, and is not something we should try to get rid of. So the world will remain competitive and therefore will need portfolio theory.
“Secondly, there is technology. Under Moore’s Law, the cost of computing is due to come down at a fantastic rate. This makes applications of PT feasible that were not when I wrote my book in 1959.”
Markowitz said he had done some work on how the internal working of portfolio theory would be different 50 years from now. “One of the things that is happening now is that, both in theory and in practice, there are questions about what kind of criteria of risk you should use – whether it should be mean variance, semi-variance or absolute deviation. In my view, what we really ought to be doing is something that is a little bit more complicated than maximising expected utility. In my 1959 book, I said mean-variance is a lot easier to do as you don’t have to get anyone to psychoanalyse people’s utility functions. I argued that if you picked carefully off the efficient frontier you will approximately maximise expected utility, even if the individual does not know what his utility function is,” he said.
“But in the next 50 years, our increasingly sophisticated investors will start writing down what their utility functions are. That would change somehow, how the calculations are done.”
Summing up, he said: “PT, which has been around for half a century, has increasingly become part of investment process; it has encouraged the globalisation of investment and the way it has been used has been influenced by the globalisation. I think this will keep on going for centuries.”
The next day, it was a question of work in progress at the workshop session, organised by Palladyne Asset Management, with which Markowitz works. He gave a joint presentation with Palladyne CEO Erik van Dijk on developing tactical asset allocation (TAA) models. Markowitz discussed a simplified model where there is some predictability in the TAA and transaction costs. “The question is in this simplified world, with these features, what should you do?” he asked. Looking at a world where there is just equity and cash in the portfolio and the TAA model is predicting “a state of the world”, this may be “optimistic”, “very optimistic”, “slightly optimistic”, “neutral”, “slightly pessimistic”, or “very pessimistic” about returns.
If the transactions cost on buying and selling securities is 1% or 2%, including any market impact costs, with the cost of having a future or call for a month as put at 10 basis points. Working through the various scenarios, but with a 2% transaction costs, to move from a 60% equity content in portfolio was not worthwhile. “Once you have 60% in your portfolio you never change, no matter what happens. So the model is very inert on the chosen parameters.”
In the scenario of extreme pessimism, the result is that almost nothing is done by way of transactions.
“Based on the work we have done, we are surprised at how inert the optimum solution is. The decision to use futures or options depends on what their costs are. With transaction costs at 2% once you get yourself to 80% or 90% equities you stay there – stationary. With 1% costs you are wandering backwards and forwards from 60% to 80%.” Markowitz said.