Putting science into asset allocation

Asset allocation is typically too complex for formal analysis because there is a lack of sufficient information. What passes for quantitative study of the subject is often pseudo-science.

As a result, real decisions are largely made with an eye more to what everybody else is doing than a rigorous study of optimal allocation to meet (often unknown) plan risk return preferences.

To start with, modern portfolio theory is a static analysis. In biological terms equilibrium - that is a lack of movement - is otherwise known as death. Markets are about dynamics not just statics, about behaviour not just numbers, about history not just economics.

Likewise equilibrium concepts of asset allocation are merely poor, if necessary, approximations of an ever-changing reality. Moreover, such approximations are backward looking, biased against benefiting from structural changes and better at analysing cycles than trends.

So how can asset allocators cope in an ever-changing world? They have to steer a course between choosing investments that have known, stable and cyclical properties and those which may offer more diversity and return but are less well understood. The easy choice is perhaps to choose what one knows, but this would typically amount to sub-optimal allocation. An extreme example would be to just buy property in the town you live - with obvious problems of associated risk pooling, especially in an earthquake zone - but excessive concentration in US Treasuries, say, is also equivalent, a problem with which some central banks are now coping.

The alternate risk is that one chooses investments one understands so poorly that one risks losing embarrassingly large amounts of money - an argument against allocating to certain highly leveraged non-transparent hedge funds. What should the balance be and how to arrive at it?

The starting point has to be to know one's preferences. Just about all institutional investors would describe themselves as being conservative. But what does this mean if everyone is conservative? To say that one wants to take minimum risk can be to confuse means with objectives, and except for the extremely myopic, risk should be seen not as a single contingency (such as, say, losing 5% of one's pension fund) but as a series of contingencies over time.

These contingencies are linked: one's ability to weather a bad event in the future is a function of how much of a cushion one has built up, and so how much risk one takes today. So rather than just fix on a minimum expected loss today, there is an optimum level of risk for even the most conservative of investors which is a function of future liabilities and future income (contributions) as well as the nature, today and tomorrow, of the investment choices.

From this, one would expect both deeply under-funded but also over-funded pension funds to take most risk.

To analyse this we could borrow from micro-economics. Convex efficiency frontiers, representing possible portfolios, are types of production functions, and rather than using a straight line Sharpe ratio to determine which portfolio to choose, one should employ concave utility curves (curves of equal risk/return preferences). These utility curves could possibly be revealed through investor/trustee questionnaires.

The whole can be made three dimensional with the addition of time. A time vector of Sharpe ratios (possibly with some convexity for the impact on borrowing on its cost) gives the optimum level of leverage for the whole portfolio, and then a constrained optimisation using a Lagrange multiplier can be used to decide asset allocation.

If this is not complex enough, plan participant risk return preferences are not usually identical to those of trustees and other investment decision makers, leading to sub optimal allocations. Incentive contracts for decision makers might help to reduce this problem but are often not implemented.

The reality is that liabilities are often not well understood and may be surveyed with serious time lags. Even where a focus has been made to understand liabilities better, the resultant optimal allocation is not a simple matching of those liabilities. Further, preferences are typically poorly understood, and efficient incentive contracts are often lacking for decision makers.

So real time asset allocation using models is often impractically difficult and could get those who try it seriously into deep trouble. Moreover, a lot of smart people already know this really.

Coming back to earth then, asset allocation studies are largely exercises in how not to shock. The provider of asset allocation (as opposed to manager selection) advice often ends up as a one-size-fits-all service. For a more tailored service the adviser can, to some extent, vary advice depending on liabilities and may also be able to cater to particular investor/trustee prejudices and comfort levels. Certain investors are known to be more innovative and therefore are approached with new ideas first.

This brings us back to the actual way decisions are made - by rule of thumb sanctified by some third party. The easy option is to do what everybody else is doing with some possible innovation at the margin to outperform. Pensioners cannot eat relative return (in this case relative to peer group), but investment decision-makers can.

Traditionally, institutional investors thought of only two asset classes: debt and equity, defined as investments which promise a regular income stream, and those which do not but are linked directly to corporate profits. Everything else can be called ‘alternative'.

The evolution from this framework has been gradual. International components have been added to the debt and equity asset classes and the trend has been to separate them and call them new asset classes. The framework appears to be crumbling at its equity/debt core on two counts. First, bonds can be volatile and their providing a steady income flow is often little more than a convenient fiction. As one moves to areas such as emerging markets, bonds often have equity-type returns.

Second, the actual allocations of some investors, for example many foundations and endowments, has moved towards a 50% allocation to alternatives. So are they now the new core, and domestic debt and equity the new alternatives?

All investments are risky. So instead of asking whether something is risky, an asset allocator should instead ask two questions. First, is the risk priced in? Generally, for instance, emerging market sovereign risk is and developed market sovereign risk is not. Second, is it correlated to other risks in the whole portfolio? US Treasuries are not risk free, neither are they uncorrelated to other asset classes.

Asset allocation is a process, taking time and effort to understand the full range of possibilities. Issues such as market size, liquidity, and also growth prospects of strategies, are important, but it is also vital to use accurate data not prejudices to establish these factors. At $4.3trn (€3.43trn), the tradeable emerging debt market is, for example, much larger than the FTSE 100. And it grew at 29.5% last year. However, not many European, let alone UK, pension funds have anything like the same size allocation. Yet.

The only free lunch in asset allocation is diversification, and this has been aided by a rapid expansion of foreign investment opportunities since the end of the Cold War, the spread of globalisation and greater international economic inter-connectedness.

By contrast, the two great prejudices in asset allocation are the equity bias and the home-country bias. The traditional asset allocation framework makes it hard to break free of these factors, but there is an alternative to labelling the bulk of asset classes as alternatives. Instead of maintaining large core domestic debt and equity allocations, all strategies could be considered as possible allocations without bias. This, combined with a more serious effort to establish preferences and to match liabilities using all the possible ways of doing this could lead to less pseudo-science and more science in asset allocation.

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