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Optimal strategic asset allocation cannot be the same for investors with different levels of wealth at different moments in time, argue Philippe Aurain and Eric Bouyé

Notwithstanding the debate around Gary Brinson's* work, investors have taken for granted that strategic asset allocation is the foremost pillar of any pension fund's investment policy. Many have chosen to define a static framework of fixed weights for asset classes, improved in some cases by a layer of tactical asset allocation to take care of short-term risk and opportunity.

So-called ‘long-term investors', whose liabilities are not due on short notice, have typically used this framework because they feel ‘easily' able to cope with difficult financial cycles, waiting patiently for better days and sometimes extracting compensation for illiquidity. By doing so they have avoided frequent rebalancing costs and the ‘saloon door' effect.

However, during the last decade's financial troubles the famous ‘fat tails' have caused extreme shocks, unexpected by investors, who have consequently been worrying about two issues: first, how sound are their long-term assumptions (including straightforward questions like, ‘Is there still a long-term case for equity investing?'); and second, how to take care of short-term extreme financial volatility to prevent it from hampering the fulfilment of long-term objectives? Along the way, they also discovered that many boards had a short-term implicit loss-limitation constraint: if the goal is to reach the port, many courses are not permitted or desirable, as some could lead to a shipwreck.

If strategic asset allocation aims to steer us around dangerous seas, a difficulty emerges: how to reconcile long-term return objectives and short-term protection?

Many researchers have tried to frame models in a multi-period context, assuming an objective of maximising expected utility. Initial studies found the optimal strategic asset allocation is independent of wealth and time horizon (it is ‘static', with fixed weights) under the assumptions that utility function is constant relative risk aversion (CRRA), that markets are perfect and complete, and that returns are independent.

Let's try to understand the intuition behind this result. Considering wealth: if the utility function is CRRA, risk tolerance is a linear function of wealth and grows proportionally with wealth. The relative proportion of risky assets remains unchanged and is independent of wealth.

Considering time: if returns are independent and identically distributed (IID), time holds no information about asset returns, mean-reversion, and so on. Returns linearly add up over time, as do variances. An increase in return is balanced by an increase in risk. The choice of the optimal portfolio is the same at each point in time. Asset allocation is independent of the time horizon.

Let's repeat this important statement: strategic asset allocation should be static if the utility function is CRRA, returns are IID and the time horizon is unique (meaning there is no constraint on wealth before maturity). This is relevant for many investors as they enjoy a sufficiently long time horizon; to make it simple, with time, many financial market imperfections disappear. Unfortunately, this is not the case for all investors.

There are two good reasons to contradict this statement: expectations and preferences.
Regarding expectations, investors may have reason to think that returns are not independent through time. Mean-reversion has been studied carefully and the results are convincing enough not to reject the hypothesis. If investors want to take advantage of this effect their asset allocation has to adjust to benefit from it - for example, by increasing allocation to risky assets to benefit from undervaluation.

In the field of preferences, investors might be willing to avoid certain courses that may lead them to have insufficient funding. To avoid some ‘states of the world' investors can frame the distribution of possible outcomes so that it integrates short-term constraints, targeted risk hedging or profit-taking.

The consequences on asset allocation are straightforward: in order to fulfil the constraints, asset allocation has to adjust dynamically. For example, the investor may specify that, in a specific dramatic case, the risky asset allocation has to be trimmed otherwise some defined stop-loss rule may not be satisfied. What should drive the right proportion of assets? Wealth (or ‘surplus', for liability-driven investments), risk aversion (roughly, defining the set of acceptable trajectories) and time horizon.

We are now ready to propose a definition for dynamic strategic asset allocation: it is a methodology to replicate a distribution of the wealth (a payoff) through states of the world and time, whose parameters depend on expectations and preferences.

In conclusion, theory and intuition converge in considering the usefulness of dynamic strategic asset allocation. By controlling risk, the investor avoids undesired trajectories for his wealth. He allocates through time depending on his wealth, expectations, the markets' parameters and, of course, his preferences.

Philippe Aurain is CIO and Eric Bouyé is strategic asset allocation specialist at Fonds de Réserve pour les Retraites

* Gary Brinson is a former investor and money manager. He founded Brinson Partners in Chicago

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