Fondering av pensionsåtaganden ock tidskonsistens

Time inconsistency

The objective of pension schemes is to provide incomes for its members in retirement; they have many long-term cash-flow commitments. The problem of time-inconsistency arises because the long-term objective may not be optimally achieved as a sequence of short-term actions, even if these are themselves optimal. Indeed the long-term objective may cease to be obtainable as a result of the short-term actions. St Augustine’s prayer, “Oh God, make me chaste, but not yet” summarises well the nature of problems of time inconsistency. Economics and finance are replete with such problems, as is human behaviour. In the game theoretical literature these problems are known as dynamic inconsistency.

As an illustration, think of a cartel which agrees to hold prices high for, say, their natural resource commodity by withholding some current production. This strategy will generate the maximum income for all from their endowment of the resource; it is optimal. Collectively, the members stand to gain much. However, all are aware that with high prices, they and other members of the cartel have an incentive to cheat and over-produce, in the hope of maximising their own immediate income, while depleting their endowment at a faster rate. The effect of such current over- production is to depress the current price. The cheating member receives less in total over the life of the resource than would be the case if it had stuck with the time-consistent cartel agreement.

When the agreement to withhold production is not credible and lacks a commitment mechanism, the cartel will be unlikely to achieve high prices as consumers will realise that individual producers will tend to cheat; pursuit of the short-term makes the long-term optimal unobtainable.

The change of behavioural focus from the long-term to the short-term does not arise from the arrival of new information; it is a question of the desire to maximise utility in the short term while disregarding the cost of this in the long-term.

Funding of pension schemes is itself time-inconsistent. Here the employee accepts deferred compensation from the employer but immediately demands funding of this deferred payment. This is a case of having one’s cake and eating it. Regulation which requires action based upon the immediate balance sheet, such as minimum funding requirements or solvency ratios, is similarly time-inconsistent and costly.

The temptation for the scheme is to engage in strategies that reduce the immediate variability of scheme assets relative to liabilities (hedging), rather than maximise the security of the long-term objective of paying pensions. In terms of investment management, this is the difference between speculation and investment. The definition here is simple: investment is concerned principally with the productive returns, the income generated, while speculation is concerned principally with the change in price over the holding period. Hedging is a form of speculation; it is time-inconsistent and costly in the long-term.

Such short-term inconsistencies are widely evident in finance – the paradoxical Black Scholes option replication strategy of buying as prices rise and selling as prices decline is one of the more obvious examples. It can also be shown that many common risk metrics, such as Value at Risk are time inconsistent. The now widely-discussed problem of pro-cyclicality in banking is an example of time-inconsistency induced by regulation.

There is a behavioural aspect to time-inconsistency; it is self-reinforcing. The hedging of risks in pension funds, a form of speculation itself, leads to increased allocations to other speculative instruments, notably hedge funds. This is an attempt to compensate for the long-term costs incurred in the hedging of current volatility.

It really is important to realise that the long-term return of investment management is dominated by the interim investment income and its reinvestment, rather than interim prices and valuations.

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