The pension problem is simple: a question of assets, liabilities and the difference between them - an asset or liability. Risk is mostly simply and generally defined as the rate of change of an object. The rate of change of an asset’s value, its risk, we know by the term return. It really is as simple as this – returns matter in asset management.

As long as its corporate sponsor is not insolvent no pension scheme is insolvent – to quote Standard & Poor’s ‘The primary threat to schemes is the insolvency of the sponsor’. Immediately the ‘deficits’ of pensions schemes can be seen as conditional shortfalls and the central question becomes when should schemes be fully funded.

The only point at which we can (and should) unconditionally answer positively is at the instant of insolvency of the sponsor parent.

We can see immediately also that neither the scheme nor the company should ever wish contributions to be made if the marginal return on fund investment assets is below the return on assets of the company, since such action would increase its likelihood of insolvency.

The shortfalls of funded assets to liabilities may be protected by taking security on the assets of the corporate sponsor as, for example, Daimler-Chrysler report having done. The shortfalls may also be insured and there are close substitutes for insolvency insurance in the form of the capital markets instruments known as credit default swaps. Indications are that the Pensions Protection Fund (PPF) would like to encourage such practices and clearly there is a cost saving in terms of the PPF levy for an insured/secured fund.

For most schemes, liabilities stretch far into the future and what matters is that we have assets to match liabilities at these future dates. It does not and should not matter how we get there; such a process is path independent. However by introducing interim ‘solvency tests’ or, even worse, an implicit continuously 100% funded concept, we are introducing path dependency into the process. This is costly. By way of illustration: matching future cash-flows exactly, a process known as dedication

in the bond markets, is strictly more expensive than matching interest rate sensitivities, which is known as immunisation.

The analysis of funded pension schemes amounts to the analysis of a with recourse securitisation. In any securitisation of assets, it is usual to maintain liquidity reserves for debt service and administration, but it is rare indeed for these liquidity reserves to exceed two or three years outgoings. This raises the question why pensions funds focus to such a large extent upon holdings of liquid, tradable assets. The more important element of a securitisation, however, is that the expected returns cover the expected debt service, and usually carry a margin of safety for unexpected variation. The analogy tells us that if we buy assets with low expected returns, we will never achieve the liability amounts, unless we buy lots of them. In turn that will raise the contribution costs, as Boots have come to realise in the period since their much-publicised move into bonds.

If, nevertheless, matching with bonds is still desired, there is actually a new, and better security structure than conventional bonds – the Evergreen, a constant maturity bond.

In the perfect storm engulfing pensions schemes there is even a measurement problem in the form of the mark to market accounting regime. It should be obvious to all that a common measure for assets and liabilities is needed. But the problem of the new accounting standards is more than this.

The question in the case of pensions schemes is compounded by the fact that the market price measure reflects different risk appetites and tolerances at different points in time – as is obvious from market bubbles and crashes. Mark to market is acceptable if the time scale is that of securities traders but completely inappropriate when the time scale is 30 or 50 years.

The relation between returns, the variability of returns and the degree of diversification is the basis of the most widely used model for asset portfolio construction – the Markowitz mean-variance asset portfolio optimisation. By examining the effect of a small error in the estimates of these input terms we can gauge the relative importance of return, risk and diversity in asset portfolios. It turns out that for reasonable values of these inputs an error in expected return is an order of magnitude more important than an error in standard deviation which in turn is approximately four times as important as an error in the correlation matrix.

Anyone familiar with bond analysis would similarly be aware that duration is typically an order of magnitude of more important than convexity. These are direct analogues of return and risk from generic assets – and accord with our earlier definition of risk. Returns are an order of magnitude more important than risk.

Some advance and promote bond-only allocations on the basis that ‘theoretically’ risk-adjusted returns should be the same for both bonds and equities. This is nonsense – the risk-adjusted return is not even the same for differently leveraged bond funds. A simple numerical example will illustrate this. Suppose that the rate of returns from bonds is 1% with a standard deviation of 2% and that the risk-free rate is 0.4%. Then we have a Sharpe ratio, a risk adjusted return, of 0.3, = (1 – 0.4) /_2. Let us now borrow at the risk-free rate and gear the portfolio to twice its original size; the returns are now 1.6%, = 2* 1 –_0.4 , and their standard deviation is 4% = 2*_2 . In this levered portfolio the Sharpe ratio is 0.4, = (1.6 – 0.4) /_4, one-third better than the un-levered. These risk-adjusted measures are simply measures of efficiency. It is both scale and efficiency that determine the total return produced, in any process.

The risk premium of an asset is a simple concept; it is the price that we would pay to get rid of the uncertainty. This is clearly a function of time. The price, or excess return, that the market offers to us also varies in time, with the market’s ability and desire to accept risk. The ability of an investor to absorb risk increases with the length of their investment horizon, if there is no path dependence. The practice of marking to market and applying ‘solvency’ tests effectively destroys this ability – rather a fine example of well-intentioned, but misguided regulation.

There is much confusion in discussions of pensions asset allocations as to the riskiness of different asset classes over time, which we shall try to clarify with a few illustrations. In the examples that follow we consider the funding ratio of a defined benefit scheme. Risk is a shortfall to known liabilities, which grow at 5% annually. Return is surplus

to these liabilities. These results are a simulation from a 40-year data set of monthly UK equity and bond index returns. The bond dataset has a mean of 6.1%, with standard deviation 7.3%, and equities 8.4%, with 17.7% standard deviation.

This shows the average surplus or deficit of the funding ratio, conditional upon a surplus or deficit. In other words if I lose, how much do I lose on average, if I win how much do I win on average. We see that as we lengthen the time horizon the loss increases and is approximately linear with respect to time. By contrast the expected surplus increases exponentially for both asset classes.

Perhaps the more widely used measure looks at the ratio of unconditional gains to losses, which is the basis of Omega functions. Again we are working with surplus and deficit relative to liabilities, which are growing at 5% annually. This can be considered as a risk adjusted measure. This is shown as figure 2.

Here we see that the ratio of expected return to expected loss is strictly positive everywhere and that while both grow exponentially, equities tend to do so at the higher rate.

In a short article such as this it is impossible to do much more than touch upon the subject of pensions and there is much that has been omitted. Topics such as longevity – is the corporate pension scheme not in fact the correct place for this risk to reside? Or the role of inter-temporal risk transfers in enhancing the apparent returns of some hedge fund strategies – insurance by another name, with incorrect accounting. We hope that by addressing the basics alone, that we have added some insight to a world that can only be described as suffering from a confusion of advice.

Con Keating is with the Finance Development Centre in London

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