One of the few things that we know about risk is that it means that, over some future period, more things may occur than actually will eventuate. The role of an active asset manager is to seek to determine which will, and then to take actions to avoid or mitigate these circumstances.
In our context, Risk is simply the undesirable subset of the Uncertain Returns set. It is a return differing only in magnitude from those returns usually described as returns. Almost twenty years ago Bill Shadwick and I introduced a measure, known as the Omega function, based upon the partitioning of the returns distribution about some chosen risk threshold. Around any return this is a pay-off or odds ratio; a form of value for money metric. As this is not central to this article, we shall simply state that further information on that metric is available on request. For now, we will observe simply that return and risk are nonlinearly related, and that this is 1:1 only at the mean or expectation of the distribution.
For completeness, we should note that investment performance evaluation often involves the comparison of the entire returns distributions of funds. As methods based upon the descriptive statistics, such as the moments, of a distribution are usually incomplete and may be systematically gamed, we have offered a simple algorithm which facilitates accurate and complete comparison of discrete samples. If we wish to compare two distributions, we need to apply an affine transformation to one or other such that the two distributions share a common range of support, at which point we may integrate the differences between the two distributions. The transformation involves the translation and rescaling of one or other distribution. Illustrations and worked examples of this method are available on request.
There are innumerable approaches to portfolio management, with most being distinguished by their approach to risk. Fortunately, there is a simple metric which allows us to compare, unbiasedly, portfolio results regardless of the strategy which generated them; this is the internal rate of return (IRR). It is a risk-experienced average rate of return. Risk events which have occurred are incorporated into the values on which it is based.
The defence of poor relative performance based upon the ex ante risk preferences associated with a portfolio is a very weak one. Nonetheless, it has become something of an all-purpose defence for underperforming fund managers. It amounts to saying: we underperformed because we had incurred costs hedging and mitigating events which did not come to pass, or had come to pass but were of lower magnitude than was expected. Of course, had those events occurred, the fund’s performance would most likely have been stellar.
Contrary to the apparent beliefs of some commentators, hedging all risks is simply not feasible. The only perfect hedge of an asset (or equivalently a liability) is its sale, The costs would be prohibitive, even in partial form, as it amounts to disinvestment, or the holding of cash. This is one of the major flaws with any general invocation of the precautionary principle. The opposite, the stoic acceptance of the outcomes of all occurring events, is perfectly feasible; it is passive investment.
Some strategies, such as funding DB pension schemes to ‘self-sufficiency’, do not fare well when viewed in this light. Funding to the level of technical provisions is to a level which is expected to be sufficient to meet scheme liabilities, with any adverse developments then being the concern and cost of the employer sponsor. By following a strategy of self-sufficiency, the scheme is introducing costly redundancies since this covers the gamut of possible risks, many of which may not occur.
By introducing a comparator benchmark, we may establish the relative costs of different strategies. While the benchmark might be almost any portfolio of investments, for AgeWage we have chosen to use a portfolio of 80% equity and 20% debt securities as this allocation has been the average over the past forty years followed by pension funds of the defined contribution type. It is of course investable, and might have been adopted by any. It is in this sense a reasonable counterfactual. We have investigated other allocations and found that the differences over the long term are small. The IRR of this passive, but rebalanced benchmark provides an IRR which reflects all of those risk events which did occur. Comparison of a particular fund’s IRR with this benchmark IRR delivers an objective measure of the value added delivered by that fund.
The AgeWage score is simply a normalisation of this relative value-added, where the average constitutes a score of 50 with inferior value below and superior above. The score may be interpreted as the likelihood of achieving the results observed.
The value for money analysis conducted in this manner is all historic, and as the well-known caution advises may well be a poor indicator of future performance.