Co-operation lies at the heart of most economic organisation. We ‘know’ that it can be beneficial. Its promotion has even found institutional form in international bodies such as the Organisation for Economic Co-operation and Development and the European Union. It permeates our everyday lives at all levels from the trivial to profound.
It permeates our everyday lives at all levels from the trivial to profound. One key institution, the company, is entirely dependent upon co-operation among and with its stakeholders. Yet when we come to its analysis, the academic work is deeply unsatisfying. We are faced with specific cases, or the abstractions of theoretical games, where strategies such as tit-for-tat dominate in repeated rounds.
Against this background, a recent short paper from Alex Adamou and Ole Peters “The evolutionary advantage of co-operation[i]” offers a new approach that holds the prospect of fresh insight into a wide range of fields, not merely economics. With co-operation constructed as risk-pooling and risk-sharing, and the insight that what matters is the time average return, not the expectation, they demonstrate that co-operation may result in all parties gaining. As Adamou and Peters put it “Pooling and sharing resources reduces fluctuations, which leaves ensemble averages (expected values) unchanged but, contrary to common perception, increases the time-average growth rate for each co-operator.” It is pleasing that co-operation arises naturally from economic self-interest and that its limits are well defined.
It also throws light on the caution exhibited by long-term investors. The penalty imposed under the time average approach, the wedge driven between the expected return and the time average, is quadratic; a portfolio with an expected return of 5% and volatility of 10% will experience a time average (or geometric) return of 4.5%; that same portfolio with volatility of 30% will deliver a time average of just 0.5%. Although long-term investors may not be subject to intermediate liquidation on disadvantageous terms, they have a tangible interest in ensuring that their portfolios are conservative and not highly volatile given the pronounced effect this has on their long-term performance.
In a first application of their insight[ii], with the academic and turgid title “Rational insurance with linear utility and perfect information”, Peters and Adamou consider the well-known puzzle of why insurance exists. They describe the puzzle in this way: “according to the expectation value of wealth, buying insurance is only rational at a price that makes it irrational to sell insurance. There is no price that is beneficial to both the buyer and the seller of an insurance contract. The puzzle why insurance contracts exist is traditionally resolved by appealing to utility theory, asymmetric information, or a mix of both”, and conclude: “In this new paradigm insurance contracts exist that are beneficial for both parties.”
The analysis throws up some other very pleasing results. A range of prices exists, where both parties will gain, which opens the prospect of negotiation of premiums for a particular risk. This admits the possibility that concerns over adverse selection and moral hazard may be accommodated and business still successfully written. A further result is that in the limit where policy loss exposures become negligible relative to the insurer’s wealth the time average converges to the expected value paradigm that is so comprehensively used in insurance pricing today.
This also throws considerable light into the design of some other financial contracts – notably pensions. The traditional defined benefit occupational pension was both risk pooling and risk sharing; it is part co-operative saving scheme and part insurance policy (against excess longevity). Intriguingly this work suggests that the insurance provided by the sponsor employer in supporting the scheme can be structured to be beneficial to it, whereas all analysis to date has considered this a pure deadweight risk for the employer. In addition, the fact that both savings and insurance elements are beneficial to scheme members should leave us in no doubt as to the inferiority of the individual defined contribution arrangements that are now so much in vogue. The collectivism of unitised DC savings really is no substitute for the risk-pooling and risk sharing of traditional DB.
Con Keating is head of research at BrightonRock Group
[i] Peters, O. & Alexander Adamou, The evolutionary advantage of co-operation, June 2015, http://arxiv.org/abs/1506.03414
[ii] Peters, O. & Alexander Adamou, Rational insurance with linear utility and perfect information, July 2015, http://arxiv.org/abs/1507.04655
Comments