It is deeply important to develop tools to assist in design for groups, rather than just individuals. Group design is one of the more difficult design issues emerging, which becomes clear when considering the difficulty in determining the architecture of a robust financial system.
A new paper out of Nowak’s group from Harvard and others presents some quantifiable characteristics of a system to inform policymakers on regulation of financial markets. Basically the measure allows the design for regulation of a system, rather than solely individual institutions as is currently done.
In their work, a toy model is constructed to illustrate the trade off between optimal strategies for individuals, and for the group as a whole. For each individual, the incentive is to diversify. But if everyone diversifies in the same way, market shocks can easily spread and affect the whole system.
Each bank has some allocation of investments. In this model the assets are all independent and identical. Modeling these asset allocations as vectors allows one to compute the distance between them for all banks. This allows for measurements of the state of the system as a whole. One of these global quantities is D:
D [is] the average distance between the asset allocations of each pair of banks, scaled so that the distance between banks exposed to nonoverlapping assets is one.
This basically means that we look at how similar the investments are between banks. We scale this distance so that if there are two banks that do not share any assets, they will be distance=1 apart. The average of all of these distances gives D.
A second global quantity is G:
[G] is defined as the distance between the average allocation across banks and the individually optimum allocation.
G describes the imbalance of the allocations. There is some individually optimal allocation that is in the self-interest of each bank (in this case to place equal investments in each asset), and G is the difference of this allocation and the average allocation. Both of these quantities characterize the set of bank allocations: the first shows how diverse they are, the second shows how balanced they are.
Now why is this so important- why is it useful? Check it out:
All of this information suggests that it may be possible in principle, and it could provide a useful guide in practice, to regulate expected systemic cost. For a given level of capital, regulators might set a lower bound on distance D and an upper bound on imbalance G.
A lower bound on distance D ensures that the banks are not identically diversifying, and an upper bound on imbalance G ensures that the allocations among banks are not too imbalanced.
Both these parameters can be derived by the regulator without the need for complicated calculations of systemic risk, and they can be decomposed into their contributions from individual actors. We also show that a given level of expected systemic cost can be achieved with a more efficient use of capital if the regulator is able to encourage a suitable level of diversity
between banks in the system. Thus, this framework presents a potentially useful tool for systemic regulation
In principle, this should be an effective tool. Regulation of systemic risk has been discussed previously in a more qualitative manner, and this paper presents some simple simulations to illustrate this concept in a quantitative way. The results extend beyond financial systems, to more generally the tension that can exist in systems between individual and global optima with respect to risk. Illustrating calculations of D and G with actual data would be great next steps.
