The aggregation problem in risk
Increased automation or adoption of high-dimensional statistics (machine learning methods) for arbitrage opportunities and asset allocation has been hailed as the new era in banking. To handle obvious challenges these bring, some (Andre Kirilenko ) have gone as far as suggesting algorithmic controls for regulation of algorithmic trading activities. The real challenge with regulation of algorithmic trading – in my opinion – is not different from that with regulation of manual trading. A solution should therefore be to gather more data on decision making rather than inspecting methodologies alone.
No matter which risk-measures are adopted, the financial decision at a bank is hardly a transparent process. This is largely due to structural reasons. The regulatory controls follow a necessarily fragmented approach since goals of the business units within an investment bank (desks or divisions) are varied. The view of the overall risk at a bank is a sum total of an entire suite of models varying across several desks at a bank. While model validation teams go through the painstaking task of validating all the model – the undertaking of an overall risk methodology is eventually about assimilating varied views tailored to the needs of the particular desks at a bank. The issue that no algorithmic control can address is that the aggregation to an overall risk is essentially of subjective nature.
Differences in perception of risk across banks is clearly not in the interest of policy (as it creates undiversified risks) but it may be in the interest of banks as such differences create risks which banks can attempt to mitigate for the clients. The task of regulating banks – made difficult due to the labyrinthine models and datasets at a bank – might actually be simplified with improved reporting and transparency if the banks end up relying more on automation. A shared and transparent view of long-term macreconomic risks – in my view – is a win-win situation for everyone.
Let me also emphasise that I am not a subscriber of the banks-are-evil camp and the reason for this fragmented view is structural. The non-uniformities in risk perceptions arise out of unknown traits of the clients that are only available to the respective desks at the banks. This information asymmetry is at the core of banking as a business. The trading or investing behaviour at trading desks is driven by any or all of i) the time-horizon of the investments ii) the type of client (if applicable) iii) the holding period of the particular type of products and iv) the market data relevant to the security. A fragmented view of risk is necessitated as every desk resorts to managing risk it in its own way.
The side-effect of such a segmentation of risk – is that there may be an insufficient market-diversification of the overall high-level risk undertaken by a large investment bank. Since a large investment bank engages with varied (nearly all) sections of the industry and it is often that only the bank has the information to separate clients who take long-term risk from those who take short-term risks, an inherent information asymmetry arises in favour of the investment banks. Consider for example the task of managing market risk associated with an equities portfolio at a bank. The equities desk is typically detached from the credit risk functions – which analyse the factors undermining the portfolio with a set of inputs different from what market risk may be interested in. If we were to understand the utility that the desks receive in a behavioural framework, the credit risk functions may elicit a utility under risk where low probabilities of loss are attached with a high amount while the market risk functions may attach a (relatively higher) probability to the portfolio’s under-performance. The probabilities inferred from historical volatility in the market risk division may be disconnected with the default probabilities that the bank may obtain from a third-party. A fragmented view of risk is evident as every desk resorts to managing risk it in its own way. While the usage of market-data by the banks for “risk” purposes is hardly uniform – the effect of their own private factors on the aggregated view of risk remains unaddressed. The different perceptions of risks within a bank create a private undiversified risk for the bank.
A Behavioural view of Aggregation
The mere admission that the allocation problem is subject to a subjective view of risk could help us understand how “private” factors could aggregate to a higher level of risk observed by central banks, regulatory agencies or those with a long-term view of risk. Viewing risk-incentives with Prospect Theory under information symmetry (i.e. bank knowing more about the client needs than the authorities) might help us better understand the incentives for market participation and for maintaining the varied notions of risk within large investment bank. That savvy investors at financial institutions do not have utility curves under risk different from retail investors has been wonderfully demonstrated by Abdellaoiu et al .
Recall that the core claim of a PT (see Tversky Kahneman) utility is that actions of individuals and firms alike are shaped by the perception of their future i.e. the probability of outcomes. In a subjective framework, the firms and institutions are assumed to be better equipped and more responsive than the individuals, and their view of risk is necessarily different from that of individual entities. The structured product salespersons and high-frequency traders all necessarily have a different perception of the same risk – which is associated with the entire market whose long-term trends the regulatory bodies may observe. In terms of the model, stochastic microevents are aggregated at different levels at organisation as they determine the subject probability at each level.
A large investment bank engages with varied (nearly all) sections of the industry and the issue of information asymmetry which it implies can be incorporated in this model as well – since the clients who take long-term risk cannot be separated from those taking short-term risks by nobody but the bank(s). The bank’s subjective view is different from that of the regulatory bodies. For example, if an investment bank B has clients P and Q so that P is client in the tech sector (which is in a high risk environment with a high chance to go bust in the next year) and Q is a client in the mining industry (which may be as stable as the country where the mines are). As a regulatory body is usually less aware of the needs of clients than the banks, the regulation may at best assume that the two types of clients are being treated the same way at a particular bank – as far as their risk profile at the bank is concerned. The subjective probability used by bank’s risk management team is necessarily different form that of the regulator.
A model for how such flows of information could quantify the incentives towards sharing of insider-information. Recall that the high-level PT utility can be expressed in the form:
Here, is a probability weighting function and is a value function (see Kahenman-Taversky for PT). Both are aggregated over time. Assuming that the value function is the same across the desks (there is no reason to believe that a dollar gained from a trading desk A should be viewed differently from another trading desk B) – the goal in the empirical analyses would be to elicit the weighted probability function parameters that “explains” decisions based on optimisation of in the data. The time horizon, type of trading (intraday, volatility etc.) and the holding period – all influence the formulation of probability and the parameters of this weighting function. The focus is to understand how the information required for activities of the bank are aggregated from the information that is available to each layer.
This behavioural view could help us understand if there are enough incentives from sharing information about risks through the markets when there are disparities in risk perspectives. If there are not sufficient incentives to participate in the market, then the differences in risk-perceptions may be a necessary evil that may sustain long-term risk in the bank. Incentives for market participation could develop if increased transparency on risk-aggregation is provided to regulatory bodies instead of focusing all the attention on details of models used to price securities in books run by each desk.
1 “Innovations in Finance with Machine Learning, Big Data and Artificial Intelligence”, J.P. Morgan Quantitative and Derivatives Strategy (2017).
2 Douglas W. Diamond and Raghuram G. Rajan, ” Fear of Fire Sales, Illiquidity Seeking, and Credit Freezes *”, The Quarterly Journal of Economics 126, 2 (2011), pp. 557-591.
3 Martin Evans and Richard Lyons, “How is Macro News Transmitted to Exchange Rates?”, Journal of Financial Economics 88 (2008), pp. 26-50.
4 H. Joel Jeffrey and Anthony O. Putman, “Subjective Probability in Behavioral Economics and Finance: A Radical Reformulation”, Journal of Behavioral Finance 16, 3 (2015), pp. 231-249.
5 Daniel Kahneman and Amos Tversky, “Prospect Theory: An Analysis of Decision under Risk”, Econometrica 3, 47 (1979).
6 Andrei Kirilenko AND Albert S Kyle AND Mehrdad Samadi AND Tugkan Tuzun, “The Flash Crash: High-Frequency Trading in an Electronic Market”, Econometrica 73, 3 (2017).
8 Bruno de Finetti, “La Prévision: Ses Lois Logiques, Ses Sources Subjectives”, Annales de l’Institut Henri Poincaré 17, 1 (1937), pp. 1–68.
9 Mohammed Abdellaoui , Han Bleichrodt and Hilda Kammoun, Do financial professionals behave according to prospect theory? An experimental study, Theory and Decision (2013) 74:411–429