Risk and uncertainty are an integral part of most human behaviour, as only rarely are the outcomes of human actions predictable with complete certainty. They are particularly evident in economic and financial affairs, with risk and uncertainty forming the basis of financial contracts and the role of financial institutions, instruments and markets. Thus financial markets exist in part to enable people to deal with risk and uncertainty in their financial affairs, and many instruments (insurance, futures, options contracts, etc.) exist in order for risk and uncertainty to be managed. If risk and uncertainty were removed entirely there would be little for the financial system to do, or what it would do would be fundamentally different from the role it actually plays.
It is not surprising, therefore, that much of the formal analysis of risk and uncertainty has been undertaken in the area of finance. However, while finance has its own special characteristics, the relevant analysis and axioms derived in this area apply, in varying degrees and forms, to other areas of behaviour.
Although in common usage the two are frequently interchanged and regarded as alternative terms for the same phenomenon, this is erroneous as they are distinct concepts. Uncertainty arises when the future is unknown but no actual probabilities (either objective or subjective) are attached to alternative outcomes. Risk arises when specific numerical probabilities are attached to alternative outcomes. Thus the foundation of a large part of risk analysis lies in probability theory. The starting-point is that, in most areas, economic agents are risk-averse in that they gain no intrinsic welfare from knowingly taking risk. It follows from this that, other things being equal, agents prefer less risky to more risky projects and behaviour, and that attempts are frequently made to avoid or limit risk. However, other things are not equal, and agents can be, and need to be, compensated for taking risk. The risk premium that is received is such a compensation. Thus, other things being equal, agents prefer high to low rates of return and low rather than high risk. This means that agents are prepared to pay a higher price for less risky assets with a given expected rate of return, and that higher returns are available only if more risk is taken.
A distinction is also drawn between risk and seriousness. The former relates to the measurable (actual or assumed) probability of event X happening, while seriousness relates to the impact on the agent if X does occur. Thus assuming X is an undesired outcome, agents will avoid exposing themselves to the possibility of X occurring: the higher is its probability, and the more serious the outcome would be for the agent, the less is the compensation offered. Thus, we are not indifferent between two risks with the same probability (say an earthquake occurring and the chance of it raining) when their seriousness differs, and conversely we are not indifferent between two risks that have the same degree of seriousness but different probabilities. Behaviour is, therefore, influenced both by the risk of an event or outcome and the potential seriousness of it if it occurs.
This, in turn, gives rise to the concept of disaster myopia where, confronted with low-probability/high-seriousness risks, agents behave as if the probability were zero rather than low and, in the event that the risk materializes, the impact on the agent is very serious. Because the probability is viewed as being zero (rather than very low) no protection is taken. There must be a greater than zero probability that reading this article will induce acute schizophrenia and yet one reader is doing so. Many banks and other financial institutions that get into serious difficulty do so because they accept low-probability/high-seriousness risks but behave as if the risk were zero. An example would be banks making loans to a small number of developing countries to an extent that greatly exceeded their capital: while the probability of default might be low it would be very serious (and in fact was serious when it occurred in the 1980s) if a default were to occur.
Risk analysis is applied to situations which have multiple, uncertain outcomes. Leaving aside the special area of finance, it involves four major processes: specifying the relevant attributes of various outcomes; establishing the probability distribution of outcomes associated with each attribute (often by analysing past periods); an evaluation of the uncertain outcomes so that choices can be made, and analysis of methods to reduce or shift risk to other agents.
The essential elements of risk analysis and management are captured in a review of the issues that are considered in banking. Banks are necessarily in the risk business because they issue debt contracts on both sides of the balance sheet, because the characteristics of these contracts are different on the assets and liabilities side (their traditional asset transformation role), and because they are highly geared institutions: a high ratio of debt liabilities to equity capital. The ultimate risk is that, because of non-repayment of loans, the bank becomes insolvent as the value of its assets falls below that of its debt liabilities. In practice, banks are subject to many different kinds of risk: credit, price, foreign currency, liquidity, operational, forced-sale, etc. For expositional purposes, we restrict the discussion to credit-risk, that is, the risk that a loan is not repaid.
Risk analysis and management for a bank involves five key processes: first, identification and measurement of risks, that is, a calculation of the probability of default; second, what can be done to lower the probability of default; third, measures to limit the damage in the event that the risk materializes, that is, default occurs; fourth, action to shift risk on to others, that is, risk-sharing, and fifth, how the residual risk is absorbed.
The first procedure is to identify and quantify the risk. The bank will use its expertise and past experience to calculate the probability of a default. This involves a screening of potential borrowers and projects and the acquisition of information to ascertain the nature and magnitude of the risk. Banks may have a comparative advantage over others in this process because of their skills and experience.
Second, the bank will seek to reduce the probability of the risk by, for instance, monitoring the behaviour of borrowers, setting conditions on the loan, devising incentive-compatible contracts to ensure that the behaviour of the borrower is such as to lower the probability of default (e.g. by requiring the borrower to invest personal resources in the project), taking collateral from the borrower so that the borrower also loses if the loan is not repaid, credit rationing, taking an equity stake in the project so that the bank has some say in its management, and so on. In these ways a lender can attempt to reduce the probability of a default. An incentive-compatible contract can also be used to reduce the potential moral hazard of the borrower: an incentive a borrower may have to deliberately default. The contract must be structured so that there is a greater incentive for the borrower to repay than to default deliberately.
Third, a bank, lender or purchaser of a financial asset will seek to limit the damage in the event of a default or fall in the price of an asset. The standard procedure is to include the loan or asset within an efficiendy diversified portfolio where the individual risks are less than perfectly correlated. In this way the overall portfolio is less risky than any particular asset within it: what remains is systematic risks, that is, the part of an investment’s total risk that cannot be avoided by combining it with other investments in a diversified portfolio. In this procedure the value of a particular investment or loan is measured in terms of its contribution to the overall risk of the portfolio rather than its inherent riskiness. Thus a risk-averse investor may rationally choose an investment which has a higher inherent risk than the existing risk of the portfolio (on the face of it, counter-intuitive) if it has the effect of lowering overall portfolio risk. A bank may construct a diversified portfolio of loans by either making different types of loans (e.g. to different types of borrowers) or by having several similar loans but to different borrowers. This is an application of the law of large numbers. Thus, if there is a 10 per cent probability that a $1,000 loan will not be repaid, the expected future value of the loan is indeterminate: either 0 or $1,000. On the other hand, with the same probabilities, if ten loans of $ 100 are made, the expected future value of the portfolio becomes $900. A bank may also seek to limit the damage of a default by, for instance, requiring collateral to be lodged (the collateral is retained in the event of a default), or by restricting the size of individual loans relative to the bank’s equity capital so that it does not become insolvent if the borrower does not repay. A bank may also limit damage through a hedge contract.
The fourth component of risk analysis and management is to shift risks on to others. The standard procedure is insurance. Here a risk-averse agent pays a premium to pass the risk to an insurance company. This is possible only if it is profitable for both parties. The gain to the insured is the passing of the risk for which benefit the insured is prepared to pay a premium. It is advantageous to insurers if they can charge premiums which generate profits after claims have been met. This will be possible if the insurer is able to acquire a diversified structure of risks. Not all risks are, however, insurable. The necessary conditions are: first, the insured risk is observable and verifiable (thus we cannot insure against having a headache) whereas we can for a broken leg); second, the risk must be diversifiable by the insurer; and third, there must be no moral hazard, that is, there must be no incentive for the insured to cause the risk to materialize. With respect to the last mentioned, for instance, a house will not be insured for more than its value as this could create an incentive for the owner to burn it down, even allowing for the transactions costs of replacing it. In principle a bank could seek to insure its loans, though in practice this is rare as the bank is itself usually a more efficient insurance vehicle, implying that, given the size and diversity of its loan portfolio, the risk premiums it can profitably build into its own loan interest rates are lower than the premiums that would be charged by an external insurer. In addition, if loans are externally insured a moral hazard is created, in that there may be an incentive for the bank to make high-risk loans in a situation where it has superior information to that of the insurance company. A bank may also effectively insure against a price risk by becoming a counter-party in a forward, futures or options contract.
Summarizing the analysis, a bank or investor will identify and measure risks, consider how to reduce the probability of a default, seek to limit the damage in the event of a default, and consider alternative mechanisms for shifting risk. Any remaining risk has to be absorbed and a bank will handle this through the pricing of its loans (i.e. set a risk premium in the loan interest rate to cover expected risk which amounts to internal insurance), and by holding an equity capital cushion to absorb potential unexpected risks.
The analysis has been conducted primarily by reference to risks in finance. However, the same principles apply in all risk analysis. As has been argued, risk analysis is inseparable from risk management.
David T.Llewellyn
Loughborough University
Further reading
Arrow, K.J. (1971) Essays in the Theory of Risk-Bearing, Chicago.
Balch, M. et al. (eds) (1974) Essays on Economic Behaviour under Uncertainty, Amsterdam.
Borch, K.H. (1990) Economics of Insurance, Amsterdam.
Brealey, R. and Myers, S. (1988) Principles of Corporate Finance, New York.
Diamond, P. and Rothschild, M. (eds) Uncertainty in Economics: Readings and Exercises, New York.
Dreze, J. (1987) Essays on Economic Decisions under Uncertainty, Cambridge, UK.
Ehrlich, I. and Becker, G. (1972) ‘Market insurance, self-insurance and self-protection’, Journal of Political Economy 80(4).
Hirshleifer, J. and Riley, J. (1970) ‘The analysis of uncertainty and information: an expository survey’, Journal of Economic Literature, 17.
Knight, F. (1921) Risk, Uncertainty and Profit, Boston, MA.
Markowitz, H. (1959) Portfolio Selection: Efficient Diversification of Investment, New Haven, CT.
Sinkey, J.F. (1992) Commercial Bank Financial Management in the Financial Services Industry, New York.
Smith, C.W. et al. (1990) Managing Financial Risk, New York.
Tobin, J. (1958) ‘Liquidity preference as behaviour toward risk’, Review of Economic Studies 25.
von Neumann, J. and Morgensten, O. (1953) Theory of Games and Economic Behaviour, Princeton, NJ.
Williams, A. and Heins, R. (1989) Risk Management and Insurance, New York.
