Strategies for Managing Financial Risk

(May 2002)

Any institution responsible for the allocation of resources over time faces both risk and uncertainty. Risk can be defined as the probability of a set of events taking place where characteristics of the underlying probability distribution are unknown. Under uncertainty, these probabilities are unknown and one must rely on subjective probabilities to arrive at a decision. For general purposes we will use the term risk to refer to both types of probability, drawing distinctions where understanding and applications are critical to the process and outcome.

There are any types of risk: political, economic, and financial, for example, with sub-categories for each. Assessing these risks can be done as long as past events are typical of what future events will be. Responding to these risks is a function of the degree of risk aversion by decision-makers. Since the marginal cost of perfect information is likely to approach infinity, no one is willing to insure against all contingencies, and thus the choice that decision-makers face is one of deciding what is the prudent level of risk exposure.

Measuring risk requires the adoption of two basic simplifying assumptions. One is that events occur with the same probability over time, that is, they display stationarity in the conditional variance, or distribution of probabilities over time. Another is that the distribution of probabilities is normal, that is, that there is neither skewness nor kurtosis (differences in the height) in a distribution. In reality, these conditions often may not hold, thereby creating bias in the measurement of risk as well as in the selection of an appropriate risk-management instrument, namely, a specific form of insurance.

Once one has adopted specific assumptions regarding the stationarity and normality of a probability distribution, the next step is to link these properties to the risk preference of individual agents. While agents may be risk averse, risk neutral, or risk loving, risk aversion is the most frequently observed pattern of behavior. Given the degree of risk aversion, one can then select the degree of insurance coverage that corresponds the allocation of a given resource.

We can illustrate some of these properties in reference to the above graph. It shows four probability density functions, or distributions, namely, A, B, C, and D. All four are symmetric, which sets aside the question of skewness so that we can concentrate on other properties of risk. We can define risk as the distribution of probabilities, which is portrayed by the shape of the curves. In cases A and B, both have the same mean, but with different probabilities around the mean. Distribution A, which we can characterize as the Gaussian standard normal distribution, one can measure risk as the dispersion of probabilities around the mean. The standard deviation serves this function, and is measured as the square root of the sum of absolute deviations from the mean for each probability in the distribution. However, when one wants to compare the degree of risk for one asset in comparison to another it is useful to have a measure of relative risk. Relative risk can be defined in terms of the coefficient of variation, which is the ratio of the standard deviation to the mean of a distribution.

Let us now look at distribution B. It is more narrowly grouped around the mean, and thus has a smaller standard deviation and a smaller coefficient of variation, i.e., it has a smaller degree of absolute and relative risk. Given two events associated with these distributions, a risk averse agent will always prefer distribution B to distribution A. The question is how much is a risk averse agent willing to pay for the choice of a lower degree of risk.

We now look at distributions C and D. Both have the same means, and these means are higher than for the iso-means of distributions A and B. Given the choice between C and D, a risk averse agent will always prefer distribution C to D since it will have a smaller standard deviation and coefficient of variation.

Finally, we link these four distributions together in asking the question of what preference ordering an agent will display. A risk averse agent may be willing to accept either C or D over A or B as long as the outcome associated with the probability distribution is positive, e.g., winning the lottery, maximizing economic gain, or some positive incentive event.

Given the properties of a probability density function, the next step in modeling risk is to link the underlying probabilities to the value of alternative outcomes. These outcomes may be positive, negative, or mixed. The choice of an agent is thus to maximize the expected value of a choice, which is the sum of the associated products of the respective probabilities to their corresponding outcomes. The challenge for policymakers is to determine the extent to which asset pricing incorporates fully the degree of underlying risk, and to develop incentive compatible contracting systems to produce risk inclusive pricing in financial and economic markets.


Managing Risk

 Product and Factor Markets in a Riskless Universe
 Efficient Markets in a Riskless World  Banking System Monetary Dynamics

An Overview of U.S. Financial Institutions 
 US Financial Market Assets   Pension Systems
 The Federal Reserve System   Deposit Insurance
 Bank Performance Criteria   Options and Futures Contracts

 The Economic and Financial Valuation of Assets
  Chaos in Asset Pricing   Commodity Price Stabilization
  Fundamentals of Finance   Equity Valuation in the U.S.
  The Measurement of Risk   The Standard Normal Distribution

 Market Strategies for Banking Optimal Risk Management
 Risk Based Capital Ratios   Internal Bank Transfers
 The CAPM Model   Earnings At Risk Models
 Economic Value Added Models   Option Pricing Models
 Expected Default Frequency Models   The Merton Risk Premium Model
 Value At Risk Models  

 Market Failure and the Optimal Role of Public Sector Intervention
  Public Sector Economic Functions   The IS-LM Model
  Asset Bubbles and Moral Hazard  

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