Chapter 7: Risk Management

Definition Risk Management

There is no uniform definition for risk, but generally, it is defined as the probability of facing loss or unintended consequences. To paraphrase from Cecchetti and Schoenholtz (2017), the dictionary definition of risk, is the “possibility of loss or injury,” highlighting the perils of putting oneself in a situation in which the outcome is unknown. But this common use of the word may not suit our purposes because we care about gains as well as losses. We need a definition of risk that highlights that the outcomes of financial and economic decisions are almost always unknown at the time of decisions. Here is the definition Cecchetti and Schoenholtz propose: Risk is a measure of uncertainty about the future payoff of an investment, assessed over a particular time horizon and relative to a benchmark. To rephrase the definition, we can say that, from a financial perspective, risk is the degree of uncertainty about the return of future net cash flows generated from a particular investment.

Market risk can be defined as the risk related to a financial institution’s financial condition resulting from unexpected market movements in the price level of certain risk factors. These risk factors can be categorized into four main classes: equity prices, commodity prices, foreign exchange rates, and interest rates.

Classification of Risks

The Basel Accords announced and published in 1988 are initially known the regulatory capital adequacy of internationally active banks. These regulations later became the regulatory episodes of capital adequacy endorsed by almost all regulatory and supervisory agencies of more than 150 countries. With the Basel documentations, the risks have been categorized into two main groups; banks’ activities have been separated into the trading book and the banking book; the former refers to market risk components, and the latter, to credit risk. With the evolution of the Basel-II, a new set of risks, called operational risk, was added to the regulation, this was joined by liquidity risk following the global financial crisis.

1. Market Risk : According to the Basel Committee, market risk is defined as the risk of losses arising from movements in market prices. The risks subject to market risk capital requirements include but are not limited to: (1) default risk, interest rate risk, credit spread risk, equity risk, foreign exchange (FX) risk and commodities risk for trading book instruments; and (2) FX risk and commodities risk for banking book instruments .
2. Credit Risk : Broadly speaking, credit risk is the risk that a borrower fails to meet obligations for a loan granted. This risk is of vital importance to banks, as their main business involves lending money to be repaid over a certain period, which in some cases, e.g. mortgages, may be 10 to 20 years or more. The quantification and management of credit risk are radically different from market risk, which focuses mainly on changes in asset prices, and which offers an infinite set of probabilities due to available data. Credit risk management focuses on three features of the default phenomenon: the probability of default, the loss in case of default, and the exposure when default occurs. In order to characterize the likelihood of clients defaulting in the future, banks, as well as companies, develop “credit scoring” models.
3. Operational Risk : The Basel Committee defined the operational risk as the “risk of loss resulting from inadequate or failed internal processes, people and systems or from external events”. Operational risk is simply any event that disrupts the normal flow of business processes and which generates financial loss or damage to the image of the bank (although the latter outcome has been explicitly excluded from the definition of the Basel Committee, still remains as a major concern).
4. Liquidity Risk : Liquidity, frequently overlooked by financial institutions, may bring substantial losses in a very short period of time. The most profitable financial instruments tend to be illiquid assets. Assets carrying the illiquidity premium are rewarded with substantial profits in good times, however, when the tide turns, such assets may rapidly deplete a bank’s resources. The most famous liquidity driven bankruptcy was the LTCM, the giant hedge fund which collapsed in 1998. In this case, even the most famous theorists have fallen into a trap, failing to abandon illiquid but valuable assets in time, causing the intervention of Mr. Greenspan and the FED.

Risk and Return

A trade-off between risk and return constitutes the basis for risk. One of the first attempts to understand the tradeoff between risk and return was by Markowitz (1952), and later by William Sharpe (1964). Others carried the theory and lead to the well-known capital asset pricing model (CAPM). In 1976, Ross developed arbitrage pricing theory (APT), an extension to the CAPM. All these researchers concentrated on risk-return trade-offs they faced, and these insights are still relevant however complex the market.

Quantifying Risk : In financial realm, risk is the volatility of expected asset returns. It can be calculated in several different ways.

Investment Choices : After defining risk and return, it is clear that investors must make a choice between different risk-return alternatives. Individuals may employ many different strategies to reduce their risks while searching for higher returns. One of the widely used methods is to construct an efficient portfolio. Asset pricing risk is used to differentiate systemic and un-systemic risk capital. However, we should always bear in mind that certain risks cannot be eliminated by diversifying.

Risk and Return For Non-Financial Institutions : How should a company decide if an investment worth the risk it entails? The shareholders are ultimate owners of the company, and the company should be run to comply with to best interests of the shareholders. For each investment project and its investment return, the company should calculate the beta (also known as the beta coefficient, used as a measure of the volatility, or systematic risk, of a security or a portfolio in comparison to the entire (stock) market or a pre-defined benchmark). If the expected investment return is greater than the one found from CAPM, then the investment should be made, otherwise rejected.

Risk Measurement

In the mid-1990s the term risk measurement was synonymous with VaR. Value-at-Risk became famous following the release of RiskMetricsTM Technical Document in 1994 by JP Morgan and is simply defined as a measure of the maximum potential change (or loss) in value of a portfolio of financial instruments with a given probability over a pre-set horizon. VaR answers the question: how much can I lose with x % probability over a given time horizon. Methods used for the calculation of VaR differ in their broad methodology and the assumptions they make. Some of them are listed as the following:

Variance-Covariance Method : The Variance-covariance (VCV) method estimates VaR by first assuming that a portfolio comprises a small number of risk factors (equities, commodities, etc.). Each risk factor is assumed to be drawn from some known theoretical distribution. The statistical distributions of these individual risk factors are combined to yield a single theoretical distribution for the returns of the entire portfolio. This distribution is then used to calculate the VaR of the portfolio. The VCV method is also known as an analytic or parametric method. It is considered the simplest of the suggested methodologies and thus is often used by banks and other financial institutions

Historical Simulation Method : The variance-covariance approach critically depends on the specification of a parametric distribution. Therefore, it is inevitable that a misspecified distribution will yield an incorrect VaR estimate. To eliminate these drawbacks, a nonparametric method has been proposed, known as Historical Simulation (HS). The Basel Committee defines the historical simulation methodology as a simulation approach that calculates the hypothetical change in the value of the current portfolio in the light of actual historical movements in risk factors (Basel Committee on Banking Supervision, 1996b). In other words, unlike the VCV method, the shape of the probability distribution needs not be specified. Regardless of the portfolio composition, any skewness and leptokurtosis in the distribution of returns are captured by the historical data. The main characteristic of HS approach is that it imposes no a priori theoretical distribution function, eliminating the need to make any explicit assumptions about the shape of the probability distribution of asset returns.

Monte Carlo Simulation : The Monte Carlo (MC) approach is based on the idea of simulating the changes in the portfolio value by randomly drawing from the imposed theoretical distribution function. The power of the MC simulation lies in its capability to provide approximate solutions applied to problems where no explicit probabilistic content is available. MC simulation has found a wide range of applications in many other fields in finance, including pricing derivatives positions, particularly within the context of option valuation. Because of its greater flexibility, the MC simulation technique has been considered the most powerful VaR method. As with the VCV approach, MC simulation employs a theoretical distribution function (usually the normal distribution, but can be designed to allow for drawing from other theoretical distributions, such as a mixture of two normal distributions or student-t).

Extreme Value Theory (EVT) and VaR : Extreme value theory (EVT) studies the tail of distributions and deals with the asymptotic behavior of the extreme order statistics of a random sample, such as the maximum or minimum order. Despite the fact that EVT was well established almost a century ago, its use in finance is quite recent. Although often used for VaR calculation, implementing EVT is not straightforward. The basic rationale behind EVT is to model the tails of the distribution by using extremes, rather than modeling the entire distribution by using all available data. The higher frequency events at the center of the distribution are not relevant for calculating VaR, which is concerned only with the tail events.

Risk Management with Financial Derivatives

The Group of Thirty’s (1993) excellent definition of financial derivatives is: “In the most general terms, a derivatives transaction is a bilateral contract or payments exchange agreement whose value derives, as its name implies, from the value of an underlying asset or underlying reference rate or index. Today, derivatives transactions cover a broad range of “underlying”—interest rates, exchange rates, commodities, equities, and other indices”. One of the most often used and well-known concept in finance is hedging. Whether it be carried out? with vanilla instruments or derivatives, hedging is always complex. Traders hedge basically two categories: (i) Short Positions, and (ii) Long Positions, i.e., short hedging and long hedging. When in a short position, the risk is rising of prices; conversely, in a long position, the risk is falling prices.

By definition, dynamic hedging requires adjusting positions on a given frequency: Daily, weekly, hourly etc. In theory, continuous hedging provides the best results, but in reality, markets are not very efficient all the time, and continuous hedging incurs trading costs which can be substantially higher than the benefits.