Measuring and Managing Market Risk
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Introduction
This reading is an introduction to the process of measuring and managing market risk. Market risk is the risk that arises from movements in stock prices, interest rates, exchange rates, and commodity prices. Market risk is distinguished from credit risk, which is the risk of loss from the failure of a counterparty to make a promised payment, and also from a number of other risks that organizations face, such as breakdowns in their operational procedures. In essence, market risk is the risk arising from changes in the markets to which an organization has exposure.
Risk management is the process of identifying and measuring risk and ensuring that the risks being taken are consistent with the desired risks. The process of managing market risk relies heavily on the use of models. A model is a simplified representation of a real world phenomenon. Financial models attempt to capture the important elements that determine prices and sensitivities in financial markets. In doing so, they provide critical information necessary to manage investment risk. For example, investment risk models help a portfolio manager understand how much the value of the portfolio is likely to change given a change in a certain risk factor. They also provide insight into the gains and losses the portfolio might reasonably be expected to experience and the frequency with which large losses might occur.
Effective risk management, though, is much more than just applying financial models. It requires the application of judgment and experience not only to know how to use the models appropriately but also to appreciate the strengths and limitations of the models and to know when to supplement or substitute one model with another model or approach.
Financial markets operate more or less continuously, and new prices are constantly being generated. As a result, there is a large amount of data on market risk and a lot of collective experience dealing with this risk, making market risk one of the easier financial risks to analyze. Still, market risk is not an easy risk to capture. Although a portfolio’s exposures can be identified with some certainty, the potential losses that could arise from those exposures are unknown. The data used to estimate potential losses are generated from past prices and rates, not the ones to come. Risk management models allow the experienced risk manager to blend that historical data with their own forwardlooking judgment, providing a framework within which to test that judgment.
We first lay a foundation for understanding value at risk, discuss three primary approaches to estimating value at risk, and cover the primary advantages and limitations as well as extensions of value at risk. We then address the sensitivity measures used for equities, fixedincome securities, and options and also cover historical and hypothetical scenario risk measures. Next, we discuss the use of constraints in risk management, such as risk budgeting, position limits, scenario limits, stoploss limits, and capital allocation as risk management tools. Lastly, we describe various applications and limitations of risk measures as used by different types of market participants and summarize our discussion.
Learning Outcomes

explain the use of value at risk (VaR) in measuring portfolio risk;

compare the parametric (variance–covariance), historical simulation, and Monte Carlo simulation methods for estimating VaR;

estimate and interpret VaR under the parametric, historical simulation, and Monte Carlo simulation methods;

describe advantages and limitations of VaR;

describe extensions of VaR;

describe sensitivity risk measures and scenario risk measures and compare these measures to VaR;

demonstrate how equity, fixedincome, and options exposure measures may be used in measuring and managing market risk and volatility risk;

describe the use of sensitivity risk measures and scenario risk measures;

describe advantages and limitations of sensitivity risk measures and scenario risk measures;

explain constraints used in managing market risks, including risk budgeting, position limits, scenario limits, and stoploss limits;

explain how risk measures may be used in capital allocation decisions;

describe risk measures used by banks, asset managers, pension funds, and insurers.
Summary
This reading on market risk management models covers various techniques used to manage the risk arising from market fluctuations in prices and rates. The key points are summarized as follows:

Value at risk (VaR) is the minimum loss in either currency units or as a percentage of portfolio value that would be expected to be incurred a certain percentage of the time over a certain period of time given assumed market conditions.

VaR requires the decomposition of portfolio performance into risk factors.

The three methods of estimating VaR are the parametric method, the historical simulation method, and the Monte Carlo simulation method.

The parametric method of VaR estimation typically provides a VaR estimate from the left tail of a normal distribution, incorporating the expected returns, variances, and covariances of the components of the portfolio.

The parametric method exploits the simplicity of the normal distribution but provides a poor estimate of VaR when returns are not normally distributed, as might occur when a portfolio contains options.

The historical simulation method of VaR estimation uses historical return data on the portfolio’s current holdings and allocation.

The historical simulation method has the advantage of incorporating events that actually occurred and does not require the specification of a distribution or the estimation of parameters, but it is only useful to the extent that the future resembles the past.

The Monte Carlo simulation method of VaR estimation requires the specification of a statistical distribution of returns and the generation of random outcomes from that distribution.

The Monte Carlo simulation method is extremely flexible but can be complex and time consuming to use.

There is no single right way to estimate VaR.

The advantages of VaR include the following: It is a simple concept; it is relatively easy to understand and easily communicated, capturing much information in a single number. It can be useful in comparing risks across asset classes, portfolios, and trading units and, as such, facilitates capital allocation decisions. It can be used for performance evaluation and can be verified by using backtesting. It is widely accepted by regulators.

The primary limitations of VaR are that it is a subjective measure and highly sensitive to numerous discretionary choices made in the course of computation. It can underestimate the frequency of extreme events. It fails to account for the lack of liquidity and is sensitive to correlation risk. It is vulnerable to trending or volatility regimes and is often misunderstood as a worstcase scenario. It can oversimplify the picture of risk and focuses heavily on the left tail.

There are numerous variations and extensions of VaR, including conditional VaR (CVaR), incremental VaR (IVaR), and marginal VaR (MVaR), that can provide additional useful information.

Conditional VaR is the average loss conditional on exceeding the VaR cutoff.

Incremental VaR measures the change in portfolio VaR as a result of adding or deleting a position from the portfolio or if a position size is changed relative to the remaining positions.

MVaR measures the change in portfolio VaR given a small change in the portfolio position. In a diversified portfolio, MVaRs can be summed to determine the contribution of each asset to the overall VaR.

Ex ante tracking error measures the degree to which the performance of a given investment portfolio might deviate from its benchmark.

Sensitivity measures quantify how a security or portfolio will react if a single risk factor changes. Common sensitivity measures are beta for equities; duration and convexity for bonds; and delta, gamma, and vega for options. Sensitivity measures do not indicate which portfolio has greater loss potential.

Risk managers can use deltas, gammas, vegas, durations, convexities, and betas to get a comprehensive picture of the sensitivity of the entire portfolio.

Stress tests apply extreme negative stress to a particular portfolio exposure.

Scenario measures, including stress tests, are risk models that evaluate how a portfolio will perform under certain highstress market conditions.

Scenario measures can be based on actual historical scenarios or on hypothetical scenarios.

Historical scenarios are scenarios that measure the portfolio return that would result from a repeat of a particular period of financial market history.

Hypothetical scenarios model the impact of extreme movements and comovements in different markets that have not previously occurred.

Reverse stress testing is the process of stressing the portfolio’s most significant exposures.

Sensitivity and scenario risk measures can complement VaR. They do not need to rely on history, and scenarios can be designed to overcome an assumption of normal distributions.

Limitations of scenario measures include the following: Historical scenarios are unlikely to reoccur in exactly the same way. Hypothetical scenarios may incorrectly specify how assets will comove and thus may get the magnitude of movements wrong. And, it is difficult to establish appropriate limits on a scenario analysis or stress test.

Constraints are widely used in risk management in the form of risk budgets, position limits, scenario limits, stoploss limits, and capital allocation.

Risk budgeting is the allocation of the total risk appetite across subportfolios.

A scenario limit is a limit on the estimated loss for a given scenario, which, if exceeded, would require corrective action in the portfolio.

A stoploss limit either requires a reduction in the size of a portfolio or its complete liquidation (when a loss of a particular size occurs in a specified period).

Position limits are limits on the market value of any given investment.

Risk measurements and constraints in and of themselves are not restrictive or unrestrictive; it is the limits placed on the measures that drive action.

The degree of leverage, the mix of risk factors to which the business is exposed, and accounting or regulatory requirements influence the types of risk measures used by different market participants.

Banks use risk tools to assess the extent of any liquidity and asset/liability mismatch, the probability of losses in their investment portfolios, their overall leverage ratio, interest rate sensitivities, and the risk to economic capital.

Asset managers’ use of risk tools focuses primarily on volatility, probability of loss, or the probability of underperforming a benchmark.

Pension funds use risk measures to evaluate asset/liability mismatch and surplus at risk.

Property and casualty insurers use sensitivity and exposure measures to ensure exposures remain within defined asset allocation ranges. They use economic capital and VaR measures to estimate the impairment in the event of a catastrophic loss. They use scenario analysis to stress the market risks and insurance risks simultaneously.

Life insurers use risk measures to assess the exposures of the investment portfolio and the annuity liability, the extent of any asset/liability mismatch, and the potential stress losses based on the differences between the assets in which they have invested and the liabilities resulting from the insurance contracts they have written.
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