Market Risk Modeling

By Joseph A. Iraci

There are many risk factors that could give rise to market risk, including: geopolitical risk, monetary and fiscal policy, changes in interest rates and foreign exchange rates, terrorist events, and natural disasters. The need to model market risk has grown as the operating environment has become more volatile and this volatility has increased the potential for large and frequent asset price swings, consequently regulators have increased expectations for banks to develop extreme but plausible scenarios for their modeling framework.

Over the years risk management has developed more sophisticated tools to better enable the modeling of market risk, and with the continuing improvement of technology being at the disposal of risk managers there is now the potential to develop scenario analysis that incorporates the impact of market, credit, and operational risk into scenario planning. This improvement supplements the existing stress testing models that are mainly based on market data and macro-economic risk factors, and the Value at Risk models that are based on probabilistic estimations. However, no matter how sophisticated the model, it starts with ensuring accurate data and assumptions, especially as it pertains to pricing.

Price Risk

Often the difference between a good asset and a bad asset is the price initially paid by the investor or trader. There are specific strategies that buy distressed assets at good prices that yield favorable returns, conversely overpaying for a blue-chip company may protect capital invested but the return going forward could be negligible because of the price paid. Of course, for any investment or trading strategy the first question that must be answered is “what is my investment objective” and the answer to that question will determine the type of investment needed to execute the strategy.

After the initial investment or trade is made at the agreed upon price, price risk becomes a consideration. It does have to be noted though that there are various models to assist the investor or trader in determining the value of the asset. For example, bonds are typically valued using the Discounted Cash Flow Model and dividend paying equities could be modeled using the Gordon Growth Model, among other models. Thus, modeling becomes a consideration at the decision-making stage of executing on an investment or trading strategy, and the complexity of the instrument determines the type of valuation model used.

Price risk is usually defined as the risk of a decline in the price of a security or portfolio, but price risk can also include inaccurate pricing, especially for more complex instruments. We have seen many headlines where losses were experienced on portfolios where trading positions were mismarked, as well as where valuation models were inaccurate based on economic conditions and modeling assumptions.

Price risk driven by price volatility can be mitigated by diversification and by hedging with financial derivatives like futures, options, and swaps. A futures contract is an obligation to honor the contract at an agreed upon future price and date, obligating both the buyer (called the long position) and the seller (called the short position). In comparison, an option is not a contractual requirement, rather it is a right to buy or sell the asset depending on the terms of the option contract. Swaps are an agreement between two parties where they exchange a series of cash flows over a specific tenure. Futures, options and swaps have different pricing methods.

  • Futures pricing are a function of the spot price of the underlying and a basis amount. Basis is the difference between the cash price of the underlying commodity and the futures price, and the relationship between the cash and future pricing affects the value of the contracts used for hedging.
  • Options pricing are a function of several variables including length of time to maturity, volatility, and strike price. Option pricing strives to measure the probability that an option will be exercised (called in the money) at expiration. As such the longer an investor has to exercise the option the greater the likelihood that it will be exercised, and the greater the volatility of the underlying asset leads to a greater probability that it will be exercised.
  • Swaps pricing are a function of the present value of a fixed and variable stream of cash flows over the life of the contract.

This article limited the pricing discussion to just futures, options and swaps. However, the universe of instruments available to investors is much larger and with much more complicated instruments. The US bank regulators issued SR 07-5, the Interagency Statement On Sound Practices Concerning Elevated Risk Complex Structured Finance Activities in 2007, which provides specific considerations for this type of activity, which got a lot of attention in the 2008 financial crisis (https://www.federalreserve.gov/boarddocs/srletters/2007/SR0705a1.pdf). Complex products have additional considerations but what all instruments have in common are suitability considerations, a reliance on internal controls to ensure accurate valuation and pricing, and a need for reliance model risk management. Inaccurate pricing compromises the best designed market risk models because all models depend on accurate pricing of instruments.

Value at Risk (VaR)

VaR has proven very useful in advancing market risk modeling, and VaR modeling uses statistics to measure the potential for loss in either an instrument or a portfolio over a specific time period. VaR represents the maximum potential loss over a given time period and at a specific confidence level. For example, assume a 95% confidence level, a VaR of $2 million, and a 1-week timeframe; there is 95% confidence that over a 1-week time horizon the loss will not exceed $2 million.

VaR was first introduced in the 1990s and it continues to have a number of strengths. It is widely used and in general has become an accepted standard. VaR relies on statistics, it is a single number, and its meaning is relatively straight forward to both communicate and interpret, it is flexible and can be applied to various asset classes.

As with any model, it also has weaknesses and limitations that need to be understood. VaR like every model depends on the accuracy of its inputs and assumptions, and it does not measure large losses beyond the confidence level thus it does not measure worst case losses. VaR is also challenging for large portfolios with many positions because of the need to calculate the correlation among the various holdings. Different VaR methods also yield different results. For example, there is the Historical VaR, Parametric VaR, and Monte Carlo VaR, and each is suitable for different situations so care needs to be taken on which to use based on the situation.

  • Historical VaR simulates the current portfolio using recent history, and it uses market data to construct a frequency distribution of daily returns.  This is based on ordered losses from worst to best, and a histogram (frequency distribution) is typically used to provide a visualization. The goal is to summarize the distribution by 1 number, which is the level of loss that will not be exceeded at some confidence level. VaR is often reported as the deviation between the mean and the confidence interval.
  • Parametric VaR assumes that the distribution of returns belongs to a particular density function, such as the normal distribution.  The dispersion parameter is measured by the standard deviation.  The disadvantage of the standard deviation is that it is symmetrical and cannot distinguish between large losses and gains.
  • Monte Carlo VaR simulates returns using Monte Carlo simulations, which involves assuming a particular density for the distribution of risk factors and then drawing random samples from these distributions to generate returns on the portfolio.

VaR continues to be a useful risk measurement tool but its strengths and weaknesses need to be kept in mind, and its usefulness becomes strengthened when it is combined with additional ways of modeling risk. Stress tests are one way of compensating for Var’s limitation of not taking into account extreme losses because stress tests can be used to model extreme but plausible events.

Stress Tests

Stress tests provide a separate risk estimate than VaR and are based on user defined scenarios that go through calculations to estimate profit and loss based on the assumptions used. VaR, in comparison, is a probabilistic estimation.

Stress tests are computer-simulated models that test for extreme but plausible events, and these scenarios can be based on historical data or hypothetical scenarios built from assumptions. The objective of a stress test is to identify potential weaknesses within firms and portfolios and to measure how well either could sustain adverse economic or market conditions from extreme tail-end events. Stress tests compliment VaR and have proven a valuable addition to the risk management toolset because stress testing can be used not only for investment portfolios but also to stress test liquidity and capital of firms.

After the 2008 recession the United States expanded stress testing and capital adequacy and the Dodd-Frank Act was passed in 2010. Starting in 2011 regulators in the United States required submission of Comprehensive Capital Analysis and Review (CCAR) documentation by banks and require banks to report on the internal procedures for managing capital under various stress test scenarios. Further, for those firms classified as too big to fail by the Financial Stability Board (usually those with assets greater than $50 billion), they must provide stress test reporting for a bankruptcy scenario. More broadly, Basel III requires global banks to have documentation on their capital levels and to administer various stress tests under extreme economic scenarios.

Stress tests are built from assumptions thus are very subjective and could be difficult to evaluate objectively, also stress tests do not assign probabilities to the various scenarios. These weaknesses could make the results challenging not just more management but for regulators as well, and stress tests do not easily lend themselves to back-testing. Despite weaknesses stress tests have proven to be a valuable addition to risk management. As we’ve continued to experience successive rounds of volatility, and it has become increasingly important to incorporate extreme tail loss theory to supplement probabilistic estimates of risk, and to ensure firms have sufficient capital and liquidity to sustain operations during adverse economic and market conditions.

Scenario Analysis

One key difference between stress tests and scenario analysis are the number of risk factors used. Stress tests tend to have fewer risk factors than scenario analysis because stress testing is usually focused on scenarios for financial, liquidity and capital stressed scenarios.

Scenario analysis, as a comparison, can have more risk factors to take into account a highly volatile operating environment and the inter-relationship of risk. This requires assumptions to be identified about the future and to determine appropriate responses, but care should be taken on the construct of the scenario analysis in order to keep it focused on warning signs for potential threats and opportunities. When used in this fashion scenario analysis can be a competitive advantage because it enables management to anticipate potential changes and to react quickly when they manifest themselves, much like the term “muscle memory” is used to explain an athlete’s response during the game where the reaction is helped by practice.

Scenario analysis can be very flexible and while economic assumptions are usually a part of the scenario, it could also include things like a breakdown in internal controls that leads to a large loss and headline risk, and strategic risk from a new technology development that disrupts the status quo. Where stress tests have strength in more quantitative scenarios, scenario analysis can be used to incorporate more subjective scenarios that include operational risk, emerging risk, and strategic risk. Further, when used in this manner, scenario analysis can also be used to form the foundation for simulation exercises, which the World Health Organization defines as a “fully simulated, interactive exercise that tests the capability of an organization or other entity to respond to a simulated emergency, disaster or crisis situation. Simulation exercises are normally run as field exercises and include a scenario that is as close to reality as possible.” (https://www.who.int/emergencies/risk-communications/simulation-exercises).

Scenario analysis and simulation exercises could also help toward ensuring business resiliency because even a firm that has a top risk management program will come up against a risk it did not anticipate or plan for. Simulation exercises cannot address every type of event that could possibly impact a firm, but they can assist in making sure a firm has monitoring mechanisms in place to identify emerging risks, escalation protocols, and a framework for both event management and crisis management.

The case for business resiliency seems to grow with each passing year. While conceptually it is similar to business continuity planning, the traditional business continuity plan addresses limited events like a weather-related event, earthquake or transit strike, whereas business resiliency takes a much broader view and at its core it strives to ensure a firm has the operational and financial resiliency not only to survive in an increasingly volatile operating environment but also to thrive.

Best Practices for Stress Tests and Scenario Analysis

  • Have an effective governance structure.
  • Have cross-functional teams and representation from different disciplines (risk management, compliance, finance, technology, operations, business management…).
  • Test all data and assumptions for relevance and accuracy.
  • Ensure adequate modeling capabilities and that methods fit the complexity of the scenario.
  • Identify trigger points for reporting and escalation.
  • Have a flexible response strategy.
  • Develop model risk management to incorporate effective challenge and independence.

Strengths and Weaknesses for Stress Tests and Scenario Analysis

Strengths

  • Assists in the strategic planning process by being able to anticipate potential events.
  • Cross-functional teams help to develop cohesiveness and assist in knowledge transfer.
  • The process should be documented to reduce reliance on a few subject matter experts.
  • Gives all stakeholders confidence the firm can weather extreme but plausible events.

Weaknesses

  • Building and maintaining stress tests and scenario analysis is a large undertaking.
  • Marketplace changes could occur more rapidly than the time needed to complete a full scenario analysis.
  • Both require technology and human capital investment.

Conclusion

Advances in technology has allowed a continual improvement in our ability to model risk. But to properly develop models and scenarios, and to anticipate extreme but plausible events, the management of risk needs the level of expertise that can only come from intellectual capital.  Tools are only as good as the people who use them.

Advances in our ability to model risk is giving risk managers the ability to align with strategy and to play a key role in the strategic planning process. Risk managers, however, must not get a false sense of confidence in quantitative modeling alone, rather we need to partner with business management and specialist functions in order to drive a holistic process that looks at risk and potential strategies from multiple angles, and to incorporate non-financial risk factors into our modeling processes. Covid-19 provides the clearest example of how financial and non-financial risk factors have the potential to be inter-connected and to impact consumers and firms across the globe.

Joseph Iraci is a Vice President of Enterprise Risk and Audit at Robinhood Markets Inc.

References

Basel Committee on Banking Supervision, “Principles for sound stress testing practices and supervision,” May 2009. Available at www.bis.org/publ/bcbs155.htm.

Basel Committee on Banking Supervision, “Stress testing principles,” October 2018. Available at  www.bis.org/bcbs/publ/d450.pdf.

Committee on the Global Financial System, “A survey of stress tests and current practice at major financial institutions,” April 2001. Available at www.bis.org/publ/cgfs18.htm.

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