By Dr Lance Smith,
chief executive officer,
Managing market risk is more than evaluating exposures and anticipating potential losses. Stressful market conditions like those during the 2008 credit crisis involve other issues: loss of liquidity, ballooning counterparty exposures and margin calls, forced sell-off of assets at deep discounts, etc. Although useful as a first line of defense, parametric Value at Risk (VaR) is not enough since it fails to take these knock-on effects into account – it is reactive in nature and deficient in measuring the full scope of portfolio risk.
Today’s risk professional must utilize a diverse range of techniques to manage risk, including:
• Stress tests
• Historical simulation
• Empirical distribution
• Monte Carlo simulation
• Various real-time analytics
VaR limits are breached when something new has happened that is not mysteriously embedded in the trailing numbers—a liquidity crisis, bankruptcy, an unexpected economic number, etc. As a result the market instantaneously enters uncharted territory. VaR cannot anticipate such events, but rather assesses the risk given current conditions. However, VaR can still serve as an early warning.
Any significant change in VaR is a sign that either the correlations and volatilities have altered, or the risk attributes of a portfolio have changed. Thus, a significant movement in VaR from one day to the next signals the need for immediate investigation. There may be some unintended sector exposures, or sensitivities to the price of oil, short-term interest rates, or other factors. A change in VaR may not tell which factors one is exposed to, but it can warn of a new exposure.
• Should include all market inputs relevant to a portfolio and strategy
• When simultaneously stressing multiple factors, the joint behavior under extreme conditions must be correctly incorporated in the scenario
Example: A typical convertible arbitrage fund trading stocks, convertibles, equity options, bond futures and credit default swaps (CDS) would monitor:
• Equity prices
• Implied volatility
• CDS spreads
• Default risks
• Yield curve exposures
An appropriate stress test might be to drop the stock price ten per cent and increase the CDS spread by 200 basis points, simulating a sudden deterioration in credit quality. But what about implied volatility? For options an increase of five points would be appropriate to specify. For the convertible bond, the implied volatility is likely to drop as investors sell out of their bond positions. This is because the volatility arbitrage in convertible bonds is not as tight as it is with ordinary options, so liquidity issues can dominate. Thus the implied volatility corresponding to the same underlying stock can actually move in opposite directions, depending upon security type.
Stress tests should be carefully designed to properly approximate market dynamics of a particular holding, portfolio or strategy. Access to quality historical data plus personal expertise is critical, but a risk management system should enable user-specified stressing of underlying factors. If you can ask the question, you should be able to compute the answer.
Under stressful conditions liquid securities become less so; the effect is magnified with securities that were illiquid to begin with. There are two consequences:
• Effect on mark-to-market
• Possible need to unwind at unfavorable prices to meet margin calls
To address these issues, positions need to be analyzed by liquidity buckets. An equity long-short fund will want to ensure that a sufficiently large position exists in its most liquid bucket to cover potential margin calls; the size will depend upon the existing degree of leverage.
Historical Simulation and the Empirical Distribution
Historical time-series data of underlying risk factors (eg, stock prices) is used to:
• Compute correlations and volatilities
• Replay specific historical scenarios (eg the crash of 1987, etc.)
• Generate an empirical distribution
In the first case, the correlations and volatilities are used in a parametric VaR calculation. The second case is straightforward; however, the concept of empirical distribution may be unfamiliar. (Unlike parametric VaR, there is no attempt to fit a distribution to a bell-shaped curve. It just is what it is, fat tails and all.)
In a historical simulation, the positions in the portfolio remain static: no trading, no re-hedging. In a dynamic marketplace this may not be realistic. In an extreme situation one might stay the course if there were absolutely no liquidity, or if one were willing to make a huge bet that the market would recover. The empirical distribution makes no such assumption, as it assumes that each day begins with the current exposure.
Monte Carlo Simulation
Monte Carlo simulation is akin to parametric VaR, only computed for nonlinear products. It depends upon the same inputs as VaR—volatilities and correlations of underlying risks—but takes convexity and optionality into account. If using Monte Carlo simulation consistently as part of a rigorous risk management protocol, be aware that it, like parametric VaR, relies upon an assumed distribution for the underlying risks. Therefore Monte Carlo should be augmented by appropriate stress tests.
In a dynamic market it is impossible to predict everything. Unanticipated situations, unexplained changes to P&L, or a market move in favor that is not yielding expected returns may arise. You should have the ability to perform on-the-fly analyses to ferret out what is going on so that you can suitably modify your trading strategies. With proper tools in place, ad hoc situations can be quickly and effectively investigated and analyzed. It is essential to understand everything you can about your portfolio.
Consider a long volatility book of options. The market has just undergone a sharp rally, yet mark-to-market is actually negative. Why? It might be explained by option positions in the “tails,” particularly out-of-the-money call options—a significant change in their implied volatility that has hurt P&L more than the benefit from the increase in underlying volatility. A calculation that returns only the vega (volatility sensitivity) of deep out-of-the-money options just prior to the rally can quantify the effect. Such an ad hoc calculation might be to compute the vega only if the delta (in absolute value) is less than five per cent, and otherwise ignore the position.
Determining exposure to a particular company, let alone sector, is not simple. Exposure can come from investments in stocks, CDS, and other securities with the same issuer as well as through ETFs. The stock may be a component of one or more ETFs, or it may be a component of an equity index on which a trader has sold options. It is important to be able to look through basket securities to their underlying components to properly assess exposures.
Market behavior can change dramatically at any time, as has been witnessed both during the credit crisis and in our present state of sustained volatility. Risk management that turns upon an assumption of precise knowledge of the distribution of returns or is one-dimensional, such as VaR, is insufficient. Instead, diversify your risk management by establishing a risk management structure that utilizes a wide variety of tools appropriate to particular strategies that complement, augment and compensate for each other’s weaknesses.
Risk cannot be boiled down to a single number. Portfolio risk is multi-dimensional and must be analyzed from a variety of perspectives, along with its behavior under many different circumstances (eg, stress tests). Designing meaningful stress tests requires experience, access to quality historical data, and an ability to calculate the effects of shifting several risk factors simultaneously.
Historical simulations are helpful, but the ability to generate an additional empirical distribution will help avoid the “stay the course” assumption and give a complementary evaluation of one’s risk.
Remember: real-world risk management is an active profession. No matter how hard we may try to anticipate potential problems, the market is ultimately more creative than any of us. To successfully manage and mitigate risks in an uncertain world, it is imperative to have proper tools and procedures in place so that you can react and investigate in real time, as well as proactively probe for underlying “fault lines” that can negatively impact portfolios given a particular set of conditions. With robust systems, procedures and personnel in place, your firm will be better equipped to safely navigate through the next storm.