- Financial markets have always displayed far more frequent extreme behaviors than normal statistical models expect.
- Financial markets have a dual nature in which standard statistics work well the vast majority of the time, but extreme structural breaks outside the realm of standard statistics occur often enough to require great care. An investment strategy that uses statistical analysis together with extreme scenarios is a powerful approach to markets’ dual nature.
- This white paper describes Western Asset’s approach to scenario analysis. This includes historical scenarios that replay or return to relevant extreme events in the past and forward-looking scenarios that focus on contingency planning for statistically unlikely future events.
Plans are worthless, but planning is everything ~Dwight D. Eisenhower
Extremes and Centers
Many natural phenomena vary widely across populations. For example, the heights of adult humans range from about 0.5 meters to about 2.5 meters. However, most people are close to the median height for their gender, with fewer and fewer people showing heights further and further away from the middle. There has never been—and absent some major feat of bioengineering never will be—a 0.25 (or 25) meter-high adult human.
Financial phenomena seem at first glance to exhibit this kind of central tendency. Most of the time changes in asset prices are clustered around the middle (roughly zero), with fewer and fewer asset price changes of magnitudes that are further and further away from the middle.
There is, however, a big difference between financial phenomena and natural phenomena. There are 25-meter-tall financial phenomena! For example, the 20.47% drop in the S&P 500 on October 19, 1987 was so unusual that no one could possibly believe it just represented normal variation in prices.
There is a vast body of work, starting with Benoit Mandelbrot in 1963,1 exploring “fat-tailed” behavior—the tendency of very unusual financial phenomena to happen more often than standard statistics would indicate. Through the 1980s and 1990s, many researchers in options worked with volatility “smiles” and “skews” that were caused by the peculiar frequencies of highly unusual behaviors in financial markets. By 2003, Robert Engle won a Nobel Memorial Prize for his work on time-varying volatility, which was a way to address the unusual extremes in financial returns.
But even the work of Mandelbrot and his successors tell us that the vast majority of the time, markets behave like the heights of human beings: they vary from the mean in a predictable and regular way. Then again, sometimes they don’t. Acting as if markets have human-height-type variability can be effective for years, sometimes even decades. But financial history is littered with events that are the equivalents of 25-meter-tall humans: the Great Depression; the stock market crash of October 19, 1987; the Russian Debt Crisis of 1998; the TMT bubble bursting in 2000; the Credit Crisis of 2008–2009…
As a result, investors face a difficult problem: being maximally defensive against extreme behavior at all times is not a reasonable strategy. Insurance against extreme events can be costly, and good investment opportunities will be passed up. The flip side of an extreme burst of unusual behavior is a long period of unusual calm, such as the post-World War II period in US markets. Few investors have the patience to stay defensive for very long periods when their defensive stance is not paying off. But ignoring the possibility of extreme events is also an unreasonable strategy that will eventually and inevitably destroy years of good investment results.
Experienced risk managers therefore follow a hybrid strategy whereby both central and extreme possibilities are evaluated. Scenario analysis is the process of assessing outcomes that ordinary statistics would rate as virtually impossible, but that deserve attention in the risk manager’s judgment. Stress testing is a more narrow exercise where a single variable is shocked by a statistically improbable amount—for example, assessing the results of a one-day move up by 100 basis points (bps) in US Treasury rates.
In this white paper, we discuss Western Asset’s approach to scenario analysis. While academic publications and even Nobel Prizes can flow from theoretical work in this area, in practice a blend of quantitative rigor and good judgment—of art and science—is necessary to deal effectively with extreme risks.
The phrases “standard statistics” and “normal variation” were used above. More precisely, these were references to a Gaussian or normal distribution of outcomes, which occurs repeatedly in natural phenomena. The very name—“normal” distribution—came about because it is so ordinary. Unfortunately, financial markets are neither natural nor ordinary.
The variability of a normal distribution is described by a “standard deviation,” which means what it says: the deviation from the average that is standard or ordinary. Exhibit 1 shows the probability based on this kind of “standard statistics” of observing an event beyond a certain number of standard deviations:
In the last column, the probability has been converted into years based on a per-business-day periodicity. So if the phenomena being observed happen on a daily basis—for example, observations of a rate of return at market close each day—then the infrequency of larger and larger standard deviations will be as shown in the last column of Exhibit 1. The Exhibit shows that an eight standard deviation event would occur once per 5.96 trillion years. The age of the universe is about 13.75 billion years, so that’s effectively never.
How do real financial events stack up in this standard deviation measure? Exhibit 2 shows some large financial events:
These movements have something in common: they were all essentially impossible according to Exhibit 1. If Exhibit 1 says they were impossible but they actually happened, then something is wrong with Exhibit 1. This has been known since Mandelbrot’s work in 1963. But the knowledge that Exhibit 1 needs adjustment is of limited value. That’s because even an adjusted Exhibit 1 won’t say which unusual thing might happen or precisely when it might happen.
Thinking the Unthinkable—What the Past Tells Us
While Exhibits 1 and 2 argue convincingly that standard statistics can be wrong about extreme events, they aren’t very helpful in saying what is right. Even though the events in Exhibit 2 happened more often than Exhibit 1 said they should, they still weren’t frequent enough to build up a robust statistical pattern. There are techniques to try to re-estimate the probabilities of such rare (but not rare enough) events, but financial history is typically not long enough for these techniques to deliver reliable statistics.
Attaching probabilities to extreme events can therefore lead to a false sense of precision: there is no solid basis on which to assess probabilities. Instead, thinking about extreme events as a type of contingency planning may be more effective.
An analogy: we suspect that the US military has secret plans to invade France. At the present time this is a fantastically remote event as the US and France are close allies. But it’s better to spend some time now thinking this through than to wait until there is a critical shortage of croque-monsieur that necessitates such an invasion. If events occur that cause a contingency to become more relevant, having thought through what might happen is an advantage. This is what President (and General) Eisenhower meant by, “Plans are worthless, but planning is everything.” The exact nature of an extreme event may change, but having thought through what may be the key components and knowing what to watch for can give us a competitive advantage as extreme events rapidly unfold.
In a financial context, thinking through extreme events can be similarly helpful. Suppose for example that we have a view that the worst case for the eurozone is an orderly breakup where some or all of the weaker economies are split off in a mutually agreed way, but the core remains strong. We may think that there is virtually no chance of a disorderly breakup where the entire eurozone descends into economic chaos and all countries go back to their local currencies. Still, it is useful to know which of our client portfolios may require intervention should we revise our judgment about the relevance of a disorderly eurozone breakup.
It’s not possible to think through every unusual event that could occur, just as the military can’t anticipate every possible assignment it might be called on to execute. But having analyzed a set of eventualities that span a wide variety of possible outcomes provides a good foundation from which refined analyses can proceed as new information arrives.
One major source of extreme scenarios is the past: a replay of historical scenarios comprising major past events, some of which were shown in Exhibit 2 above. It is very unlikely that a historical scenario will repeat in the future. However, as Mark Twain is supposed to have said, “History does not repeat itself, but it does rhyme.” The insights gained from well-chosen historical scenarios can be useful going forward.
The historical scenario process starts by gathering the key financial variables at the time: interest rates, credit spreads, foreign exchange rates; breakeven inflation rates; volatility surfaces; commodity and equity levels. Collectively we call these the “state of the world.”
Note that the list does not include macroeconomic variables like GDP and unemployment. That’s because the goal is to estimate the behavior of a portfolio2 if the historical situation were to repeat itself. Portfolios do not respond directly to macroeconomic variables: they respond to financial market conditions. Financial market conditions may in turn be responding to the macroeconomic environment, but the link between the macro environment and financial market conditions can be tenuous and variable. In a historical scenario, the actual market conditions can be observed so there is no need to speculate.
Historical scenarios can be further subdivided into replay scenarios and return scenarios. A replay scenario contemplates changing financial variables over a period of time. For example, a “Replay Credit Crisis” scenario might gather information about changes in financial market variables from June 2007 to November 2008. These changes would then be applied to the current portfolio to assess how it would have behaved in the June 2007–November 2008 time frame. Time effects such as carry, rolldown and option theta can be incorporated into replay scenarios.
A return scenario contemplates an instantaneous shock. For example in a “Return to November 2008” scenario, the exposures in today’s portfolio would be applied to moves of whatever sizes would bring the state of the world variables back to November 2008 levels.
Because return scenarios reflect hypothetical moves that go backward in time, they can result in shocks that seem counterintuitive and even unrealistic. As of this writing, in a very low interest rate environment, a “Return to November 2008” scenario would include a rise in interest rates since the majority of central bank easing occurred subsequent to November 2008. It is unlikely that a future credit crisis would include a backup in interest rates. On the other hand, a scenario replaying a rate drop environment could result in negative rates when applied starting from a lower base. These features need to be understood and dealt with—for example by capping or flooring rates—so as not to vitiate the lessons that could be learned from these historical scenarios.
Replay scenarios are generally static in the sense that if a portfolio does not change, the result of the replay scenario does not change.3 Return scenarios will change as current market conditions change; if interest rates are currently 2% and are returned to 4% in the scenario, that will cause a different result than if current rates are 3%. Exhibit 3 summarizes the differences between these two types of historical scenarios:
Thus to track the evolution of a historical scenario over time as a function of changing portfolio composition, a replay scenario may be more appropriate. A return scenario can change even if the portfolio doesn’t. On the other hand a return scenario can give a picture of how bad things could get.
Thinking the Unthinkable—Looking Ahead
In addition to historical scenarios, extreme events can be embodied in forward-looking scenarios. These types of scenarios allow the analyst to consider things that have never happened before. There are infinite possibilities for the future, so experience and judgment are required to select forward-looking scenarios that are relevant and that span a wide variety of extreme outcomes. Judgment is required to decide how extreme is extreme. For example, a scenario involving massive nuclear destruction of all global civilization as we know it is probably not worthwhile for a manager of financial assets, as financial assets will cease to have meaning.
To create a forward-looking scenario, Western Asset develops a qualitative narrative describing a possible future state of the world. For example, currently the future of the eurozone is a topic of great interest. Narrative scenarios describing a range of possible eurozone outcomes are created, drawing from a variety of sources including Western Asset economists, portfolio managers, risk managers, and external experts. Ranges of macroeconomic variables might be specified at this stage. As noted above, macroeconomic variables are not directly useful in specifying the behavior of a portfolio, but can give general context.
Often a range of forward-looking scenarios is developed to try to span a wide set of outcomes. For example, Western Asset has developed a rosy “Growth Surprise and Major Economic Reforms” scenario for the eurozone under the assumption that there is a definitive and satisfactory resolution to the region’s structure leading to a dramatic improvement in asset values. At the other end of the spectrum, a grim “Disorderly Breakup” scenario assumes economic chaos infects even the stronger countries. Exhibit 4 shows the five eurozone scenarios Western Asset uses to give an idea of the range of possible outcomes.
The narrative then needs to be translated into specific capital market variables that directly affect our clients’ portfolios. That means the “state of the world” variables that were indicated above need to be specified, as represented in Exhibit 5.
It is unrealistic to expect the process shown in Exhibit 5 to be a precise one. Even if the narrative and high-level factors turn out to describe a situation that actually unfolds, it is impossible to get every interest rate, every exchange rate, and every credit spread right. If you are told that German GDP will slow by 1% under a collapse in demand for exports, what will the US dollar/Japanese yen exchange rate be? There is a wide range of plausible answers to that question.
When a forward-looking scenario is constructed, the aim is to get a reasonable instantiation of the narrative that will help stimulate discussion about the future behaviors of portfolios. The discussion may take the form of a party saying, “I don’t think it would play out that way,” and then thinking through how it would play out.
While the forward-looking scenario construction process is not a precise accounting exercise, neither is it formless. Scenarios should not contain inconsistencies that would lead to riskless, or low-risk arbitrage: for example, a scenario in which there are no capital controls, but a country’s currency devalues by 25 standard deviations versus the dollar while its yield curve and the US yield curve remain unchanged is probably inconsistent.
An important simplification is made in the construction of forward-looking scenarios. Each outcome would likely play out over time, providing investors with opportunities to actively rebalance as new information became available. Modeling such dynamic behavior is extremely difficult, so these scenarios are collapsed to a single point in time.
Beyond active rebalancing, time effects are another significant challenge that can arise in modeling scenarios that play out over time. As we noted above, time effects include yield, curve roll-down, option theta, and other return contributions known at the beginning of a period. Time effects will depend on various assumptions on how principal matures and amortizing bonds are reinvested. These are generally omitted from forward-looking scenarios because of their complexity.
While many phenomena display a wide range of outcomes, financial markets have always displayed extreme behaviors in ways that differ significantly from the ways natural phenomena display extremes. Paradigms for financial markets that rely entirely on models that successfully explain natural phenomena can therefore be incomplete. This can represent a significant danger for investors who ignore the possibility of extreme events.
Financial markets have a dual nature in which standard statistics work well the vast majority of the time, but extreme structural breaks outside the realm of standard statistics occur often enough to require great care. While focusing only on extreme events in financial markets is an unrealistic investment strategy, ignoring them is not an option. A hybrid strategy that uses statistical analysis together with extreme scenarios is a powerful approach to markets’ dual nature.
This white paper describes Western Asset’s approach to scenario analysis. Historical scenarios that replay or return to relevant extreme events in the past and forward-looking scenarios that focus on contingency planning for statistically unlikely future events can provide a framework for dealing with the dual nature of financial markets.
- Benoit Mandelbrot, 1963. “The Variation of Certain Speculative Prices,” The Journal of Business, Vol. 36, pp. 394ff.
- References to “portfolio” usually mean “active portfolio;” i.e. the difference between a portfolio and its benchmark.
- If a cap or floor is hit this might cause a different result, but otherwise replay scenarios are invariant under changes in current market conditions as long as the portfolio is the same.