Agent-based Models and Plan risk at Fabric

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The current methods used to assess market and portfolio risk extend back to the early 1990s. These methods were developed for banks and broker/dealers and then were extended to the portfolio management and hedge fund community. They focus on short-term risk, which is measured in days for the broker/dealer’s blotter and in months for hedge funds and investment managers. Perhaps because of this, these methods measure risk using recent history, usually just one or two years, thereby assuming that risk in the future will be the same as in the past. These methods are not appropriate for measuring risk over the long term, and thus they fail for asset owners, such as pension funds, family offices, and individuals. In this paper, we explain how Fabric casts risk management for individual asset owners. 

Banks and hedge funds focus on monthly or even daily variability in their profit and loss, whereas the time horizon of an individual is measured in years or even generations. In such a time frame, the day-to-day variability in the market—as measured, for example, by value at risk—amounts to noise that is best ignored (but usually is not). Rather, what matter are material risks. Material risks are those that can threaten the individual’s prospects for meeting their goals, those that can derail financial plans that extend out perhaps 30 or 40 years into the future. Material risks include major market downturns, especially those that take years to recover from. By looking at returns over the past year or two, the current methods fail to reflect the dynamics that become increasingly important over the long term, dynamics that propel the markets over time and generate periods of major downturns and instability. These dynamics cannot be ignored as engines of risk for individuals. 

Also, unlike for a bank or portfolio manager, risk comes at an individual from two directions: (1) market risk that directly affects individual wealth and (2) personal risk that comes from the uncertainty of life events and changes in risk tolerance and preferences. These interact to make an individual’s risk calculation complex and dynamic. In the face of this complexity, the notion that we can optimize a portfolio is wishful thinking, as is the idea that we can look at the current situation in isolation and “set it and forget it” when it comes to portfolio construction for risk management. 

Given that risk management for an individual is a moving target—that it is dynamic, multifaceted, and complex—we need a new approach to address it. One approach is agent-based modeling. Agent-based models are used in fields in which complex dynamics are at work, from  modeling traffic congestion on a highway to assessing the adequacy of exits for crowded venues, such as stadiums and arenas. It is not surprising that these methods are applicable to financial markets, where crowding and leverage can lead to sudden rushes to exit and where liquidity can dry up at the most inopportune times.

 

Material versus Day-to-Day Risk

The contrast between material risk and day-to-day risk is illustrated in Figure1, which shows the 100-day volatility of the S&P 500 from 1936 to 2022. Interspersed among the “background radiation” level of volatility of about 12% per year are periods of high volatility that pop up decade by decade: stagflation and the oil shock in the 1970s; the October 19 market break in 1987; the Asia crisis and implosion of Long-Term Capital Management in the late 1990s, which warmed up for the trifecta of the Internet bubble, deflation of irrational exuberance, and earnings scandals of the early 2000s; and then the 2008 financial crisis followed by European credit aftershocks. (The combination of these latter events in this litany, one after the other, is what led to one of the lost decades.) And, of course, another example of this volatility is the violent whipsaw from Covid-19 beginning in March 2020.

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Figure 1: 100-Day Rolling volatility of the S&P 500

 

In terms of market risk, we have two types of volatility. The background level comes from the standard uncertainty surrounding such things as earnings expectations, the economic cycle, and related Fed policy. The occasional bursts come from leverage-liquidity cascades, the return to earth from times of “irrational exuberance,” the periods of collapse in credit and economic cycles, and other such events. The first case can be thought of as a period of low vulnerability in the market, and the second case can be thought of as the manifestation of high vulnerability coupled with adverse events. 

When it comes to material risk, the current methods of risk management do not account for the realities of the market, especially when they are vulnerable. When the market is vulnerable and an adverse event occurs, markets drop quickly. For the S&P 500, market drops of 30% or more take place over the course of two years or less. By comparison, for standard risk methods, which employ geometric Brownian motion (GBM), on average, such drops take place over the course of four years.3 Furthermore, the path of market prices is asymmetric; markets tend to fall quickly with the recovery taking longer, whereas for the geometric Brownian motion (GBM) in most risk models, the path down and back up is symmetric. So we find that a systematic flaw in the risk models is being used to evaluate individuals’ investment portfolios: assets erode in value more quickly than what is suggested by traditional models, and they take comparatively longer to recover. That longer recovery has real-life implications, especially for investors whose financial plans tend to be centered around achieving distinct goals at discrete periods in time.

Ironically, at the same time that current methods underestimate material risk in the market, they overestimate the long-term risk. In the very long term, returns don’t dive to zero, nor do they go into outer space. A mechanism of mean reversion is at play. Yet, extend out the standard methods, which assume risk grows with the square root of time, and you end up with truly fantastic possibilities. Looking out 50 years—a time period that matters to someone currently in their 20s—the chance that an initial investment of $10,000 will turn into $1,300,000 is 5%. At the same time, the chance that the investment turns into just $90,000 is also 5%. Compare that range of outcomes with the long-term stability of returns for the S&P 500 shown in Figure 2 below.

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Figure 2: Long-term returns of the S&P 500 (log-scale)

 

Measuring Material Risk: Agent-Based Models

We need to take a new approach to risk to deal with these market realities: one that works for those with a long-term horizon. The methods to do this have only recently been gaining traction in finance. They are based on agent-based models (ABMs). 

ABMs have been employed successfully to model many different kinds of phenomena within economics and finance. The Bank of England, for example, uses an ABM to stress test the country’s banking system. The ABM approach has proven to be useful in unraveling the dynamics that played out in the interbank market during the 2008 financial crisis, a task canonical models of banking were ill-equipped to do. Similarly, the cycles of leveraging/ deleveraging and the cyclical nature of debt dynamics have been well captured through ABMs, as have the intraday liquidity dynamics of the limit-order book. 

An ABM can look at the actual structure of the market and the actual institutions that operate in it. These institutions comprise the agents of the model. As in the actual market, they are heterogeneous—they vary in terms of their time frames for investing and acting in the market, the level of risk they are willing to take, and the strategies they employ. Agents in this context may include, for example, Wall Street market makers in high-yield bonds who stop answering their phone when the credit markets crack, hedge funds whose investor liquidity terms are mismatched to the liquidity of the assets they own, or individuals who may have piled much of their net worth into cryptocurrencies or non-fungible tokens. 

Each agent observes the market environment and takes action based on its particular heuristics. True to the heterogeneous nature of agents in the market, heuristics can vary from one agent to the next. No single set of rules or universal optimization program dictates what the agent will observe and how it will act. 

Agents’ actions change the market environment, most notably asset prices and portfolio holdings. The cycle moves from observing the market to taking action and to thereby altering the market environment. The feedback loop between agents’ actions and the movement in the markets generates a complex dynamic system that can display emergent phenomena where the actions of individual agents can lead to surprising effects that are not evident through a simple, linear aggregation of their actions. 

At their core, ABMs explain the behavior of a system by simulating the individual constituent agents that take actions in that system and how these agents interact with each other and with their environment. When building an ABM, these interactions are distilled into a set of rules called heuristics that capture how agents react to changes in the system. Thus, ABMs take a bottom-up approach in which simulating the individual agents’ interactions leads to an understanding of the emergent dynamics of the system itself.

 

ABMs and Market Reality

Agents’ heuristics are a function of multiple parameters, such as their risk tolerance, their levels of leverage, and how quickly they respond to market conditions. These agent parameters along with other model parameters determine the parameter space of the model that needs to be calibrated and estimated. The starting point for calibration is to have the model closely match the statistical moments of the market—that is, the volatility (as measured by the standard deviation), skew, and kurtosis. A model founded on GBM will not be a faithful representation of market dynamics because the returns follow a Gaussian distribution that has no skew and zero excess kurtosis, whereas equities have fatter tails than a Gaussian distribution and a negative skew.7 If only fit to these three moments, the model is over-specified; that is, it has more parameters than the values to be fit, so other market characteristics also are considered that capture the dynamics of the markets. One well documented dynamic is volatility clustering. The volatility of the markets is not fixed in time, and, as one might intuit, periods of high volatility tend to be followed by more periods of high volatility. Along with skew and fat tails, this is another facet of the markets that is not taken into account by models founded on a Gaussian distribution. 

Figure 3 shows volatility clustering for the S&P 500. Periods of large returns—whether positive or negative—are clustered with other large returns. In the second panel of Figure 3, we show a simulation from Fabric's ABM. We observe that the return time series produced by the ABM also contains clusters of high and low volatility, with amplitudes of the high-volatility periods similar to those observed for the S&P 500. By comparison, as seen in the bottom panel of Figure 3, no such clustering occurs for the GBM process, which reflects the results obtained for the standard methods based on draws from a normal distribution.

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Figure 3: Comparison of the time series of returns for S&P 500, a sample run from Fabric's ABM, and a sample run from GBM. 

 

As a final comparison, in Figure 4, we show how the 100-day rolling volatility of the S&P 500 compares with that of an ABM.

Screen Shot 2023-06-08 at 11.35.24 AMFigure 4: Comparison of 100-Day rolling volatilities of the S&P 500, a sample run from Fabric's ABM, a sample run from a GBM. 

 

We observed earlier in Figure 1 that there is a background level of volatility of the S&P 500 of around 12% with occasional spikes. Once again, we observe a remarkable similarity between the actual S&P 500 and the output for one simulation of the ABM. The bottom panel shows the rolling volatility for GBM, which represents the picture for the standard method that draws from a normal distribution. This clearly misses the point when it comes to reflecting the nature of market volatility.

 

Adding the personal edge to financial risk 

Even with improvements to risk modeling that can deal with the market realities of long-term risk, trying to apply standard risk management methods to the risk problem of an individual is like bringing a knife to a scissor fight. Risk issues for portfolios have one edge, returns. Those for an individual add another edge, personal goals. As with a pair of scissors, these edges interact; the individual’s goals will be affected by the market’s effects on their portfolio, and the structure of the portfolio might be changed in turn. To make matters more complicated, financial planning is not static or one dimensional. People’s priorities change, as do their time frames, as do the risks they are willing to take in life. Thus, we look at risk within a goals-based approach to investing, in which market risk is viewed in the context of an individual’s time horizon and objectives.

One way to look at goals-based investing is a financial take on Maslow’s hierarchy of needs. The bottom rung is owning investments that are a bulwark against deprivation, against being thrown out on the street—perhaps metaphorically, perhaps literally. With this concern satisfied, individuals hope to have the investments to maintain their lifestyle. As they go farther up the rungs of the ladder, they might pursue more ambitious objectives, “self-actualizing” goals, such as having a second home, retiring early, or having the resources to provide generous support for children or charities. So we have financial needs—and thus financial risk—associated with security, lifestyle, and aspirations.

These come with varying time frames. Meeting next month’s mortgage payment is not only a high priority but also requires thinking for the very short term, while an objective like “I want to live at least at my current standard of living when I retire 20 years from now” can be contemplated and planned only from a distance. Investment choices and their related risk characteristics also change with the investment horizon. Markets can move violently in the short term, but in the long term, capital market assumptions become an increasingly reliable guide for expectations. So, the time horizon determines which risks can be considered noise and which are material. For goals that are very far off, most market dislocations can be bypassed without taking action. For goals that are not quite so far away, the prospects of a lost decade may be an issue. And for goals that are short term, any material risk will be a concern.

Also, the difference in investment risk can become stark as an individual moves from the lower to higher rungs. The security rung will be oriented toward bonds with low risk and high liquidity, the lifestyle rung will be oriented by a standard bond/equity mix, and the aspirational rung will be oriented by high risk and low liquidity through such alternatives as private equity, real estate, and hedge funds or through concentrated and possibly levered stock positions.

Breaking up risks in this way suggests a target portfolio distribution that is a departure from the symmetric, bell-shaped normal distribution usually assumed for risk analysis. For security, the individual will dampen the downside tail to buttress against big losses, while aspirational gains will extend the upside tail. The downside tail is skinnier and the upside tail is fatter than with a Gaussian process. These rungs do not have clear lines of demarcation, changes for investment choices over time are likely to be gradual, and considerations will vary from one individual to the next.

 

Bringing Personal Risk and ABMs together

Just as the markets have dynamics, the individual does as well. The feedback from the market to the individual in a model adds the individual into the mix. Although an individual’s actions have little feedback into the market, similar actions across many individuals will. And just as the market features multiple strategies and agent types, each with separate heuristics, so too do individuals. Indeed, just as one institution can have a mix of strategies, expressed through its range of portfolio managers or traders, an individual’s heuristic can be multilayered as they work through the implication of the market for the various rungs of their goals. Thus, an ABM provides a natural structure for adding the components of personal risk into the overall risk management process and portfolio rebalancing. Individuals and other asset owners can be treated as agents in the ABM, with their heuristics encompassing their investment decisions.

 

Conclusion 

With its exclusive focus on short-term portfolio risk of financial institutions, risk management has pushed individuals and other asset owners to the side. The demands of risk management for these market participants not only are different from those of financial institutions but also are, in fact, more complex. They reside in a multidimensional world. They face periods of vulnerability coupled with events that lead to material risks that are not informed by recent market history and that might manifest over a longer time horizon. They are bound up with the shifting menu of an individual’s goals, which change with life circumstances as well as with the ups and downs of their portfolio.

How do we look at risk for those with a long time frame, be it a decade, a generation, or a lifetime? We use forward-looking models that reflect market dynamics and depict the interaction between market vulnerability and events. We represent the multidimensional nature of resulting scenarios. We focus on both edges of risk facing the individual—that is, the market and the personal. 

All of this requires a fresh mindset and new tools. The approach that Fabric proposes is the technology of ABMs. These models can incorporate the current market environment, project forward risk, and employ scenarios by incorporating market dynamics. Because the individuals can be incorporated as agents with their own heuristics, these models embrace both the market and the individual, thereby providing a framework that is best suited to the long-term investor’s decisions and goals.

 

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