Quants bring ‘triptych’ of variables to risk measurement

Risk and portfolio managers at La Francaise and LFIS are squeezing more information out of stress tests

Value-at-risk and expected shortfall (ES) are ubiquitous in finance. They are used by banks and asset managers to estimate the risk of portfolios. Regulators use them to set capital requirements.

But the metrics have well-known drawbacks. Both VAR and ES are backward-looking, relying on the past to predict the future. The methodologies only consider returns and volatility, ignoring the underlying scenarios and factors that determine performance. And while they provide a reasonable measure of the risk profile of linear, long-only portfolios that invest in a single asset class, the results need to be taken with a grain of salt when dealing with more complex structures, such as those with hedges or non-linear payoffs.

To overcome these limitations, risk managers complement VAR and ES with stress tests to gauge the resilience of portfolios in adverse market conditions.

Quants at La Française Group and LFIS in Paris have taken that one step further, developing a forward-looking methodology they are calling an extended reverse stress test (ERST).

The new test provides not just a loss estimate, but also the specific scenario associated with the loss, expressed as a vector of values of all risk factors, coupled with a measure of how plausible the scenario is.

ERST was developed by Pascal Traccucci and Benjamin Jacot, global head of risk and quantitative risk manager, respectively, at La Française, working together with Luc Dumontier, head of factor investing, and Guillaume Garchery, the heads of factor investing and quant research, respectively, at LFIS.

They call their method a ‘triptych approach’ because it allows them, with only one of three variables – plausibility, loss and scenario – to derive the other two.  

“The model is typically applied starting either from the scenario variable or from the level of loss,” says Traccucci. He explains that “managers often have VAR in mind, but not a scenario corresponding to it, so we set the VAR and the scenario” to help the investment decision process.  

Normally, a risk manager has a maximum loss boundary and wants to know how probable it is, and what scenario might lead to it. Conversely, a portfolio manager might start with a scenario and want to know how big the losses could be and how probable that is.

Plausibility is a variable that quantifies, in units of standard deviation, the distance of the scenario under consideration to the average scenario, which is built as the vector of average value of each factor. It is calculated using the Mahalanobis distance, the span between two points in a multidimensional space – in this case, the vectors of risk factors. The calculation gives some idea of whether a scenario is plausible enough to be considered, or if it should be discarded.

The model is typically applied starting either from the scenario variable or from the level of loss

Pascal Traccucci, La Française

“We wanted to develop a tool that was useful to both risk and portfolio managers,” says Dumontier. “Indeed, portfolio managers can provide not only their worst-case scenario, but their best and expected case scenario as well and derive a plausibility level of both.”

A senior risk expert at a large global asset management firm praises the research as both innovative and practical.

“The matter of plausibility of scenarios is, in my experience, regularly brought up when discussing results of stress tests,” he says. “The method is very interesting and potentially of immediate use.”

ERST builds on reverse stress tests. Instead of measuring the portfolio impact of adverse conditions, reverse stress tests assume a loss and then try to determine the scenarios that could lead to it. 

Crucially, the methodology can be applied to portfolios with non-linear, quadratic payoffs. This is important for La Française and LFIS, which manage several complex risk premia funds that employ non-linear, long-short strategies across multiple asset classes, sometimes using complex derivatives structures.

Research on the model started in 2016 in the risk management department. Soon, portfolio managers got involved, and La Française and LFIS have been using the model for a year now. The team says ERST is versatile enough to be applied in different contexts, including investments in real estate or private equity funds with illiquid assets. In the future, the methodology could be extended to stress-test not only individual portfolios, but the entire firm at the book level.