This is a summary of “Portfolio Choice with Path-Dependent Scenarios” by Mark Kritzman, CFA, Ding Li, Grace (TianTian) Qiu, and David Turkington, CFA, published in the First Quarter 2021 issue of the Financial Analysts Journal.
This study proposes a new approach to scenario analysis, where scenarios are defined as paths rather than single averages. The approach enables probabilities and asset class returns to be estimated more reliably and produces richer portfolio metrics.
What’s the Investment Issue?
One common technique for selecting portfolios is scenario analysis. This approach involves defining potential economic scenarios, assigning probabilities to them, translating the scenarios into expected asset class returns, and then computing and comparing performance metrics to make a portfolio selection.
Key challenges that investors face involve deciding how to assign probabilities to prospective scenarios and how to translate these scenarios into asset class returns. Typically, under the scenario analysis approach, economic scenarios are defined as a set of single-period average values for relevant economic variables. The authors of this study advocate an alternative approach: defining scenarios as paths for economic variables, which enables investors to consider sequential outcomes.
How Do the Authors Tackle the Issue?
The authors illustrate the case for defining scenarios as paths rather than average values. They look at GDP growth figures from 1929 to 2019 and search for the three-year period that was most similar to the Global Financial Crisis of 2006–2008. They construct and compare two versions of the data: one that considers year-by-year paths and another that considers average three-year growth rates.
They propose defining scenarios as a set of multiple values for relevant economic variables that represent the early, middle, and late stages of a pattern—where patterns might cover months, quarters, or years. The likelihood of different scenarios can be estimated by calculating their statistical similarity to historical sequences. This calculation can be performed using a statistic called the Mahalanobis distance. This is a measure that characterizes the distance between two multivariate observations, while accounting for the expected variation of the underlying variables from their averages.
To convert these economic scenarios into estimates of expected returns for selected asset classes, the authors recommend partial sample regression. This technique is useful because it provides a more straightforward link between economic variables and asset returns than a simulation analysis, such as a Monte Carlo simulation. The authors note that one of the key advantages of their methodology is that it imposes an internal consistency across probability estimation and return forecasting.
Finally, they illustrate their proposed methodology with a case study. They construct six distinct and plausible economic scenarios in the United States following the COVID-19 pandemic, which they name as follows: Baseline V, Shallow V, U-Shaped V, W-Shaped V, Depression, and Stagflation. Each scenario is defined by the three-year paths of two macroeconomic variables: real GDP growth and inflation. The authors compute Mahalanobis distances to assess the respective probabilities of each scenario.
They then consider three asset classes: US stocks, bonds, and cash. They apply the partial sample regression technique to calculate the expected real returns of these asset classes that are associated with each of the economic scenarios. They use their findings to produce a variety of path-dependent metrics by which to evaluate three alternative portfolios: conservative, moderate, and aggressive.
What Are the Findings?
The key contribution this study makes is proposing a new technique for scenario analysis. The case study it examines is intended as an illustrative example of this approach.
The authors find that the results differ depending on whether scenarios are defined as paths or as multi-year averages. For example, when looking for the three-year period most similar to the Global Financial Crisis, they observe that the scenarios defined as paths bear much more resemblance to the pattern of growth observed from 2006 through 2008.
In the case study that illustrates their proposed methodology, the authors find that the probabilities associated with the six economic scenarios they have selected range from a high of 30% (U-Shaped V) to a low of 2% (Depression). The asset class returns that they compute for these scenarios are intuitively consistent with the scenario descriptions.
Specifying scenarios as paths produces a richer set of data than when using single-period averages. As well as annualized cumulative return for each portfolio, the authors have visibility into portfolio metrics that otherwise would not be known.
What Are the Implications for Investors and Investment Managers?
The authors argue that investors could benefit in several ways from defining prospective economic scenarios as paths for economic variables rather the current convention of using single-horizon averages. Most importantly, this approach enables investors to measure statistical similarity more reliably—improving their ability to assign probabilities to scenarios and to forecast asset class returns. The authors note that their approach is distinct from simulation methods such as Monte Carlo simulation, insofar as it is more direct—and therefore more intuitive for most investors—and requires fewer scenarios to be considered. They also show that defining scenarios as paths can be used to produce a richer set of portfolio metrics to facilitate better and more informed decision making.