Ivan Mitov Ph.D., Georgi Mitov Ph.D., Todor Bilarev Ph.D., and Tanyo Petrov also contributed to this article.
In the wake of the COVID-19 pandemic, members of FactSet’s Risk and Quant team have been sharing their insights and views on how to make sense of the world in which we now find ourselves, how to categorize or quantify how the markets behave, and how to build a framework to think about the future while we adjust ourselves and our investments.
Consistent with our philosophy around market risk and the multiple lenses in which it is necessary to evaluate risk, the main idea of this article is to introduce the concept of multi-period optimization and its novel application for studying portfolio positioning during different recovery scenarios. The purpose is not to predict what the most likely recovery scenarios are, but to illustrate how using a multi-period lens can help you analyze the impact of the COVID-19 global pandemic on portfolios and evaluate the effect of different recovery scenarios in a structured way. The story is told via three questions:
As is so often the case in the finance industry, techniques and concepts from one segment find adoption in other areas. Examples include the increasing demand for ex-ante analytics (commonplace for institutional clients) by sophisticated retail clients. Multi-period optimization is another; a concept traditionally the preserve of long-horizon investors such as pension funds and endowments are now finding greater interest with a wider audience.
Single-period portfolio optimization and the concept of optimal allocations using risk/return concepts is so ubiquitous that many often don’t consider that the solution gives the optimal allocation for a single homogeneous horizon; investment horizons and objectives are rarely so.
Multi-period optimization solves for the optimum allocation for multiple periods, each potentially with its own risk, return, objectives, and constraints in a single calculation. One application is finding the optimal link between Strategic Asset Allocation (SAA) and Tactical Asset Allocation (TAA). For many, the link between the TAA, which aims to allow short-term opportunities to be exploited, and the SAA is implemented only as the flexibility to deviate from the SAA by a fixed amount.
Intuitively, underweighting an asset class as a TAA decision knowing that an overweight position is anticipated for the next period feels like a problem built for optimization; finding the most optimal allocation to exploit both short-term and longer-term allocations while minimizing transaction costs and other related portfolio frictions.
A stylized example shows this value in a case where the asset class returns are known in advance. The single-period optimization uses the known asset class returns one year ahead and the multi-period uses asset class returns one year and five years ahead.
In the presence of turnover constraints, those following a single-period optimization approach will be limited even in the case of perfect knowledge of the future. The multi-period example considers the additional information contained in the five-year returns and results in a better performing portfolio. The five-year returns allow the optimizer to choose the optimum allocation in the presence of turnover constraint. It is worth noting that if turnover constraints were removed, then there will be no difference between the single- and multi-period examples.
The applications of multi-period optimization are so much greater than only solving for a more optimum allocation between SAA and TAA. Applications include incorporating changing risk/return appetite over the course of the investment horizon (glide paths), differing constraints over multiple periods, incorporating cashflows and liabilities, and as we’ll see in the next section, evaluating the impact of market stresses.
During times of market stress and change, a question often asked is whether the strategy and the portfolio that was agreed upon during the last review now needs to be adjusted. Market shocks and stresses are well understood, if not where the next one will come from, at least in the relative frequency which they occur. New generation risk modeling and portfolio construction techniques incorporate much of what we have learned over the last two decades.
As such, a well-diversified portfolio should be robust to market shocks and stresses. The usual approach to evaluate the robustness would be to calculate the portfolio performance under different stress tests. Where these tests often fall short is when they capture only part of the picture; while it’s important to evaluate portfolio performance under stressed conditions to ensure survival (e.g., solvency, not getting fired), it’s at least equally important to assess the impact of those scenarios on achieving the ultimate portfolio objectives.
At the end of the investment horizon, few investors would agree that successfully navigating the various bumps in the road but failing to achieve portfolio objectives is a good result.
One application of multi-period optimization is to use it to add this extra dimension to assess the impact of market scenarios on the portfolio achieving its objectives. While optimization is a necessity to undertaking this type of analysis, think of the optimization component in this instance as defining the portfolio strategy to be followed in a more sophisticated way than a rules-based approach such as re-balancing to set weights or other metrics.
The impact of the COVID-19 market drop in March 2020 is examined on a balanced portfolio of 40% equity and 60% fixed-income allocation; a 20-year investment horizon with an optimization objective of finding the best risk/return utility. This is compared with the same analysis performed three months prior.
|
|
Dec. 31, 2019 |
Mar. 31, 2020 |
|
Portfolio value ('000 USD) |
1,171 |
1,057 |
|
Expected return (annualized) |
6.19% |
5.48% |
|
Volatility (annualized) |
22% |
23% |
|
Sharpe Ratio |
2.14 |
1.84 |
|
Probability of achieving cumulative return target of 150% |
75% |
63% |
|
Expected ending wealth ('000 USD) |
3,505 |
3,077 |
Source: FactSet
When looking at the long-term probability of achieving a return target, the COVID-19 scenario has a significant impact (all metrics are worse in March than December). When viewed relative to the wider global impact of COVID-19, the portfolio and its long-term goal show more resilience.
In the case of this example, the two-fold message to the investor is:
While the example tells a more complete story for an investor than an instantaneous stress test, what it does not take into account is how the world changes, and how it is expected to recover from COVID-19. For this, we can continue to use the multi-period approach.
Examining “house” views on recovery scenarios can help you understand both impact to portfolio allocations and the construction of the scenarios themselves by providing another lens with which to evaluate the differences between scenarios.
Unlike the previous article where recovery scenarios were defined for a U.S.-equity universe, the scenarios used in this example are stylized versions of the V-shaped, U-shaped, and L-shaped recovery defined solely by expected quarterly returns for asset classes over a five-year period. All three scenarios follow the same “dip,” but then have different recovery periods before reverting to the 20-year historical mean return for the asset classes (whether this assumption holds true is another story). A multi-period optimization calculation with frequency quarterly is executed for each scenario to determine the optimal allocations between asset classes.
The first step in the multi-period optimization calculation is to generate multiple paths for the possible future values of the portfolio. When visualized, the V-, U-, and L-shape can be seen in the paths generated.
Once generated, multi-period optimization can be performed. Two common ways to look at the results are through the perspective of a “Dynamic Allocation” approach or a“Fixed-Mix” approach.
Dynamic Allocation strategies allow for the weights to dynamically change to reflect the optimum allocation at each period. Looking at how the dynamic allocation changes in future periods give an immediate sense of how the portfolio allocations should evolve to implement the strategy. This strategy is akin to taking a peek at the road ahead.
Fixed-Mix strategies give the optimum allocation for the entire investment horizon, considering all of the information from the multi-period calculation. The output is a single set of weights.
The forward-looking Dynamic Allocations for the portfolio between the V- and U-shapes are similar in nature, with the U-shape taking a few more quarters before returning to the long-term allocations. Interestingly a position in U.S. High Yield is introduced with the U-shape but not the V-shape—a suggestion that the longer recovery allows for more room to maneuver while staying within turnover constraints.
In the Fixed-Mix strategy, there is little difference in allocations between the V-shaped and U-shaped scenarios largely as the recovery in both scenarios follows the same trajectory albeit with a six-month lag in the case of the U-shape. The long-term investor should treat both recovery scenarios the same.
The L-shaped recovery is the most pessimistic and the Dynamic Allocations show the scenario playing out over a period of 10 quarters before settling at the long-term allocations.
Comparing the expected outcomes at the end of the five-year investment horizon is a consistent story; both V- and U-shaped scenarios achieve similar results whereas the L-shaped recovery is the most pessimistic. Take those results in conjunction with how the scenarios are defined, and the probability of each scenario occurring gives a powerful quantitative set of tools.
|
|
V-Shaped |
U-Shaped |
L-Shaped |
|
Starting portfolio value ('000 USD) |
1,171 |
1,171 |
1,171 |
|
Expected return (annualized) |
4.90% |
5.07% |
2.06% |
|
Volatility (annualized) |
19% |
21% |
16% |
|
Sharpe Ratio |
1.4 |
1.2 |
0.67 |
|
Probability of achieving 25% return goal |
53% |
54% |
25% |
|
Expected ending wealth ('000 USD) |
1,491 |
1,500 |
1,297 |
Source: FactSet
Multi-period thinking isn’t a new idea, however, the tools and techniques required to implement a robust risk-based approach are at the leading edge of FinTech capabilities. The applications of such tools are wide; in this article, we’ve chosen to present three of them:
Be Aware, Adapt, Innovate—or What We Learn from Mandelbrot, Noah, and COVID-19
By Dr. B. Racheva-Iotova
Part 1: VaR 99% and COVID-19: Back-Testing Studies on the FactSet Short-Term Risk Model Covering the Period of COVID-19 Outbreak
By Dr. B. Racheva-Iotova, Ivan Mitov Ph.D., Viviana Vieli, Velislav Bodurov
Part 2: Constructing Semi-Subjective Scenarios for Possible Recovery and Assessing the Scenarios’ Plausibility Based on Monte Carlo Risk Models
By Georgi Mitov Ph.D., Emil Margaritov Ph.D., Shamin Parikh, Dr. B. Racheva-Iotova