How to Identify Independent Sources of Risk for Multi-Asset Managers and Portfolios

Key Takeaways

• Much in the way that residue is what is “left over,” the goal of residualization is to isolate leftover risk after accounting for other entangled or correlated risks

• The benefits of residualization are amplified when applying it across a holistic set of risk factors, including individual factors that might benefit from being residualized to multiple other factors

• The residualization process in Solovis Risk Pro is intended to provide a truer picture of the total risk contribution of assets, avoiding the illusion of diversification from similar risks contributed by many different asset classes

Allocators managing multi-asset portfolios face a persistent challenge: understanding which risks are truly independent and which are, in fact, the same risk expressed across different asset classes. The factor lens addresses this challenge by using a process called residualization to construct independent factors that decompose risk and return for investments and portfolios.

A prior discussion covered how factors in Risk Pro are orthogonal to each other, and showed an example of how the equity factor appeared to be the largest driver of risk for a high-yield fixed income index. That example emphasized the importance of using independent risk factors to understand diversification, rather than a traditional asset class framework.

This piece addresses how residualization is used to seek factor independence, provides an example of how it is done, and shares considerations for applying it more broadly within the factor lens.

Using Residualization to Unbias “Home Bias”

Residualization can be a mouthful, but it is a surprisingly simple concept. Much in the way that residue is what is “left over,” the goal of residualization is to isolate leftover risk after accounting for other entangled or correlated risks.

Consider the Local Equity Factor as an example. This factor aims to capture equity home bias, or the tendency to invest in domestic over foreign equity. Global equity risk¹ muddies the waters when trying to isolate the impact of the Local Equity Factor on portfolios. Remove the relationship with global equity, and the result is an independent risk factor that helps explain performance of an investor’s local equity market.

The following example illustrates the residualization process² for the worst day in the Local Equity Factor’s history: Black Monday, October 19, 1987.

Step 1: Quantify the relationship of global equities with US equities.³ This is done by considering global equity performance and running a regression to measure US equities’ sensitivity to that performance (specifically, US equities’ trailing 3-year beta to global equities).⁴

Step 2: Remove global equities’ relationship by subtracting it from US equity performance.

Source: Solovis. For illustration purposes only.

After accounting for the relationship with global equities, US home bias in portfolios was a headwind on Black Monday. Specifically, the Local Equity Factor was down more than -6%.

While this example highlights how residualization can isolate an individual risk factor, the benefits of residualization are even greater when applied across a holistic set of risk factors. It can also be especially useful for individual factors that might benefit from being residualized to multiple other factors.

This leads to a discussion about residualization across the broader factor lens.

Expanding Residualization to Broader and More Entangled Risks

The factor lens provides a practical framework to analyze risk in investments and portfolios, via the use of a curated list of independent factors. To achieve this, residualization is approached with a tier system, which ultimately seeks low to zero correlations across risk factor pairs over time.

Related to the chart below:

• Tier 1 Core Macro Factors are considered to be the most liquid and are not residualized against anything

• Tier 2 Core Macro Factors are residualized against Tier 1 Core Macro Factors

• Tier 3 Secondary Core Macro Factors are residualized against both Tier 2 and Tier 1 Core Macro Factors

• Local Equity, Equity Short Volatility, and Foreign Exchange Carry are only residualized against the Equity Factor, while Fixed Income Carry is only residualized against the Interest Rates Factor

• Trend Following and equity styles (Low Risk, Momentum, Quality, Value, Small Cap, and Crowding) undergo no residualization

Trend Following is intended to capture active managers’ short- to medium-term trend-following behavior, which can take long or short directional risk in different factors at different times. Trend following positioning does not provide the consistency to benefit from residualization.

Equity styles generally exhibit naturally low correlations across the factor lens, but are designed to be equity market neutral in their construction rather than through residualization.

The factor lens Residualization Approach to Seek Independent Factors

Source: Solovis. For illustration purposes only.

As an example, the Emerging Markets (EM) Factor represents EM risk that is above and beyond embedded Equity, Interest Rates, Credit, and Commodities risk. Without residualization, it can be difficult to understand the true impact of EM exposure on investments without mistaking it for a mix of these other factors.

This is evidenced by examining the properties of the EM Factor before residualization. Specifically, its correlation with the Equity Factor is a meaningful 0.75 historically (as shown in the correlation matrix below), which implies significant overlapping risk. After residualization, the EM Factor has a correlation of virtually 0 with the Equity Factor. Working from the raw input, rather than the residualized Emerging Markets Factor, may lead to less informed and less precise asset allocation decisions.

Correlations of Emerging Markets to Inputs Before and After Residualization

Emerging Markets Input = Before Residualization

Emerging Markets = After Residualization

Source: Solovis. The chart displays a correlation matrix for the Emerging Markets Factor in the factor lens over its full history from 11/9/1994 to 11/23/2023.

What Are Expected Results from Applying this Residualization System?

When analyzing assets in Risk Pro, this residualization process has the effect of increasing the amount of risk assigned to higher-order factors such as Equity and Interest Rates. For example, the large majority of risk correlated to equity returns (such as moves driven by shocks to global growth expectations or investor risk aversion) will be consolidated in Equity Factor exposure, regardless of what asset initially generated that risk. This is intended to provide a truer picture of the total risk contribution of assets, avoiding the illusion of diversification from similar risks contributed by many different asset classes.

Another result is that virtually all correlations between factor pairs are low or close to zero over their full shared histories. This makes analyzing multi-asset portfolios and interpreting sources of risk a more reliable and straightforward exercise. Put another way, relatively dispersed exposure to multiple factors in the factor lens suggests that the portfolio is diversified among many independent sources of return.

Source: Solovis. The chart displays a correlation matrix for all 18 factors in the factor lens over their full history from 10/3/1997 to 11/23/2023.

Quantifying Unique Sources of Risk Across Multi-Asset Portfolios

A difficult challenge for allocators is not only to holistically analyze multi-asset portfolios, but also to disentangle how unique sources of risk affect portfolio sleeves, managers, or individual holdings. Risk Pro uses residualization to quantify these unique sources of risk and helps identify where in the portfolio they can be found.

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References

^1. This refers to the Equity Factor in Risk Pro, which is represented by currency hedged global equities.

^2. For illustration purposes, consideration of the risk-free rate has been removed; it is typically accounted for in the factor construction and residualization process.

^3. This example is given using the USD lens of the factor lens. As a result, the Local Equity Factor captures a home bias from investing in US equities over foreign equities.

^4. Specifically, the residualization process in Risk Pro involves a rolling multivariate, exponentially-weighted regression using rolling 5-day returns. The lookback period is 3 years, and the half-life is 6 months. A shorter time horizon for the rolling residualization window is used relative to most institutional investor time frames. Research indicated that this specification was a long enough lookback period such that the factor relationships were not overly sensitive or noisy, and short enough to capture changes in factor relationships during volatile market environments like 2008 or the COVID-19 market crisis.