Blog Posts — April 23, 2020

Who Blew Up My Tracking Error?

by Melissa R. Brown, CFA

The world of active risk has seen profound changes in the past two months. Take the hypothetical case of the portfolio manager at Rip Van Winkle Asset Management, who went to bed after rebalancing her portfolio on February 20th, and woke up (admittedly from a very long sleep) on March 23rd only to find out that her portfolio’s active risk levels had tripled “overnight”.

“Who blew up my tracking error?” we hear her exclaim.[1]

We see ample evidence that one of the investment-management problems adding to the woes of difficult absolute and relative performance amid higher overall portfolio volatility is that tracking error may have breached its limits on the upside. Some managers may have chosen to increase risk in pursuit of better active returns, but others may have done nothing to deserve such a fate. Teasing apart the components of active risk can tell us a lot about what happened.

As we noted in our quarterly Insight report, factor volatilities exploded in the first quarter, some doubling or tripling, and many nearing historically high levels. At the same time, many factor correlations saw extremely large (and statistically significant) changes. Portfolio bets that were offsetting and, therefore, diversifying risk last quarter may now be highly correlated and consequently driving risk higher. These changes in volatility and correlation occurred suddenly as markets headed south and returns to many common style and industry factors were much larger than expected.

Exhibit 1 highlights the changes in volatility (proportional to the original level) and the changes in risk-model correlations between January 31 and April 15, 2020, for the Axioma US Medium-Horizon Fundamental Model. For example, the strong performance of Profitability, along with the negative returns of a number of other factors, led to quite a few substantial decreases in correlation, which, in turn, may have meant a decrease in active risk for a portfolio with positive exposures to both. The large increase in correlation between Profitability and Size may have led to a substantial increase in active risk for a portfolio invested in Profitability with a large-cap bias.

Exhibit 1. Changes in Volatility and Correlation, Axioma US Medium-Horizon Model, 31 January to April 15, 2020

Source: Qontigo

Even as benchmark risk has started to settle down active risk may still be rising. Exhibit 2 highlights the changes in active risk between January 31 and April 15, 2020, for the STOXX USA 900 Ax Factor Indices[2], which are designed to target one specific style factor or a combination of factors, while simultaneously limiting exposures to other factors or industries[3]. The indices were rebalanced in March, but active risk, which had already climbed before the rebalance, continued to mount afterward. At rebalance, the indices target an active risk level of 5%, which, of course, may drift in between, and clearly did so in April.

Exhibit 2. Predicted Tracking Error, STOXX USA 900 Ax Factor Indices

Source: Qontigo

Of course, active risk can change for reasons other than what is in the covariance matrix, as a result of changes in holdings or the characteristics of existing holdings. For example, even without rebalancing, stocks’ exposures and specific risk were likely to have changed[4]. Or, portfolios may have rebalanced into names with substantially different factor exposures or stock-specific risks. And, of course, the impact of the covariance matrix remains.

To illustrate the potential drivers of the higher tracking error in the STOXX USA 900 Ax Factor Indices, we used the risk-analysis capabilities in our optimizer to look at the changes in active risk that resulted from changes in the composition of the portfolio (from the rebalance), the risk exposures (characteristics) of the stocks in the portfolio, stock-specific risk, and then drivers from the risk model (covariance matrix).

It is clear that the nature of the portfolio will determine the impact of any changes, as would the initial tracking error. The portfolios each had about 25% two-way turnover near the end of March. To be sure, the volatilities and correlations were the major drivers of the changes in active risk for all the indices, as shown in Exhibit 3. We also note that the overall increase in stock-specific volatility had a significant—and similar—impact on all the indices. Changes in the composition of the index, and changes in the stocks’ risk exposures, in contrast, had quite varying effects that were highly portfolio dependent, some adding to overall active risk and some reducing it.

Some examples: Whereas the new composition of the Momentum index after the rebalance added more than one percentage point to the active risk, composition drove tracking error down for Value, Low Risk and Size, and had little impact on Quality and Multifactor. At the same time, the characteristics of the stocks in the portfolio had neutral or negative impacts on all but the Value portfolio, suggesting the exposures shrunk closer to zero over the period.

It is more difficult to tease out the impact of the various elements of the covariance matrix, but we can make some assumptions. The Quality index, for example, has a high positive exposure to Profitability and a smaller—but still significantly negative—exposure to Leverage. There is also a high negative correlation between them, meaning that both would have contributed to the increase in active risk. In contrast, the Quality portfolio also has a small-cap bias (negative exposure to Size). But since Profitability and Size are positively correlated, this would have dampened (or possibly even reversed) higher active risk because of their highly negative correlation, even given their big increases in volatility. Thus, we potentially see a smaller increase in active risk than we would have expected given the portfolio’s major tilts.

Exhibit 3. Decomposition of the Change in Active Risk, STOXX USA 900 Ax Factor Indices

Source: Qontigo

What can portfolio managers take away from this analysis?

  • First, managers were not alone in seeing a sharp and sudden increase in active portfolio risk. Whether they chose to rebalance or not, the covariances would have driven risk continuously up.
  • Second, a number of other portfolio-specific changes likely occurred, which may or may not have looked like what happened to other managers. Aside from rebalancing the portfolio to reign in factor exposures, there was probably not much the manager could do, as stocks’ factor exposures and specific volatility, along with factor volatilities, would have changed no matter what—and changing factor correlations may have made it far more difficult to diversify.
  • Third, this was not just an issue for factor-based managers. Most discretionary managers like to see as little factor exposure as possible in their portfolios, instead focusing portfolio risk on individual names where they expect to add value. As we noted, the increase in stock-specific volatility also rose substantially, and diversification became far more difficult during this period.

[1] Several years ago, we released a paper called “Who Shrunk My Tracking Error?”, in which we addressed the problem that many portfolio managers were having reaching their target active risk levels. Oh, for the good old days!

[2] Indices include: STOXX® USA 900 Ax Quality, STOXX® USA 900 Ax Value, STOXX® USA 900 Ax Low Risk, STOXX® USA 900 Ax Momentum, STOXX® USA 900 Ax Size, STOXX® USA 900 Ax Multi-Factor

[3] For more detail on these portfolios please see our whitepaper here.

[4] We covered this topic extensively in our webinar “Managing Your Portfolio in an Extreme US Factor Environment”. You can view the recording here.