The alpha equation: Balancing active risk sources in multi-asset portfolios

We are often asked by asset allocators how we approach decisions about where to take active risk in a portfolio, and there are indeed many different potential methods. We think discipline is key and to help we offer this guide to active risk budgeting: the process of deciding how much active risk to take (i.e., how much to deviate from benchmark weights) at the asset class and security levels in pursuit of one’s alpha objectives.

For any actively run portfolio, the excess return (alpha) objective is determined by the active risk that is taken and the return that was generated by that active risk (Figure 1). With that as our starting point, we will summarize our research on three key aspects of the risk-budgeting process:

1. The amount of active risk (tracking error) that can be generated — We believe historical data can be used to form practical expectations about the magnitude of active risk that can be generated through active asset allocation (AA) deviations (i.e., deviations in asset class weights) and security selection (SS) deviations (i.e., deviations within an asset class). In our analysis, we found it was possible to use AA deviations to generate tracking error of up to around 6% on a standalone basis. SS deviations generated tracking error of roughly 4% – 5% in equities and 0.5% – 3% in fixed income.
2. The excess return that can be assumed from the chosen amount of active risk — The relationship between excess return and active risk is measured through the information ratio (IR; the ratio of active return to active risk). SS deviations can typically be assigned higher IRs than AA deviations due to the higher breadth of the opportunity set.
3. The interaction between different sources of active risk at the broader portfolio level — It is critical to evaluate how the sources of active risk are likely to interact with one another and impact the portfolio’s tracking error and IR. We found, for example, that AA active risk and SS active risk tend to be positively correlated with each other and negatively correlated with the economic cycle.

Ultimately, effective active risk budgeting requires that assets be combined in an optimal way to preserve the desired tracking error, diversify away unwanted tracking error, and efficiently convert active risk into active return. To help, we conclude the paper with a step-by-step framework that allocators can use to implement the research findings in their own active risk budgeting processes.

Figure 1

The amount of active risk (tracking error) that can be generated

There are limits to how much active risk can be generated (without using leverage or introducing concentration and fee challenges), which we explore at both the AA and SS levels. Importantly, our focus here is on standalone AA and SS benchmark deviations. As we discuss later in the paper, combining different AA and SS deviations leads to diversification, which can significantly reduce the tracking error achieved at the broad portfolio level.

AA benchmark deviations — The tracking error that can be generated by adjusting exposure to an asset class relative to the benchmark is determined by 1) the starting weight of the asset class within the benchmark, 2) its correlation to the rest of the portfolio, and 3) its relative volatility.

To gauge the potential limits of tracking error at the AA level, we started with the illustrative multi-asset benchmark shown in Figure 2 and adjusted the weight of each asset class by 100%, funded equally from the other asset classes. We were able to generate a top tracking error of about 6% on a standalone basis — in global equities — but this required a large tilt and a substantial equity portion in the benchmark to begin with. Other asset classes, such as high-yield bonds and emerging market debt, tended to have a smaller impact on tracking error, given their smaller starting weight, higher correlation with the starting portfolio, and lower relative volatility.

Figure 2

Not surprisingly, more granular sub-asset-class deviations tend to have a much smaller impact on tracking error. For example, we find that regional equity calls typically generate about half the tracking error of the overall asset-class deviations.

SS benchmark deviations — At the SS level, the magnitude of tracking error varies greatly by asset class. For example, Figure 3 shows the tracking error ranges of active managers in different equity and fixed income categories, with median values indicated by the black lines. Equity managers generated tracking error of about 4% – 5% and fixed income managers generated tracking error of roughly 0.5% – 3%. There were a few exceptions, with small-cap equities, Chinese equities, and multi-asset credit coming in above these ranges.

Figure 3

In addition to using an active manager to achieve SS deviations, direct investing in securities is of course also an option. We would also note that there are a variety of non-security-specific levers that can impact tracking error, including changes in portfolio concentration (with fewer securities, tracking error tends to rise) and deviations in factor exposures. The point here is not to argue in favor of any particular approach to generating tracking error but to highlight the importance of understanding where tracking error is being generated in a portfolio.

The excess return that can be assumed from the chosen amount of active risk

The next consideration is the extent to which active risk can translate to excess return — i.e., the IR assumption, which is a function of the breadth of opportunities and investment skill.

The breadth of opportunities — SS-focused managers typically have greater breadth in their opportunity set than AA-focused managers — the number of securities in their universe is simply higher than the number of asset classes available to an AA-focused manager. There are many characteristics that can be used to measure breadth, and the opportunity for active risk taking, across different markets. In Figure 4, we show our Fundamental Factor Team’s equity market efficiency scorecard, which uses measures of market inefficiency to demonstrate the breadth of opportunities for active management in different regional equity markets. The results suggest that markets such as China, Japan, and emerging markets are less efficient and therefore may have a higher breadth of opportunities for active management.

Figure 4

While active AA managers face lower breadth than SS managers, it’s important to monitor the changing breadth of the active AA opportunity set over time. To illustrate this, we used principal components analysis (PCA) on 14 typical AA decisions (e.g., equities versus cash and EM equities versus DM equities) and measured breadth based on the number of “uncorrelated bets.” As shown in Figure 5, breadth ranged from five to nine uncorrelated bets over time, depending on the extent to which decisions shared the same underlying drivers. In other words, at times there were differentiated drivers behind the 14 AA decisions and therefore the number of uncorrelated bets was higher; at other times, decisions were dominated by a few big drivers (e.g., risk-on/risk-off) and the number of uncorrelated bets was lower.

Figure 5

Investment skill — The other key factor in the IR assumption — skill — is dependent on manager research and typically evaluated using historical realized IR values. Figure 6 shows the realized IRs of SS managers relative to their stated benchmark. The large range of values within each universe highlights the importance of manager research in gauging skill. Looking across each universe, we note that most equity managers were in the 0.2 – 0.4 range on average, with the exception of US large-cap managers. Fixed income managers were also generally in the 0.2 – 0.4 range, though multi-asset credit, aggregate, and securitized managers fell into the 0.5 – 0.7 range.

Figure 6

The interaction between different sources of active risk at the portfolio level

In this section, we focus on the impact of combining active AA and SS managers in a portfolio. We typically see a positive relationship between AA and SS managers as sources of active risk, indicating that they tend to take more or less active risk at the same time. To demonstrate this relationship, we ran a correlation analysis using the median historical tracking error from AA and SS managers in several categories (we acknowledge that the relationships will depend on the types of managers included, and that one cannot actually invest in the “median manager”). The top chart in Figure 7 shows the historical rolling 60-month tracking error for each category and the bottom chart shows the historical monthly correlations of the tracking error. The results suggest that, on average, AA and SS managers had higher tracking error at the same time. This may be driven in part by managers increasing tracking error concurrently when better opportunities present themselves, but we think it is largely a byproduct of higher-volatility regimes — that is, higher market volatility typically leads to more volatile alpha and, therefore, higher tracking error across the board.

Figure 7

Our analysis also considers the historical relationship between each source of active risk and the economic cycle, as measured by the OECD Composite Leading Indicator. The three categories of managers we looked at all had a negative relationship with the cycle, indicating higher active risk when the cycle is worsening and vice versa (likely because many managers take active risk by adding beta). With correlations below one, there may be a diversification benefit to including both the AA and SS managers in a portfolio. However, the diversification benefit may vary as managers take more or less active risk at the same time (again, a likely byproduct of higher volatility regimes). In addition, adding to active risk when the cycle is worsening may add to the risk in the overall portfolio.

Additional thoughts on IR assumptions and SS active risk
In our research on the interaction between different active risk decisions, we also looked at the compounding nature of IR assumptions, which results from the diversification of tracking error and can lead to unrealistically high assumptions when different active risk sources are combined. We also considered the impact of combining different sources of SS active risk and found that idiosyncratic security-specific risk can be quickly diversified away, while leaving behind factor, sector or regional risks that can compound and potentially become the dominant drivers of risk within a portfolio. To retain idiosyncratic risk, allocators may want to focus on combining managers who operate in different universes. More on these research topics is available on request.

TILT: A framework for active risk budgeting

Figure 8 illustrates our TILT (Targets, Inputs, Limits, Transform) framework, which allocators can use to help incorporate research insights from this paper into their own active risk budgeting processes. Below we highlight a few key points.

Targets: Allocators first need to set an overall active risk target for their portfolio. This will lay the groundwork for decisions about AA and SS active risk sources.

Inputs: As outlined in this paper, there are three key inputs into an active risk budgeting process: the amount of active risk that can be achieved from different sources, the IR assumption for each source, and the relationship and interaction between the sources.

Limits: Allocators will likely have practical limits that need to be incorporated into an active risk budgeting process. For example, they may limit the number or weight of different active risk sources. They may also limit the use of leverage, which we find can typically be more easily applied to active AA strategies, as SS strategies can quickly reach practical limits (e.g., on collateral, fees, and capacity).

Transform: The final step is to transform the targets, inputs, and limits into portfolio weights. We do not see this as a “one size fits all” process. Typically, the targets, inputs, and limits would be used to generate an initial estimate of strategy weights, which would then be subject to testing — including how the combined strategies may impact expected portfolio outcomes. The weights would then be adjusted, tested, and readjusted until the desired risk/return profile is achieved. Allocators can also test for changes in the inputs (e.g., correlation between strategies) and for outcomes during market stress periods. We also think allocators should aim to stress-test each weight combination to ensure the limits are not breached, the weights align with intuition about where active risk should be taken, and the expected portfolio outcomes meet the targets. 

Figure 8

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