Active risk: Meaning, Criticisms & Real-World Uses

Active Risk: Understanding Deviations from the Benchmark

Active risk, a core concept in Portfolio Theory, quantifies the potential variability of a portfolio's returns relative to its chosen benchmark. It represents the degree to which an actively managed portfolio deviates from its benchmark index, reflecting the investment manager's intentional decisions to overweight or underweight certain securities or asset classes in pursuit of higher returns. Unlike passive strategies that aim to replicate a market index, active management inherently embraces active risk in an effort to outperform the market.

History and Origin

The concept of active risk has evolved alongside the development of modern portfolio management. Early approaches to risk measurement often focused on the absolute volatility of a portfolio, as championed by pioneers like Harry Markowitz with his work on Modern Portfolio Theory in the 1950s¹⁰, ¹¹. As the investment landscape matured and the use of market benchmarks became commonplace, particularly with the rise of index funds, the need to measure a portfolio's deviation from these benchmarks became crucial.

This led to the increasing emphasis on relative risk measures. Active risk emerged as a key metric to evaluate the efficacy of active management decisions, distinguishing the risk taken relative to a benchmark from the overall market risk. The pursuit of outperformance through active strategies became more rigorously quantifiable, with metrics like active risk providing insights into the manager's conviction and divergence from the benchmark. Firms like CFA Institute and Research Affiliates regularly publish research and insights related to active management and risk assessment, reflecting the ongoing evolution of these concepts in investment analysis⁸, ⁹.

Key Takeaways

Active risk measures the potential for a managed portfolio's returns to differ from its benchmark.
It arises from the deliberate investment decisions made by active managers to generate alpha.
A higher active risk generally indicates a greater deviation from the benchmark, implying a more aggressive active management approach.
While active risk is often associated with the potential for outperformance, it also signifies the potential for underperformance relative to the benchmark.
Understanding active risk is crucial for investors to assess how closely a fund's performance aligns with its stated strategy and risk tolerance.

Formula and Calculation

Active risk is typically calculated as the standard deviation of the difference between the portfolio's return and the benchmark's return over a specified period. This difference is often referred to as "active return" or "excess return."⁷

The formula for ex-post (realized) active risk, often denoted as (\omega) or (TE), is:

TE = \sqrt{\frac{\sum_{t=1}^{n} (R_{p,t} - R_{b,t})^2}{n-1}}

Where:

(TE) = Active Risk (also known as Tracking Error)
(R_{p,t}) = Return of the portfolio at time (t)
(R_{b,t}) = Return of the benchmark at time (t)
(n) = Number of periods
The term ((R_{p,t} - R_{b,t})) represents the active return for each period.

A low active risk suggests that the portfolio's returns closely track those of its benchmark, similar to a passively managed fund. Conversely, a higher active risk indicates that the portfolio's returns diverge more significantly from the benchmark, which is characteristic of a more aggressive active management style. This calculation helps assess the consistency of a manager's deviations.

Interpreting Active Risk

Interpreting active risk involves understanding what a specific value implies about a portfolio's management style and potential outcomes. A portfolio with very low active risk behaves much like its benchmark, indicating limited active management or "benchmark hugging." On the other hand, a portfolio with high active risk signifies that the manager is taking significant, deliberate positions that differ from the benchmark, aiming for substantial outperformance.

For instance, an active risk of 1% means that, historically, the portfolio's annual return has deviated from the benchmark's return by approximately 1% in most years. Investors should evaluate active risk in the context of their own investment strategy and risk tolerance. A higher active risk might be acceptable for those seeking greater potential for alpha, while those prioritizing consistent benchmark-like performance would prefer lower active risk. It is also important to consider the risk-adjusted return alongside active risk, often measured by metrics such as the information ratio, to evaluate whether the additional risk taken is adequately compensated by excess returns⁶.

Hypothetical Example

Consider an investment manager, Portfolio Manager A, who oversees a U.S. large-cap equity fund benchmarked against the S&P 500.

Scenario:

Year 1: Portfolio return = 12%, S&P 500 return = 10%. Active Return = 2%.
Year 2: Portfolio return = 8%, S&P 500 return = 9%. Active Return = -1%.
Year 3: Portfolio return = 15%, S&P 500 return = 13%. Active Return = 2%.
Year 4: Portfolio return = 5%, S&P 500 return = 6%. Active Return = -1%.
Year 5: Portfolio return = 11%, S&P 500 return = 10%. Active Return = 1%.

To calculate the active risk (standard deviation of active returns):

Calculate the average active return: ((2% - 1% + 2% - 1% + 1%) / 5 = 0.6%)
Calculate the squared difference of each active return from the average:
- ((2% - 0.6%)^{2 = (1.4%)}2 = 0.000196)
- ((-1% - 0.6%)^{2 = (-1.6%)}2 = 0.000256)
- ((2% - 0.6%)^{2 = (1.4%)}2 = 0.000196)
- ((-1% - 0.6%)^{2 = (-1.6%)}2 = 0.000256)
- ((1% - 0.6%)^{2 = (0.4%)}2 = 0.000016)
Sum the squared differences: (0.000196 + 0.000256 + 0.000196 + 0.000256 + 0.000016 = 0.00092)
Divide by (n-1) (where (n=5)): (0.00092 / (5-1) = 0.00092 / 4 = 0.00023)
Take the square root: (\sqrt{0.00023} \approx 0.01516) or (1.516%)

In this hypothetical example, Portfolio Manager A has an active risk of approximately 1.516%. This value indicates the typical dispersion of the portfolio's returns around the benchmark's returns due to the manager's investment strategy.

Practical Applications

Active risk is a critical metric in various aspects of financial analysis and portfolio management. It helps institutional investors, such as pension funds and endowments, evaluate the effectiveness of their chosen active management mandates. Fund managers use active risk as a guide to ensure their portfolio deviations remain within acceptable limits set by their investment guidelines. For instance, many mutual funds and exchange-traded funds (ETFs) that aim to closely track an index will strive for minimal active risk.

In the realm of risk management, active risk provides insight into the potential for "unintended bets" or significant divergences from the market. It is also used in performance attribution, where it helps decompose a portfolio's overall return into components attributable to market exposure (beta) and active decisions (alpha). According to the CFA Institute, while traditional active management faces challenges, active decision-making is evolving and remains embedded in investment strategies, highlighting the continued relevance of metrics like active risk⁵. Organizations like Research Affiliates conduct extensive research on various aspects of asset allocation and risk, often incorporating insights derived from active risk analysis in their models⁴.

Limitations and Criticisms

While active risk is a widely used measure, it has several limitations and criticisms. One primary critique is that a high active risk does not inherently guarantee outperformance; it merely indicates a significant deviation from the benchmark. An actively managed portfolio could take substantial active risk and still underperform its benchmark. Furthermore, some studies suggest that actively managed mutual funds with consistently low active risk (meaning they closely hug their benchmark) tend to exhibit lower alpha and average performance compared to funds with higher active risk³.

Another limitation is that active risk, being a historical measure, may not accurately predict future deviations. Market conditions, a manager's style drift, or changes in the portfolio's composition can alter future active risk levels. Investors must also consider that active management, which generates active risk, often comes with higher fees compared to passive investing. This necessitates that any outperformance (alpha) generated must be sufficient to cover these additional costs. The challenge for active managers is to generate sufficient alpha to justify the fees and the active risk taken².

Active Risk vs. Tracking Error

The terms active risk and tracking error are frequently used interchangeably in finance, and for good reason: they represent the same core concept. Both refer to the standard deviation of the difference between a portfolio's returns and its benchmark's returns over time¹.

However, the choice of term often subtly reflects the context or emphasis. "Active risk" tends to highlight the deliberate, active decisions a manager makes to deviate from a benchmark in pursuit of better performance. It emphasizes the risk taken by an active manager. "Tracking error," on the other hand, often implies how closely a portfolio tracks or replicates its benchmark, with a lower tracking error indicating tighter replication. While a passive fund would aim for minimal tracking error, an active fund would accept, or even seek, a higher tracking error as a byproduct of its strategy to generate alpha. Fund managers calculate both to understand performance relative to their objectives.

FAQs

Q1: Is a high active risk always bad?
A: Not necessarily. A high active risk means the portfolio's returns are likely to deviate significantly from the benchmark. If the manager's active decisions are successful, this can lead to substantial outperformance (positive alpha). However, it also means a higher chance of underperformance if the active bets do not pay off. It is about aligning with the investor's objectives and the manager's skill in generating consistent return.

Q2: How does active risk relate to diversification?
A: Diversification typically aims to reduce idiosyncratic (company-specific) risk within a portfolio. Active risk, however, is a measure of risk relative to a benchmark, stemming from intentional deviations from that benchmark. While a well-diversified portfolio might still have significant active risk if its holdings differ substantially from the benchmark, effective diversification within the active portion can help manage unintended concentrations that could lead to negative active returns.

Q3: Can passive funds have active risk?
A: Ideally, pure passive investing strategies, like index funds, aim to have zero or near-zero active risk. Their goal is to replicate the benchmark's performance as closely as possible. However, due to factors like trading costs, rebalancing, cash drag, or even imperfect replication strategies, even passive funds can exhibit a small degree of active risk, often referred to as tracking error.

Q4: Is active risk the same as standard deviation?
A: Active risk uses standard deviation in its calculation, but they are not the same. Standard deviation measures the absolute volatility of a portfolio's returns. Active risk, however, specifically measures the standard deviation of the difference between the portfolio's returns and the benchmark's returns. So, standard deviation is an absolute measure of total risk, while active risk is a relative measure of risk versus a benchmark.

Q5: How do investors use active risk in their decision-making?
A: Investors, especially those evaluating actively managed funds, use active risk to understand a manager's commitment to their stated investment strategy. It helps them assess how much a fund is truly "active" versus merely mimicking a benchmark. Combined with other metrics like the Information Ratio, active risk helps investors gauge if the level of deviation taken is justified by the manager's ability to generate excess returns.