Relative risk: Meaning, Criticisms & Real-World Uses

Relative Risk: Definition, Formula, Example, and FAQs

Relative risk, within the realm of risk management and portfolio theory, quantifies the risk of an investment or portfolio compared to a specific benchmark or another investment. It measures how much an asset's or portfolio's performance deviates from its chosen standard. Investors and analysts use relative risk to gauge whether an investment is more or less volatile or prone to losses than a comparative option, such as a market index or a competitor's portfolio. Understanding relative risk is crucial for assessing potential tracking error and evaluating the effectiveness of active management strategies. It helps in understanding the nuances of performance relative to a chosen standard, rather than in isolation.

History and Origin

The concept of comparing an investment's performance and risk against a benchmark evolved with the development of modern financial markets and the rise of professional investment management. As the investment landscape grew more complex, particularly with the proliferation of mutual funds and institutional portfolios, the need to evaluate how well managers were performing relative to their stated objectives or a common market standard became paramount. Early iterations of portfolio evaluation focused primarily on absolute returns. However, the understanding that returns are often achieved by taking on certain levels of risk led to more sophisticated measures. The widespread adoption of index funds and passive investing strategies further underscored the importance of relative risk, as these funds explicitly aim to track a benchmark's performance, making their deviation from that benchmark a key measure of their effectiveness. The Securities and Exchange Commission (SEC) has long emphasized the importance of clear risk disclosures for investors, underscoring the necessity for transparency in understanding investment risks, whether absolute or relative.¹⁰,⁹,⁸

Key Takeaways

Relative risk measures an investment's risk in comparison to a benchmark or another investment.
It is particularly relevant for actively managed funds aiming to outperform an index or for passive funds aiming to track one.
A higher relative risk often indicates a greater potential for both outperformance and underperformance compared to the benchmark.
Understanding relative risk aids in assessing a portfolio's deviation from its target and its exposure to specific market movements.
It is a key consideration in asset allocation and manager selection.

Formula and Calculation

Relative risk is most commonly quantified through measures like tracking error (also known as active risk or active deviation). Tracking error measures the standard deviation of the difference between the returns of a portfolio and the returns of its benchmark.

The formula for tracking error ((TE)) is:

TE = \sqrt{\frac{\sum_{i=1}^{n} (R_{pi} - R_{bi})^2}{n-1}}

Where:

(R_{pi}) = Return of the portfolio in period (i)
(R_{bi}) = Return of the benchmark in period (i)
(n) = Number of periods

A related concept, often derived from tracking error, is the information ratio, which assesses the active return on investment per unit of active risk. It gives context to the tracking error by relating it to the excess return achieved.

Interpreting Relative Risk

Interpreting relative risk involves understanding the context of the investment's objective. For an actively managed investment portfolio, a significant relative risk (high tracking error) indicates that the portfolio manager is making substantial bets that deviate from the benchmark. This can lead to either significant outperformance or significant underperformance. Conversely, a low relative risk suggests that the portfolio's returns closely mirror those of the benchmark, which is desirable for passive funds but might indicate a lack of active management for an actively managed fund.

Investors evaluate relative risk in conjunction with their risk tolerance and investment goals. For instance, an investor seeking to closely replicate market returns might prefer a fund with very low relative risk, signifying tight tracking to its benchmark. Those seeking aggressive growth might accept higher relative risk in hopes of greater returns.

Hypothetical Example

Consider two hypothetical mutual funds, Fund A and Fund B, both aiming to outperform the S&P 500 index over a year.

Fund A:

Monthly Returns: +2%, -1%, +3%, +1%, +2%, -0.5%, +1.5%, +2.5%, -1.2%, +1%, +3%, +0.8%
Average Return: 1.17%

S&P 500 Benchmark:

Monthly Returns: +1.8%, -0.8%, +2.8%, +1%, +2%, -0.4%, +1.4%, +2.4%, -1.1%, +0.9%, +2.9%, +0.7%
Average Return: 1.13%

Let's calculate the difference in returns ((R_{pi} - R_{bi})) for each month:

Month 1: 2% - 1.8% = 0.2%
Month 2: -1% - (-0.8%) = -0.2%
...and so on.

After calculating the differences for each month and squaring them, summing them, and dividing by (n-1), we would take the square root to find the tracking error.

Suppose Fund A's calculated tracking error is 0.5%. This indicates that Fund A's monthly returns deviate from the S&P 500 by an average of 0.5%. If Fund B's tracking error for the same period was 2.0%, Fund B exhibits much higher relative risk than Fund A. An investor interested in broad market exposure with minimal surprises would likely prefer Fund A, while an investor seeking potentially higher return on investment from active bets might tolerate Fund B's higher volatility relative to the benchmark.

Practical Applications

Relative risk is a foundational concept in various financial applications:

Active vs. Passive Management: For actively managed funds, relative risk is a key metric. Fund managers whose goal is to outperform a market benchmark must take on relative risk. The deviation from the index, known as tracking error, is the active risk they undertake to generate alpha. For passive funds, the objective is to minimize relative risk to ensure their returns closely mirror the underlying index.⁷,⁶
Performance Attribution: Analysts use relative risk metrics to attribute performance. By dissecting the sources of a portfolio's deviations from its benchmark, they can determine whether excess returns (or losses) are due to specific asset selection, sector allocation, or other active decisions.
Risk Budgeting: Large institutional investors and wealth managers often set a "risk budget" for their portfolios, allocating a certain amount of allowable relative risk to different segments or managers. This helps ensure overall diversification and prevents any single active bet from disproportionately impacting the total portfolio.
Hedge Funds: Many hedge fund strategies explicitly target relative value opportunities, betting on the divergence or convergence of related securities. Their risk exposure is inherently relative to the relationship between those securities.
Regulatory Compliance and Disclosure: Regulators, like the SEC, require investment vehicles to clearly disclose the risks associated with their investments. While not always explicitly termed "relative risk," the disclosures often highlight how a fund's investment strategy might lead to performance that differs significantly from a broad market or peer group.⁵,⁴

Limitations and Criticisms

While valuable, relative risk measures have limitations:

Benchmark Selection Bias: The interpretation of relative risk is highly dependent on the chosen benchmark. An inappropriate or poorly constructed benchmark can lead to misleading conclusions about a portfolio's risk profile. For example, comparing a small-cap equity fund to a large-cap index would naturally show high relative risk, regardless of the manager's skill. The Bogleheads community, for example, emphasizes the importance of selecting appropriate, low-cost index funds for benchmarking to maintain a clear investment philosophy.³,²
Focus on Deviation, Not Magnitude: Relative risk, particularly tracking error, focuses on the deviation from a benchmark but doesn't inherently tell you about the magnitude of potential losses. A portfolio could have low relative risk but still suffer significant market risk if the entire market declines.
Historical Data Dependence: Like many risk metrics, relative risk calculations rely on historical data, which may not be indicative of future outcomes. Market conditions, fund strategies, and the underlying assets' volatility can change.
May Encourage "Closet Indexing": An overemphasis on minimizing relative risk, especially in actively managed funds, can incentivize "closet indexing," where managers largely mimic the benchmark to avoid significant tracking error, yet still charge active management fees. This reduces the potential for outperformance while maintaining higher costs than a true index fund. This behavior dilutes the purpose of active management and can lead to less optimal outcomes for investors seeking true alpha.¹

Relative Risk vs. Absolute Risk

Relative risk and absolute risk represent distinct approaches to measuring investment risk, often leading to confusion.

Feature	Relative Risk	Absolute Risk
Definition	Risk compared to a benchmark (e.g., index)	Risk in isolation; total variability of returns
Focus	Deviation from a standard; active management bets	Potential for losses or variability of returns
Key Metrics	Tracking Error, Beta, Information Ratio	Standard Deviation, Value at Risk (VaR), Sharpe Ratio
Primary Use	Evaluating active management, benchmarking	Assessing overall portfolio volatility, downside exposure
Goal	Outperform or closely track a benchmark	Achieve target returns or minimize overall portfolio variability, irrespective of a benchmark

While absolute risk measures the total volatility and potential downside of an investment on its own, relative risk assesses how an investment behaves compared to another. For example, a portfolio might have a high absolute risk (high standard deviation) due to volatile assets but a low relative risk (low tracking error) if it closely mirrors a volatile benchmark. Conversely, a portfolio could have moderate absolute risk but high relative risk if it significantly deviates from a stable benchmark. Investors consider both to get a comprehensive view of their systematic risk and unsystematic risk exposures.

FAQs

What is a good relative risk?

A "good" relative risk depends entirely on the investment objective. For a passive index fund, a low relative risk (e.g., low tracking error) is desirable, indicating it closely mirrors its benchmark. For an actively managed fund, a moderate to high relative risk might be acceptable or even necessary if the manager is taking calculated bets to achieve significant outperformance. It's about aligning the risk with the fund's stated strategy and the investor's expectations.

How does relative risk impact fund selection?

Relative risk significantly impacts fund selection, especially between active and passive strategies. Investors looking for broad market exposure and low fees might prioritize passive funds with minimal relative risk (tight tracking). Those seeking a manager's expertise to potentially beat the market would consider active funds, evaluating their relative risk to determine if the manager's "active bets" are appropriate for their risk tolerance and if the potential for outperformance justifies the higher relative risk and fees.

Is Beta a measure of relative risk?

Yes, Beta is a common measure of relative risk. It quantifies an investment's volatility in relation to the overall market. A beta of 1 suggests the investment's price moves with the market, a beta greater than 1 means it's more volatile than the market, and a beta less than 1 indicates less volatility. It is a specific type of relative risk because it measures an asset's systemic risk compared to a broad market index.

How is relative risk different from the Sharpe Ratio?

Relative risk, such as tracking error, focuses on how much an investment deviates from its benchmark. The Sharpe Ratio, on the other hand, is an absolute risk-adjusted return measure. It calculates the excess return per unit of total risk (standard deviation) taken. While relative risk tells you about tracking, the Sharpe Ratio tells you about the efficiency of returns generated per unit of total risk, irrespective of a specific benchmark.