Relative volatility: Meaning, Criticisms & Real-World Uses

What Is Relative Volatility?

Relative volatility is a measure in financial analysis that quantifies an asset's price fluctuations in comparison to a benchmark index or another asset. Unlike absolute measures that simply report an asset's market volatility in isolation, relative volatility provides context by showing how an asset moves in relation to a broader market or a specific portfolio component. This comparative perspective is crucial for investors seeking to understand the proportionate risk an asset contributes within an investment portfolio. By examining relative volatility, investors can assess whether an asset is more or less volatile than its peer group or the overall market, aiding in strategic decisions for risk management and portfolio optimization.

History and Origin

The concept of measuring and understanding volatility in finance gained prominence with the advent of modern portfolio theory. Harry Markowitz's seminal 1952 paper, "Portfolio Selection," laid the groundwork for quantifying risk as the variability of returns, typically measured by standard deviation. This work was foundational to what became known as Modern Portfolio Theory, which emphasized the importance of considering how assets interact within a portfolio to manage overall risk.⁷ Building on Markowitz's insights, the Capital Asset Pricing Model (CAPM), developed independently by William Sharpe, Jack Treynor, John Lintner, and Jan Mossin in the early 1960s, further formalized the relationship between risk and expected return, introducing the concept of beta as a measure of an asset's systematic risk relative to the market.⁶ While these early models focused on absolute and systematic risk, the practical need to compare and contextualize an asset's price movements against others naturally led to the application of these principles in calculating relative volatility.

Key Takeaways

Relative volatility assesses an asset's price fluctuations in comparison to a benchmark or another security.
It provides a contextual understanding of an asset's risk profile within a diversified portfolio.
The beta coefficient is a widely used measure of relative volatility against the overall market.
Analyzing relative volatility helps in making informed decisions about asset allocation and risk budgeting.
It is particularly useful for portfolio managers evaluating the risk contributions of individual holdings.

Formula and Calculation

The most common measure of relative volatility is the beta coefficient. Beta quantifies the sensitivity of an asset's returns to the returns of a market benchmark index, such as the S&P 500.

The formula for beta ((\beta)) is:

\beta_i = \frac{\text{Cov}(R_i, R_m)}{\text{Var}(R_m)}

Where:

(\beta_i) = Beta of asset (i)
(\text{Cov}(R_i, R_m)) = The covariance between the returns of asset (i) and the returns of the market (m). Covariance measures how two variables move together.
(\text{Var}(R_m)) = The variance of the returns of the market (m). Variance is a measure of the market's overall volatility, typically represented by the square of its standard deviation.

A beta of 1 indicates that the asset's price moves in line with the market. A beta greater than 1 suggests the asset is more volatile than the market, while a beta less than 1 indicates it is less volatile. A negative beta implies the asset moves inversely to the market.

Interpreting the Relative Volatility

Interpreting relative volatility, particularly through the beta coefficient, is fundamental to understanding an asset's risk characteristics within a broader market context. A beta of 1.25, for example, suggests that for every 1% move in the market, the asset is expected to move 1.25% in the same direction. Conversely, an asset with a beta of 0.80 would typically move 0.80% for every 1% market movement. Investors use these values to gauge how sensitive their holdings are to systemic market shifts.

Relative volatility helps in assessing the potential impact of market-wide events on specific investments. Assets with high relative volatility (high beta) are often considered more aggressive and may experience larger gains in bull markets but also larger losses in bear markets. Assets with low relative volatility (low beta) are typically more defensive, offering more stability but potentially lower upside during market rallies. This insight is critical for constructing an investment portfolio that aligns with an investor's risk tolerance.

Hypothetical Example

Consider two stocks, Stock A and Stock B, and a market benchmark index over a year.

Scenario:

Market Index (M): Experienced a 10% increase with a standard deviation of 5%.
Stock A: Increased by 15% during the same period. Historical analysis shows its returns have a high positive correlation with the market.
Stock B: Increased by 8% during the same period. Historical analysis shows its returns have a lower positive correlation with the market.

Let's assume, through calculation of covariance and variance, we find:

Beta of Stock A: 1.3
Beta of Stock B: 0.7

Interpretation:
Stock A has a relative volatility of 1.3, indicating it is 30% more volatile than the market index. When the market moves up by 10%, Stock A is expected to move up by 13% (10% * 1.3). This suggests Stock A is a more aggressive investment.

Stock B has a relative volatility of 0.7, meaning it is 30% less volatile than the market index. If the market moves up by 10%, Stock B is expected to move up by 7% (10% * 0.7). Stock B would be considered a more defensive investment, exhibiting less sensitivity to broader market swings.

This hypothetical example illustrates how relative volatility helps investors understand the proportional risk and return characteristics of individual securities within a dynamic market environment, guiding decisions on asset allocation and portfolio structure.

Practical Applications

Relative volatility is a cornerstone of modern portfolio management and is widely applied across various aspects of finance. In investment portfolio construction, understanding an asset's relative volatility, particularly its beta to a market benchmark index, is crucial for achieving desired risk-return profiles. Portfolio managers use relative volatility to identify securities that can either amplify returns during market rallies (high beta) or provide stability during downturns (low beta). This insight facilitates effective diversification across different asset classes and industries.

Furthermore, relative volatility plays a significant role in risk budgeting, where the total risk of a portfolio is allocated among its various components. By assessing each asset's contribution to overall portfolio volatility relative to a chosen benchmark, managers can make informed decisions about position sizing and hedging strategies. Regulatory bodies also recognize the importance of market risk disclosures, with the U.S. Securities and Exchange Commission (SEC) requiring companies to provide both qualitative and quantitative information about market risk exposures in their financial statements.⁵,⁴ These disclosures often involve measures related to an instrument's sensitivity to market changes, which implicitly ties into concepts of relative volatility.

Limitations and Criticisms

While relative volatility, particularly as measured by beta, is a widely used metric in financial analysis, it comes with several limitations and criticisms. A primary concern is that beta is typically calculated using historical data, meaning past relationships between an asset and its benchmark may not necessarily predict future movements.³,² Market conditions, company-specific factors, and economic environments can change, causing an asset's true sensitivity to the market to evolve. Therefore, a historical beta might not always accurately reflect future relative volatility.

Another criticism revolves around the assumptions underlying models that heavily rely on relative volatility, such as the Capital Asset Pricing Model. These models often assume that correlations between assets remain constant and that investors are rational and solely focused on mean-variance optimization. In reality, correlation can change dramatically during periods of market stress, sometimes increasing when diversification benefits are most needed.¹ Furthermore, focusing solely on relative volatility might lead investors to overlook other important aspects of risk, such as liquidity risk or concentration risk within specific sectors or asset classes. The inherent simplifications can lead to an incomplete picture of an investment's true risk profile, potentially resulting in suboptimal risk management strategies.

Relative Volatility vs. Absolute Volatility

The distinction between relative volatility and absolute volatility lies in their respective frames of reference. Absolute volatility, often measured by standard deviation, quantifies the total price fluctuation of a single asset or portfolio independently. It provides an inherent measure of how much an asset's price has deviated from its average over a given period, without comparison to anything else. For example, if a stock has an absolute volatility of 20%, it means its price has historically moved 20% around its average return in annualized terms.

In contrast, relative volatility provides context by comparing an asset's movements to a benchmark index or another asset. The most common measure, beta, expresses how much an asset's price tends to move for a given movement in the overall market. An asset with a beta of 1.5 is considered to have higher relative volatility than the market, implying it is 50% more volatile than the benchmark. While absolute volatility tells you "how much" an asset moves, relative volatility tells you "how much it moves compared to something else." Both are essential for risk management, with absolute volatility providing a raw risk figure and relative volatility offering insights into an asset's systemic risk contribution and its behavior within a larger portfolio.

FAQs

How is relative volatility used in portfolio construction?

Relative volatility, often represented by beta, helps portfolio managers assess how individual assets contribute to the overall risk-adjusted return of an investment portfolio. Assets with high relative volatility can increase portfolio risk during market downturns but also enhance returns during rallies. Managers use this to balance their portfolios for optimal diversification.

Can relative volatility be negative?

Yes, relative volatility, particularly the beta coefficient, can be negative. A negative beta indicates that an asset's price tends to move in the opposite direction of the market benchmark index. Such assets can be valuable for diversification, as they may provide stability or even gains when the broader market is declining.

Is beta the only measure of relative volatility?

While beta is the most common and widely recognized measure of relative volatility against a market benchmark index, other relative measures can be used depending on the specific comparison. For example, one might compare the volatility of two individual stocks to each other, or a sector's volatility relative to its industry average. However, beta is uniquely tied to systematic risk within the framework of the Capital Asset Pricing Model.

Why is historical data a limitation for relative volatility?

Relying solely on historical data for relative volatility measures like beta can be a limitation because past performance is not indicative of future results. Market conditions, economic cycles, and company-specific factors are dynamic, meaning the relationship between an asset and its benchmark can change over time. Therefore, historical relative volatility may not always accurately predict future relative movements.