Returns variability

Returns variability, often referred to as a measure of risk, quantifies the extent to which an investment's returns fluctuate over a period. Within the realm of portfolio theory, understanding returns variability is crucial for investors and financial professionals alike, as it provides insight into the potential deviation of actual returns from expected outcomes. It is a key component in assessing the stability and predictability of an investment portfolio. Returns variability is intrinsically linked to the concept of uncertainty; higher variability indicates a wider range of possible outcomes, both positive and negative, for an investment.

History and Origin

The systematic study of returns variability as a quantifiable measure of risk gained prominence with the advent of Modern Portfolio Theory (MPT). Developed by economist Harry Markowitz in his seminal 1952 paper, "Portfolio Selection," MPT provided a mathematical framework for assembling portfolios to maximize expected return for a given level of risk, or minimize risk for a given expected return. Markowitz's work revolutionized finance by shifting focus from analyzing individual assets in isolation to considering how assets behave together within a portfolio. His insights highlighted that an asset's risk and return should be assessed not solely on its own, but on its contribution to the overall portfolio's risk and return characteristics.⁶,⁵ This framework underscored the importance of diversification and mathematically defined risk in terms of the variability of returns, most commonly using standard deviation. A publication from the Federal Reserve Bank of San Francisco notes that Markowitz's work was foundational in establishing how investors can make trade-offs between risk and return.⁴

Key Takeaways

• Returns variability measures how much an investment's returns have fluctuated around its average return over time.
• It is a primary indicator of an investment's risk; higher variability typically implies greater risk.
• Standard deviation is the most common statistical measure used to quantify returns variability.
• Understanding returns variability is vital for asset allocation and constructing portfolios that align with an investor's risk tolerance.
• While useful, returns variability has limitations, particularly when return distributions are not normal or during periods of extreme market events.

Formula and Calculation

The most widely used measure for returns variability is the standard deviation of historical returns. Standard deviation quantifies the dispersion of a set of data points around their mean. For a series of historical returns, it indicates how much the actual returns deviated from the average expected return.

The formula for the standard deviation of historical returns is:

Where:

• (\sigma) = Standard deviation (returns variability)
• (R_i) = Individual return in the dataset
• (\bar{R}) = Mean (average) return of the dataset
• (N) = Number of observations (returns) in the dataset
• (\sum) = Summation symbol

This calculation provides a single number that represents the typical deviation from the mean, offering a concise measure of the investment's historical returns variability.

Interpreting Returns Variability

Interpreting returns variability involves understanding what the calculated number signifies in the context of investment analysis. A higher numerical value for returns variability, such as a higher standard deviation, indicates that an investment's historical returns have been more spread out from its average, implying greater potential fluctuations and, consequently, higher risk. Conversely, a lower value suggests that returns have been more consistent and closer to the average, indicating lower risk.

For example, an investment with an average annual return of 8% and a standard deviation of 2% implies that its returns have typically fallen between 6% and 10% (8% ± 2%). An investment with the same 8% average return but a 10% standard deviation indicates much wider fluctuations, with returns typically ranging from -2% to 18%. This broader range suggests higher returns variability and therefore higher risk. Investors use this information to compare different investment opportunities and align their choices with their individual risk tolerance. Metrics like the Sharpe Ratio also incorporate returns variability to assess risk-adjusted performance.

Hypothetical Example

Consider two hypothetical portfolios, Portfolio A and Portfolio B, over a five-year period:

First, calculate the average return ((\bar{R})) for each portfolio:

• Portfolio A: ((10 + 8 + 9 + 11 + 12) / 5 = 50 / 5 = 10%)
• Portfolio B: ((25 - 5 + 15 - 10 + 30) / 5 = 55 / 5 = 11%)

Next, calculate the returns variability (standard deviation) for each:

• Portfolio A:
  ((10-10)^2 + (8-10)^2 + (9-10)^2 + (11-10)^2 + (12-10)^2)
  (= 0^2 + (-2)^2 + (-1)^2 + 1^2 + 2^2)
  (= 0 + 4 + 1 + 1 + 4 = 10)
  (\sigma_A = \sqrt{10 / (5-1)} = \sqrt{10 / 4} = \sqrt{2.5} \approx 1.58%)

• Portfolio B:
  ((25-11)^2 + (-5-11)^2 + (15-11)^2 + (-10-11)^2 + (30-11)^2)
  (= 14^2 + (-16)^2 + 4^2 + (-21)^2 + 19^2)
  (= 196 + 256 + 16 + 441 + 361 = 1270)
  (\sigma_B = \sqrt{1270 / (5-1)} = \sqrt{1270 / 4} = \sqrt{317.5} \approx 17.82%)

Despite Portfolio B having a slightly higher average return (11% vs. 10%), its returns variability (17.82%) is significantly higher than Portfolio A's (1.58%). This example illustrates that Portfolio A provided more consistent returns, while Portfolio B experienced substantial swings, including negative returns in some years. This type of analysis helps investors gauge the risk inherent in different investment portfolio options, especially during volatile periods such as the dot-com bubble burst around 2000, which saw significant market downturns and heightened variability.,³

Practical Applications

Returns variability is a fundamental metric with numerous practical applications in finance and investing:

• Portfolio Construction and Management: Investors use returns variability to build investment portfolio that align with their risk tolerance. By combining assets with different levels of returns variability and correlations, they can optimize their asset allocation to achieve a desired balance between risk and expected return.
• Performance Evaluation: Returns variability is critical for evaluating the risk-adjusted performance of investment managers and funds. For instance, the Sharpe Ratio measures the excess return per unit of standard deviation, allowing for a standardized comparison of different investments.
• Risk Management: Financial institutions and regulatory bodies employ returns variability to assess and manage exposure to market risk. This helps in setting risk limits, calculating capital requirements, and stress-testing portfolios against adverse market scenarios.
• Investor Education and Disclosure: Financial advisors are obligated to explain investment risks to clients. Returns variability is a key concept used to illustrate the potential ups and downs of an investment, helping clients understand the inherent uncertainties. The U.S. Securities and Exchange Commission (SEC) provides resources to help investors understand common investment risks.
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Limitations and Criticisms

While returns variability, particularly as measured by standard deviation, is widely used, it has several limitations and criticisms:

• Assumption of Normal Distribution: Standard deviation assumes that returns are normally distributed, meaning they follow a symmetrical, bell-shaped curve. However, financial market returns often exhibit "fat tails," implying more frequent extreme positive or negative events than a normal distribution would predict. ¹This can lead to an underestimation of true tail risk, where large, unexpected losses can occur.
• Treats Upside and Downside Equally: Returns variability treats both positive and negative deviations from the mean as equally risky. Investors, however, are typically more concerned with downside risk (losses) than upside variability (unexpected gains). Metrics like downside deviation or Value at Risk (VaR) attempt to address this distinction.
• Historical Data Reliance: The calculation of returns variability relies on historical data. Past performance is not indicative of future results, and market conditions can change, making historical variability an imperfect predictor of future fluctuations. Sudden shifts in inflation, interest rates, or geopolitical events can drastically alter future returns variability.
• Does Not Account for Causes of Variability: Returns variability indicates the magnitude of fluctuations but does not explain why they occurred. For a deeper understanding of risk, one must analyze the underlying factors, such as systematic risk (market-wide risks) and unsystematic risk (company-specific risks).

Returns Variability vs. Volatility

The terms returns variability and volatility are often used interchangeably in finance, and for practical purposes, they refer to the same concept: the degree of dispersion of returns around an average. Both quantify the uncertainty or risk associated with an investment's performance. Typically, when financial professionals discuss volatility, they are referring to the standard deviation of returns. While returns variability describes the general characteristic of fluctuating returns, volatility is the specific, quantifiable measure (most often standard deviation) used to express that variability. There is no significant conceptual difference between the two terms in common financial usage; volatility is essentially the numerical representation of returns variability.

FAQs

What causes returns variability?

Returns variability is caused by a multitude of factors, including macroeconomic events (like changes in interest rates or inflation), company-specific news (e.g., earnings reports, product launches), geopolitical events, investor sentiment, and overall market risk.

Is higher returns variability always bad?

Not necessarily. While higher returns variability implies higher risk, it is also often associated with the potential for higher expected return. Investors seeking aggressive growth might accept higher variability in pursuit of greater returns. The key is to ensure that the level of returns variability aligns with an individual's risk tolerance and investment objectives.

How can I reduce returns variability in my portfolio?

The primary method for reducing returns variability in an investment portfolio is through effective diversification. By combining assets whose returns do not move perfectly in sync (i.e., they have low or negative correlations), the overall variability of the portfolio can be lower than the sum of its individual components. Asset allocation across different asset classes (stocks, bonds, real estate) and geographies is a common strategy.

Is returns variability the same as Beta or Alpha?

No. While related to risk, returns variability (measured by standard deviation or volatility) measures the total historical fluctuations of an asset or portfolio. Beta specifically measures an asset's or portfolio's sensitivity to overall market movements (systematic risk). Alpha measures the excess return of an investment relative to the return of a benchmark index, after adjusting for Beta and other factors, representing the value added by a manager.