Acquired variance drag: Meaning, Criticisms & Real-World Uses

What Is Acquired Variance Drag?

Acquired Variance Drag, often referred to simply as volatility drag or variance drain, is a concept within Portfolio Theory that quantifies the reduction in compounded returns caused by the volatility of an investment's returns over time. It highlights how large fluctuations, both positive and negative, can lead to a lower actual growth rate for a portfolio, even if the average (arithmetic) return appears favorable. This drag is a crucial consideration for investors aiming for long-term wealth accumulation, as it directly impacts the power of compounding ¹⁸, ¹⁹.

History and Origin

While the specific term "Acquired Variance Drag" may have evolved over time, the underlying mathematical concept has been recognized in finance for decades. The effect of volatility on compounded returns is inherently tied to the difference between the arithmetic mean and the geometric mean of returns. The geometric mean, which accounts for compounding, will always be less than or equal to the arithmetic mean, with the difference growing larger as volatility increases¹⁷. This principle has been discussed in academic and investment circles, emphasizing that wealth accumulation is a compounding process that can be hindered by significant price swings¹⁶. Financial professionals often use the geometric mean as a more accurate measure of returns for investment portfolios precisely because it accounts for this compounding effect.

Key Takeaways

Acquired Variance Drag represents the negative impact of return volatility on an investment's actual compounded growth.
It highlights the divergence between arithmetic mean returns and geometric mean returns, with the geometric mean being the true measure of compounded growth.
Higher volatility leads to a greater Acquired Variance Drag, meaning a larger difference between the simple average return and the actual wealth accumulation.
This drag implies that even with a strong average return, significant drawdowns require disproportionately larger gains to recover, hindering long-term portfolio growth.
Understanding Acquired Variance Drag is crucial for long-term investors in managing risk and setting realistic return expectations.

Formula and Calculation

Acquired Variance Drag can be approximated by a straightforward formula when dealing with small returns over many periods. It quantifies the difference between the arithmetic average return and the geometric average return.

The relationship between the geometric mean ((R_g)), arithmetic mean ((R_a)), and variance of returns ((\sigma^2)) can be approximated by:

R_g \approx R_a - \frac{\sigma^2}{2}

Where:

(R_g) = Geometric Mean Return (actual compounded return)
(R_a) = Arithmetic Mean Return (simple average return)
(\sigma^2) = Variance of Returns

The "Acquired Variance Drag" itself is approximately equal to (\frac{\sigma^2}{2}). This formula illustrates that as the variance (a measure of volatility) of returns increases, the difference between the arithmetic and geometric means also increases, leading to a greater drag on compounded returns¹⁵.

Interpreting the Acquired Variance Drag

Interpreting Acquired Variance Drag involves understanding its implications for long-term investment performance. A higher Acquired Variance Drag indicates that the portfolio's actual compounded growth rate is significantly lower than its average periodic return. This means that large fluctuations in returns, even if they average out to a positive number, effectively "drag down" the overall wealth accumulation.

For instance, an investment with an average annual return of 10% but high volatility might experience a substantial Acquired Variance Drag, resulting in an actual compounded return of only 7% or 8%. This difference is vital for investors because wealth is a compounding process; current period returns are based on the previous period's ending value¹⁴. Therefore, periods of significant losses require disproportionately larger gains to recover the initial capital, eroding the benefits of positive returns and dampening the effect of compound interest ¹², ¹³. Investors should focus on the geometric mean as a more realistic representation of their portfolio's long-term growth, rather than solely relying on the arithmetic mean¹¹.

Hypothetical Example

Consider an investment of $100,000 over two years.

Scenario 1: Low Volatility

Year 1: +10% return. Portfolio value: $100,000 * (1 + 0.10) = $110,000
Year 2: +10% return. Portfolio value: $110,000 * (1 + 0.10) = $121,000

In this scenario:

Arithmetic Mean Return = (10% + 10%) / 2 = 10%
Geometric Mean Return = (\sqrt{(1+0.10) * (1+0.10)} - 1 = \sqrt{1.21} - 1 = 1.1 - 1 = 10%)
Acquired Variance Drag = 10% - 10% = 0%

Scenario 2: High Volatility

Year 1: +50% return. Portfolio value: $100,000 * (1 + 0.50) = $150,000
Year 2: -20% return. Portfolio value: $150,000 * (1 - 0.20) = $120,000

In this scenario:

Arithmetic Mean Return = (50% + (-20%)) / 2 = 15%
Geometric Mean Return = (\sqrt{(1+0.50) * (1-0.20)} - 1 = \sqrt{1.50 * 0.80} - 1 = \sqrt{1.20} - 1 \approx 0.0954 \text{ or } 9.54%)
Acquired Variance Drag = 15% - 9.54% = 5.46%

Even though the arithmetic average return in Scenario 2 (15%) is higher than in Scenario 1 (10%), the Acquired Variance Drag in Scenario 2 means the actual ending wealth ($120,000) is less than what a consistent 10% return would have yielded ($121,000). This demonstrates how volatility, even with a strong average, can erode overall wealth. This effect is often observed in asset classes that experience significant price fluctuations.

Practical Applications

Acquired Variance Drag has several practical applications in financial analysis and investment planning:

Performance Evaluation: It provides a more accurate lens for evaluating investment performance over multiple periods. Investors and analysts often use the geometric mean return, which inherently accounts for Acquired Variance Drag, when assessing long-term portfolio growth or comparing different investment strategies ¹⁰.
Risk Management: Understanding Acquired Variance Drag underscores the importance of managing portfolio volatility. Strategies aimed at reducing extreme price swings, such as diversification and asset allocation, can mitigate this drag and lead to more consistent long-term returns⁷, ⁸, ⁹. Reuters has noted that market volatility can increase demand for products designed to buffer against such swings, like defined outcome funds⁶.
Retirement Planning: For long-term goals like retirement planning, minimizing Acquired Variance Drag can significantly impact the final accumulated wealth. A portfolio that experiences less volatility, even if its arithmetic average return is slightly lower, may ultimately outperform a more volatile one over extended periods due to the power of compounding⁵.
Expected Return Forecasting: While the arithmetic mean is often used for single-period expected return forecasts, the geometric mean is more appropriate when considering multi-period returns and the impact of volatility. This distinction is crucial for setting realistic long-term financial goals.

Limitations and Criticisms

While Acquired Variance Drag is a mathematically sound concept, its practical application and interpretation come with certain limitations and considerations:

Focus on Historical Data: The calculation of Acquired Variance Drag relies on historical return data. Future volatility may differ significantly from past volatility, meaning that historical drag may not accurately predict future drag. Investment professionals always emphasize that past performance is not indicative of future results.
Approximation for Small Returns: The simplified formula for Acquired Variance Drag ((\frac{\sigma^2}{2})) is an approximation that works best for small returns and when volatility is not excessively high. For highly volatile assets or very large returns, the approximation may become less accurate, and direct calculation of the geometric mean is more precise.
Not a Direct Loss: It's important to clarify that Acquired Variance Drag is not a direct financial loss in the way a trading loss is. Instead, it represents the opportunity cost of volatility—the difference between the theoretical growth if returns were perfectly smooth (arithmetic mean) and the actual growth experienced due to fluctuations (geometric mean).
Volatility and Opportunity: Some argue that while volatility creates drag, it also creates opportunities for investors who can manage it effectively. For instance, dollar-cost averaging can benefit from market downturns, and strategic rebalancing can capitalize on market swings. ⁴However, panic selling during periods of high volatility can lock in losses and exacerbate the impact of the drag.
³* Simplistic View of Risk: While volatility is often equated with risk, it is only one dimension of investment risk. Other factors, such as liquidity risk, credit risk, and inflation risk, are not captured by Acquired Variance Drag alone.

Acquired Variance Drag vs. Skewness

Acquired Variance Drag specifically addresses the reduction in compounded returns due to the magnitude of price fluctuations, as measured by variance. It highlights that the wider the swings in returns, the greater the gap between the simple average return and the actual growth rate.

In contrast, skewness is a statistical measure that describes the asymmetry of the probability distribution of returns. A positively skewed distribution indicates that there are more frequent small losses and a few large gains, while a negatively skewed distribution suggests more frequent small gains and a few large losses. While Acquired Variance Drag focuses on the "cost" of volatility itself, skewness describes the shape of the return distribution. An investment with significant negative skewness, even if it has moderate volatility, could present different risks (e.g., infrequent but severe losses) that are not directly captured by Acquired Variance Drag. Both concepts are part of a broader understanding of return distribution and risk beyond just average returns.

FAQs

What causes Acquired Variance Drag?

Acquired Variance Drag is caused by the mathematical reality that losses have a greater impact on a portfolio's value than equivalent percentage gains. For example, a 50% loss requires a 100% gain to break even. When returns fluctuate significantly, this asymmetry means that large downward movements are more damaging to compounded growth than large upward movements are beneficial, even if the arithmetic average of the returns is high.
²

How can investors mitigate Acquired Variance Drag?

Investors can mitigate Acquired Variance Drag primarily by reducing the volatility of their portfolio returns. Strategies include diversification across asset classes, prudent asset allocation, and considering lower-volatility investments if appropriate for their risk tolerance. While some volatility is inherent in investing, managing extreme swings can help preserve long-term compounded growth.

Is Acquired Variance Drag the same as risk?

No, Acquired Variance Drag is not the same as risk, although it is closely related to market risk, particularly volatility. Volatility is a measure of the dispersion of returns, which is often used as a proxy for risk. Acquired Variance Drag is the consequence of that volatility on compounded returns, illustrating the extent to which return fluctuations reduce actual wealth accumulation over time. It's a specific aspect of how risk manifests in performance.

Why is the geometric mean more relevant for long-term investors?

The geometric mean is more relevant for long-term investors because it accurately reflects the compounded rate of return, considering the effect of reinvesting earnings and the impact of volatility. Unlike the arithmetic mean, which is a simple average and doesn't account for compounding, the geometric mean shows the actual average annual rate at which an investment has grown over multiple periods, providing a more realistic picture of wealth accumulation.¹