Economic return deviation

What Is Economic Return Deviation?

Economic Return Deviation refers to the extent to which an investment's actual return diverges from its anticipated or average return over a specific period. It is a fundamental concept within Portfolio Theory, providing insights into the unpredictability and Volatility inherent in financial markets. Understanding economic return deviation is crucial for investors and Fund Managers seeking to measure and manage risk within their portfolios. This deviation is often quantified using statistical measures that highlight how scattered or concentrated returns are around a central point, such as an Expected Return.

History and Origin

The foundational principles behind understanding return deviation are deeply rooted in the development of modern financial economics. While the specific phrase "economic return deviation" might be a descriptive term rather than a formal, named metric with a singular inventor, the concept of quantifying the variability of returns gained prominence with the advent of Modern Portfolio Theory (MPT). Harry Markowitz, often considered the "father of modern portfolio theory," introduced the concept of analyzing investment portfolios in terms of both risk and return. His seminal 1952 paper, "Portfolio Selection," published in The Journal of Finance, laid the groundwork by demonstrating how diversification could reduce portfolio risk without sacrificing expected returns, a breakthrough that recognized the importance of how individual asset returns move relative to each other. Modern Portfolio Theory highlighted that investors should not view individual assets in isolation but rather consider their contribution to the overall portfolio's risk and return profile.¹⁵, ¹⁶

Key Takeaways

• Economic Return Deviation quantifies how much an actual investment return differs from its expected or average return.
• It is a critical measure in Investment Performance analysis, providing insight into investment risk.
• The primary statistical measure used to calculate economic return deviation is Standard Deviation of returns.
• Higher economic return deviation generally indicates greater Market Risk and potential for significant fluctuations in returns.
• Investors utilize this metric to assess consistency and align portfolio choices with their Risk Tolerance.

Formula and Calculation

The most common method for calculating economic return deviation, particularly as a measure of historical volatility, involves the Standard Deviation of returns. Standard deviation quantifies the dispersion of a set of data points around their mean (average). For investment returns, it shows how much an asset's returns have deviated from its average return over a given period.¹⁴

The formula for the standard deviation of historical returns is:

Where:

• (\sigma) = Standard Deviation (Economic Return Deviation)
• (R_i) = The individual return for period i
• (\bar{R}) = The average (mean) return for the entire period
• (n) = The number of periods
• (\sum) = Summation symbol

This formula first calculates the difference between each return and the mean return, squares that difference, sums all the squared differences, divides by (n-1) (for sample standard deviation), and then takes the square root.¹², ¹³

Interpreting the Economic Return Deviation

Interpreting economic return deviation is essential for understanding the risk associated with an investment. A higher economic return deviation indicates that the investment's actual returns have historically fluctuated widely around its average return, implying higher Volatility and risk. Conversely, a lower deviation suggests that returns have been more consistent and closer to the average.¹¹

For example, an investment with an average annual return of 8% and an economic return deviation (standard deviation) of 20% signifies that, historically, its annual returns have typically ranged between -12% and 28% (8% ± 20%) approximately 68% of the time, assuming a normal distribution. In contrast, an investment with an 8% average return and a 5% deviation would suggest much more stable returns, generally falling between 3% and 13%. This insight helps investors gauge the potential swings in value and determine if an investment's risk profile aligns with their Risk Tolerance and Asset Allocation strategy.

Hypothetical Example

Consider two hypothetical portfolios, Portfolio A and Portfolio B, over five years:

First, calculate the average return for each portfolio:

Average Return for Portfolio A ((\bar{R}_A)): ((10 - 5 + 20 + 2 + 13) / 5 = 40 / 5 = 8%)
Average Return for Portfolio B ((\bar{R}_B)): ((5 + 4 + 6 + 5 + 5) / 5 = 25 / 5 = 5%)

Next, calculate the squared deviations from the mean for each year and sum them:

Portfolio A:

• ((10 - 8)^{2 = 2}2 = 4)
• ((-5 - 8)^{2 = (-13)}2 = 169)
• ((20 - 8)^{2 = 12}2 = 144)
• ((2 - 8)^{2 = (-6)}2 = 36)
• ((13 - 8)^{2 = 5}2 = 25)
  Sum of Squared Deviations for A = (4 + 169 + 144 + 36 + 25 = 378)

Portfolio B:

• ((5 - 5)^{2 = 0}2 = 0)
• ((4 - 5)^{2 = (-1)}2 = 1)
• ((6 - 5)^{2 = 1}2 = 1)
• ((5 - 5)^{2 = 0}2 = 0)
• ((5 - 5)^{2 = 0}2 = 0)
  Sum of Squared Deviations for B = (0 + 1 + 1 + 0 + 0 = 2)

Now, calculate the Economic Return Deviation (Standard Deviation) for each:

• Portfolio A: (\sigma_A = \sqrt{378 / (5-1)} = \sqrt{378 / 4} = \sqrt{94.5} \approx 9.72%)
• Portfolio B: (\sigma_B = \sqrt{2 / (5-1)} = \sqrt{2 / 4} = \sqrt{0.5} \approx 0.71%)

Despite Portfolio A having a higher average return (8% vs. 5%), its economic return deviation of approximately 9.72% indicates significantly higher volatility compared to Portfolio B's 0.71%. This example highlights that higher returns often come with higher economic return deviation, reinforcing the risk-return trade-off in Portfolio Management.

Practical Applications

Economic return deviation is a cornerstone metric in various aspects of finance and investing. In Portfolio Management, it helps evaluate and construct portfolios that align with an investor's Risk Tolerance. Investors use it to assess the Volatility of individual securities or an entire portfolio. For instance, a highly volatile stock will exhibit a high economic return deviation, indicating larger price swings.

Fund Managers often rely on this metric during Security Analysis to compare different investment opportunities. It forms a critical component of Risk-Adjusted Return calculations, such as the Sharpe Ratio, which evaluates the return earned per unit of risk taken. Furthermore, regulatory bodies, including the Securities and Exchange Commission (SEC), emphasize transparent and fair disclosure of investment performance, including measures of risk like volatility. The SEC Marketing Rule, for example, sets guidelines for how investment advisers can advertise performance, requiring certain disclosures that implicitly relate to the consistency and deviation of returns.
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For individual investors, understanding economic return deviation helps in practical Diversification strategies, as combining assets with low correlation can reduce the overall portfolio's deviation. During periods of elevated Market Volatility, being aware of the typical economic return deviation of one's portfolio can help manage expectations and avoid reactive decisions.
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Limitations and Criticisms

While economic return deviation, particularly as measured by standard deviation, is widely used, it has certain limitations. A primary criticism is that it treats all deviations from the mean equally, whether they are positive or negative. In finance, downside deviation (when returns are below the mean) is often perceived as "risk" in a more meaningful way than upside deviation. Investors are generally more concerned about losses than unexpected gains.

Another limitation is its reliance on historical data. Economic return deviation is typically calculated using past returns, which may not be indicative of future performance or Volatility. Market conditions can change rapidly, rendering historical deviations less relevant. For instance, unforeseen economic shocks or systemic events, like those often discussed in the Global Financial Stability Report published by the International Monetary Fund, can lead to deviations far beyond historical norms.
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Furthermore, the calculation assumes that returns are normally distributed, which is often not the case in real financial markets. Actual market returns frequently exhibit "fat tails" (more extreme positive and negative events than a normal distribution would predict) and skewness. This means that a standard deviation might underestimate the probability of extreme losses or gains. Despite these criticisms, economic return deviation remains a vital tool in Risk Management due to its simplicity and broad acceptance, especially when complemented by other risk metrics and qualitative analysis.

Economic Return Deviation vs. Tracking Error

Economic Return Deviation, when broadly referring to the variability of an investment's returns, is a general measure of risk. It quantifies how much an investment's actual performance has fluctuated around its own average return.

Tracking Error, on the other hand, is a more specific form of deviation. It measures the difference between the returns of an investment portfolio and its designated Benchmark (e.g., an index like the S&P 500). While economic return deviation focuses on the absolute volatility of an investment, tracking error focuses on its relative volatility compared to a specific benchmark.
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Here’s a breakdown of their differences:

A low economic return deviation indicates stable returns, while a low Tracking Error indicates that a portfolio closely mimics its benchmark. An actively managed fund might aim for a higher tracking error if its manager intends to significantly outperform the benchmark, accepting greater deviation from it.

#¹, ²# FAQs

What does a high economic return deviation mean for an investor?

A high economic return deviation means that an investment's returns have historically varied significantly from its average. For an investor, this implies higher Volatility and a greater potential for both larger gains and larger losses. It signals a higher level of Market Risk associated with the investment, which may not be suitable for those with a low Risk Tolerance.

Can economic return deviation be negative?

No, economic return deviation, as typically measured by Standard Deviation or variance, cannot be negative. Standard deviation is always a non-negative value because it represents the magnitude of dispersion. Even if returns are consistently negative, the deviation around their (negative) mean will still be a positive number.

How does diversification affect economic return deviation?

Diversification aims to reduce the overall economic return deviation of a portfolio. By combining different assets whose returns do not move in perfect lockstep, the extreme positive or negative performance of one asset can be offset by others. This strategy helps to smooth out portfolio returns, leading to a lower overall economic return deviation for the portfolio than the sum of its individual components.

Is economic return deviation the same as risk?

Economic return deviation is a quantifiable measure of risk, specifically the Volatility of returns. While it is a key component in assessing investment risk, risk encompasses broader concepts, including the potential for permanent loss of capital, liquidity risk, and systemic risk. Economic return deviation measures the variability around an Expected Return, serving as a statistical proxy for how risky an investment has been historically.