Adjusted average return: Meaning, Criticisms & Real-World Uses

What Is Adjusted Average Return?

Adjusted Average Return is a modified measure of investment performance that seeks to provide a more accurate or relevant representation of returns by accounting for specific factors. Unlike a simple average, which might present a misleading picture, an Adjusted Average Return integrates elements such as compounding effects, the impact of inflation, or various forms of risk. This concept falls under the broader financial category of investment performance measurement, crucial for evaluating how an investment has truly performed over time. The goal of calculating an Adjusted Average Return is to offer a more insightful perspective that aligns with real-world investment scenarios and objectives.

History and Origin

The evolution of methodologies for calculating and presenting investment returns stems from the need for transparency and comparability in financial markets. Early forms of performance measurement often relied on simple arithmetic averages, but as investment strategies became more complex and global, the limitations of these basic calculations became apparent. Concerns arose about how firms might selectively present performance data to attract clients, leading to a demand for standardized reporting.¹⁴

A significant step towards creating ethical and consistent performance reporting standards was the development of the Global Investment Performance Standards (GIPS). Initiated by the Association for Investment Management and Research (AIMR), a predecessor to the CFA Institute, the AIMR Performance Presentation Standards (AIMR-PPS) were first published in 1993.,¹³ Recognizing the need for a universally accepted approach, the CFA Institute (formerly AIMR) sponsored the Global Investment Performance Standards Committee in 1995 to develop global standards.¹² The first edition of the GIPS Standards was published in April 1999, aiming to ensure full disclosure and fair representation of investment performance worldwide.¹¹ These standards mandate specific calculation methodologies and disclosures to promote investor confidence and fair competition, highlighting the importance of measures that reflect true economic experience rather than just simple averages.¹⁰

Key Takeaways

Adjusted Average Return is a refined measure of investment performance that goes beyond a simple arithmetic average.
It incorporates factors like the effect of compounding, the eroding power of inflation, or the associated risks.
Common forms of Adjusted Average Return include geometric mean return (for compounding) and real return (for inflation).
These adjustments provide a more accurate and realistic view of an investment's historical performance, especially over multiple periods.
Regulatory bodies often require transparent reporting of adjusted returns to prevent misleading performance claims.

Formula and Calculation

An Adjusted Average Return isn't a single universal formula but rather a category of calculations that modify a raw average to account for specific financial phenomena. Two primary examples illustrate this concept: the Geometric Mean Return and the Real Return.

Geometric Mean Return (for Compounding):
The geometric mean return is particularly important for investments over multiple periods because it accounts for the effect of compounding, where returns in one period influence the base for subsequent periods.

R_g = \left[ (1 + R_1) \times (1 + R_2) \times \dots \times (1 + R_n) \right]^{\frac{1}{n}} - 1

Where:

(R_g) = Geometric Mean Return
(R_1, R_2, \dots, R_n) = Returns for each period (e.g., annual returns)
(n) = Number of periods

This formula accurately reflects the average rate at which an investment grows over time, assuming that intermediate cash flow is reinvested.

Real Return (for Inflation):
The real return adjusts the nominal return for the impact of inflation, providing a measure of how much an investment's purchasing power has increased.

R_{real} = \frac{(1 + R_{nominal})}{(1 + I)} - 1

Where:

(R_{real}) = Real Return
(R_{nominal}) = Nominal return (the stated return before adjusting for inflation)
(I) = Inflation rate for the period

This calculation helps investors understand the true increase in their wealth, accounting for changes in the cost of goods and services. Understanding these formulas is critical for proper valuation and financial analysis.

Interpreting the Adjusted Average Return

Interpreting an Adjusted Average Return requires understanding the specific adjustment made and its implications for investment analysis. For example, a geometric mean return provides the average per-period return that, if compounded over the entire period, would yield the same cumulative result as the actual, fluctuating returns. This makes it a more suitable metric for assessing long-term wealth accumulation than a simple arithmetic average, especially in portfolio management.⁹ A higher geometric mean indicates more consistent growth.

When considering a real return, a positive value indicates that the investment's value increased faster than the rate of inflation, meaning your purchasing power improved. A negative real return, conversely, means your investment lost purchasing power, even if the nominal return was positive. Comparing an Adjusted Average Return to a relevant benchmark that is also adjusted for similar factors (e.g., a real return benchmark) provides a clearer picture of outperformance or underperformance. These adjusted metrics are vital for making informed decisions, as they move beyond surface-level figures to reveal the true economic impact of investment decisions.

Hypothetical Example

Consider an investment in a stock over three years with the following annual nominal returns:

Year 1: +50%
Year 2: -20%
Year 3: +10%

1. Calculate the Arithmetic Mean Return:

\text{Arithmetic Mean Return} = \frac{(0.50) + (-0.20) + (0.10)}{3} = \frac{0.40}{3} \approx 0.1333 \text{ or } 13.33\%

A simple arithmetic mean suggests an average annual return of 13.33%. However, this doesn't account for the compounding effect or the sequence of returns.

2. Calculate the Geometric Mean Return (an Adjusted Average Return):

\text{Geometric Mean Return} = \left[ (1 + 0.50) \times (1 - 0.20) \times (1 + 0.10) \right]^{\frac{1}{3}} - 1 \\ = \left[ (1.50) \times (0.80) \times (1.10) \right]^{\frac{1}{3}} - 1 \\ = \left[ 1.32 \right]^{\frac{1}{3}} - 1 \\ \approx 1.0969 - 1 \\ \approx 0.0969 \text{ or } 9.69\%

Step-by-Step Walkthrough:

Initial Investment: Let's assume an initial investment of $1,000.
End of Year 1: $1,000 * (1 + 0.50) = $1,500
End of Year 2: $1,500 * (1 - 0.20) = $1,200
End of Year 3: $1,200 * (1 + 0.10) = $1,320

The cumulative growth over three years is $320 ($1,320 - $1,000), representing a 32% increase. The geometric mean return of 9.69% reflects this compounded growth:
$1,000 \times (1 + 0.0969)^3 \approx $1,000 \times 1.32 \approx $1,320$.

This example clearly shows that the geometric mean, as an Adjusted Average Return, provides a more accurate representation of the actual compounded growth experienced by the investment, particularly when returns exhibit volatility.

Practical Applications

Adjusted Average Return metrics are widely used across the financial industry for various purposes, from internal portfolio management to regulatory compliance and client reporting.

Performance Reporting and Marketing: Investment managers use adjusted average returns, particularly geometric returns, to present historical performance to clients and prospective investors. This provides a realistic view of how a portfolio has grown over time, accounting for compounding. Regulators like the U.S. Securities and Exchange Commission (SEC) emphasize the importance of fair and accurate performance presentations. The SEC's Marketing Rule, for instance, requires advisers to standardize certain parts of performance presentations and ensures that gross performance is accompanied by net performance to avoid misleading implications.⁸,⁷
Manager Selection and Due Diligence: Institutional investors and financial advisors rely on adjusted return figures to compare the performance of different fund managers or investment strategies. Metrics like the Sharpe Ratio, which adjusts return for risk, help in identifying managers who generate superior returns relative to the risk taken. Other risk-adjusted measures like Alpha and Beta also fall under this umbrella, helping assess a manager's skill and market sensitivity, respectively.
Financial Planning and Goal Setting: For individual investors and financial planners, understanding real returns (adjusted for inflation) is critical. It allows them to assess whether their investments are truly growing their purchasing power and if they are on track to meet long-term financial planning goals such as retirement or college savings. The Federal Reserve Bank of San Francisco, for example, conducts research on inflation and its impact on asset returns, highlighting the importance of considering inflation's effect on investment outcomes.⁶

Limitations and Criticisms

While Adjusted Average Returns offer a more nuanced view of investment performance, they are not without limitations. The specific method of adjustment chosen can significantly influence the resulting figure, and misapplication or misinterpretation can still lead to flawed conclusions.

One common criticism, particularly when comparing arithmetic mean return to geometric mean return, is that while the geometric mean accurately reflects the compounded growth of an initial sum over time, the arithmetic mean may be more appropriate for estimating the expected return of an investment in a single, future period, especially if returns are independently and identically distributed. However, for a multi-period investment, the arithmetic mean tends to overstate the actual rate of return because it does not account for the impact of volatility and compounding.,⁵ For example, a study by Research Affiliates (also published in the Financial Analysts Journal) highlighted that using arithmetic averages for forecasting long-term portfolio performance can paint an overly optimistic picture, leading to significant biases in cumulative performance forecasts.⁴

Furthermore, the accuracy of any Adjusted Average Return depends heavily on the quality and integrity of the underlying data. Inaccurate inputs, such as incorrect cash flow timing, flawed valuation methods, or misstated inflation rates, will result in an unreliable adjusted figure. The choice of the adjustment factor (e.g., a particular inflation index or a specific risk measure like standard deviation) can also introduce subjectivity and potential for manipulation if not applied consistently and transparently.

Adjusted Average Return vs. Arithmetic Mean Return

The distinction between Adjusted Average Return and Arithmetic Mean Return is fundamental in investment analysis. The Arithmetic Mean Return is simply the sum of a series of returns divided by the number of observations. It is easy to calculate and understand, making it suitable for short-term analysis or for estimating the average return in a single future period.³

However, the Arithmetic Mean Return has significant limitations when applied to multi-period investment performance, especially when returns are volatile or involve compounding. It does not account for the sequence of returns or the impact of gains and losses on the capital base. For instance, if an investment gains 100% in one year and loses 50% in the next, the arithmetic mean is (100% - 50%) / 2 = 25%. Yet, an initial $100 investment would become $200 after a 100% gain, and then $100 after a 50% loss, resulting in a 0% actual return over the two years.²

Adjusted Average Return, on the other hand, is a broader concept that encompasses various methodologies designed to overcome the shortcomings of the simple arithmetic mean. The Geometric Mean Return is a prime example of an Adjusted Average Return, specifically addressing the compounding effect to show the true growth rate over multiple periods. Similarly, a real return adjusts for inflation, providing a more accurate picture of purchasing power growth. Therefore, while the Arithmetic Mean Return offers a quick snapshot, an Adjusted Average Return provides a more accurate, context-specific measure that reflects the actual economic experience of an investment over time.

FAQs

Why is a simple arithmetic average often misleading for investment returns?

A simple arithmetic average can be misleading because it does not account for the compounding of returns, where gains or losses in one period affect the base for subsequent periods. It also doesn't reflect the sequence of returns, which significantly impacts the final value of an investment over time, especially with volatility.

What are common types of Adjusted Average Return?

Common types include the Geometric Mean Return, which adjusts for compounding, and the Real Return, which adjusts for the effects of inflation. Other adjustments might factor in risk, such as in the Sharpe Ratio.

When should I use an Adjusted Average Return instead of a simple average?

You should use an Adjusted Average Return whenever you need to understand the true, compounded growth of an investment over multiple periods, or when you want to evaluate returns in terms of purchasing power (by adjusting for inflation) or relative to the risk taken. It is essential for accurate financial planning and comparing different investment options.

Do regulators require the use of Adjusted Average Returns?

While regulators like the SEC do not explicitly mandate a single "Adjusted Average Return" formula, they require investment advisers to present investment performance in a fair and non-misleading manner. This often necessitates the use of calculations like geometric returns for multi-period performance and explicit disclosures regarding gross versus net returns, ensuring transparency about the actual returns clients experience.¹