Average Return: Meaning, Calculations and Examples

Average return refers to the mean rate of return an investment generates over a given period. It is a statistical measure that summarizes the historical performance of an asset, portfolio, or project by averaging its returns across multiple time intervals. Essentially, it answers the question: “What has been the typical return over time?”

In finance, “return” typically refers to the gain or loss on an investment, expressed as a percentage of the initial investment. Returns can stem from various sources, such as price appreciation (e.g., a stock increasing in value), dividends, interest payments, or other income streams. The average return smooths out fluctuations in these returns to provide a single, digestible figure.

There are different types of average returns depending on the calculation method used, including the arithmetic average return and the geometric average return. Each serves a distinct purpose and offers unique insights into investment performance. Average return is widely used because it’s simple to compute and understand, but it also has limitations that investors must consider, such as its inability to account for volatility or the compounding effect over time.

Why Average Return Matters

Understanding average return is critical for several reasons:

Performance Evaluation: It allows investors to compare the historical performance of different investments, such as stocks, bonds, or real estate, to determine which offers the best returns.
Decision-Making: Investors and businesses use average return to assess whether an opportunity meets their financial goals or benchmarks, like beating inflation or a market index.
Risk Assessment: While average return doesn’t directly measure risk, it provides a starting point for analyzing an investment’s consistency when paired with metrics like standard deviation.
Planning: For long-term goals like retirement or wealth accumulation, average return helps estimate how much an investment might grow over time.

However, average return is just one piece of the puzzle. It doesn’t capture the full picture of an investment’s risk, timing, or compounding effects, which is why it’s often used alongside other metrics like the Sharpe ratio, internal rate of return (IRR), or compound annual growth rate (CAGR).

Types of Average Return

There are two primary methods to calculate average return: the arithmetic average and the geometric average. Each has its own formula, use case, and interpretation.

1. Arithmetic Average Return

The arithmetic average return is the simplest method. It involves summing the returns from each period and dividing by the number of periods. It assumes that returns are independent from one period to the next and does not account for compounding.

Formula: Arithmetic Average Return=R1+R2+R3+⋯+Rnn \text{Arithmetic Average Return} = \frac{R_1 + R_2 + R_3 + \dots + R_n}{n} Arithmetic Average Return=nR1+R2+R3+⋯+Rn Where:

R1,R2,R3,…,Rn R_1, R_2, R_3, \dots, R_n R1,R2,R3,…,Rn = Returns for each period
n n n = Number of periods

Use Case: This method is ideal for short-term analysis or when evaluating average performance without considering the impact of reinvested returns.

2. Geometric Average Return

The geometric average return, also known as the compound average return, accounts for the effect of compounding. It calculates the average rate of return that would produce the same final value if applied consistently over the periods. This makes it more suitable for long-term investments.

Formula: Geometric Average Return=[(1+R1)×(1+R2)×(1+R3)×⋯×(1+Rn)]1n−1 \text{Geometric Average Return} = \left[ (1 + R_1) \times (1 + R_2) \times (1 + R_3) \times \dots \times (1 + R_n) \right]^{\frac{1}{n}} – 1 Geometric Average Return=[(1+R1)×(1+R2)×(1+R3)×⋯×(1+Rn)]n1−1 Where:

R1,R2,R3,…,Rn R_1, R_2, R_3, \dots, R_n R1,R2,R3,…,Rn = Returns for each period (expressed as decimals, e.g., 5% = 0.05)
n n n = Number of periods

Use Case: The geometric average is preferred for assessing long-term investment performance because it reflects the actual growth trajectory of an investment.

How to Calculate Average Return

Let’s break down the calculation process for both types of average return with step-by-step explanations.

Arithmetic Average Return Calculation

Suppose an investment has the following annual returns over four years:

Year 1: 10%
Year 2: -5%
Year 3: 8%
Year 4: 12%

Steps:

Add the returns: 10+(−5)+8+12=25 10 + (-5) + 8 + 12 = 25 10+(−5)+8+12=25
Divide by the number of periods: 254=6.25% \frac{25}{4} = 6.25\% 425=6.25%

The arithmetic average return is 6.25% per year.

Geometric Average Return Calculation

Using the same returns:

Year 1: 10% (0.10)
Year 2: -5% (-0.05)
Year 3: 8% (0.08)
Year 4: 12% (0.12)

Steps:

Convert returns to growth factors: 1+R 1 + R 1+R for each year
- Year 1: 1+0.10=1.10 1 + 0.10 = 1.10 1+0.10=1.10
- Year 2: 1+(−0.05)=0.95 1 + (-0.05) = 0.95 1+(−0.05)=0.95
- Year 3: 1+0.08=1.08 1 + 0.08 = 1.08 1+0.08=1.08
- Year 4: 1+0.12=1.12 1 + 0.12 = 1.12 1+0.12=1.12
Multiply the factors: 1.10×0.95×1.08×1.12=1.2635 1.10 \times 0.95 \times 1.08 \times 1.12 = 1.2635 1.10×0.95×1.08×1.12=1.2635
Take the nth root (where n=4 n = 4 n=4): 1.263514=1.0607 1.2635^{\frac{1}{4}} = 1.0607 1.263541=1.0607
Subtract 1 and convert to percentage: 1.0607−1=0.0607 1.0607 – 1 = 0.0607 1.0607−1=0.0607 or 6.07%

The geometric average return is 6.07% per year.

Key Difference

Notice that the geometric average (6.07%) is slightly lower than the arithmetic average (6.25%). This is because the geometric method accounts for the compounding effect and the impact of negative returns, which reduce the overall growth rate.

Examples of Average Return in Action

To illustrate how average return works in practice, let’s explore a few examples across different investment scenarios.

Example 1: Stock Investment

An investor buys shares of a company and tracks the annual returns over five years:

Year 1: 15%
Year 2: -10%
Year 3: 20%
Year 4: 5%
Year 5: 8%

Arithmetic Average: 15+(−10)+20+5+85=385=7.6% \frac{15 + (-10) + 20 + 5 + 8}{5} = \frac{38}{5} = 7.6\% 515+(−10)+20+5+8=538=7.6%

Geometric Average: [(1.15)×(0.90)×(1.20)×(1.05)×(1.08)]15−1 \left[ (1.15) \times (0.90) \times (1.20) \times (1.05) \times (1.08) \right]^{\frac{1}{5}} – 1 [(1.15)×(0.90)×(1.20)×(1.05)×(1.08)]51−1 [1.40589]15−1=1.0706−1=0.0706 or 7.06% \left[ 1.40589 \right]^{\frac{1}{5}} – 1 = 1.0706 – 1 = 0.0706 \text{ or } 7.06\% [1.40589]51−1=1.0706−1=0.0706 or 7.06%

The investor might use the arithmetic average (7.6%) to gauge typical yearly performance and the geometric average (7.06%) to estimate the compounded growth rate of their investment.

Example 2: Mutual Fund

A mutual fund reports the following returns over three years:

Year 1: 12%
Year 2: -8%
Year 3: 15%

Arithmetic Average: 12+(−8)+153=193=6.33% \frac{12 + (-8) + 15}{3} = \frac{19}{3} = 6.33\% 312+(−8)+15=319=6.33%

Geometric Average: [(1.12)×(0.92)×(1.15)]13−1 \left[ (1.12) \times (0.92) \times (1.15) \right]^{\frac{1}{3}} – 1 [(1.12)×(0.92)×(1.15)]31−1 [1.18624]13−1=1.0586−1=0.0586 or 5.86% \left[ 1.18624 \right]^{\frac{1}{3}} – 1 = 1.0586 – 1 = 0.0586 \text{ or } 5.86\% [1.18624]31−1=1.0586−1=0.0586 or 5.86%

The fund’s marketing team might highlight the arithmetic average (6.33%) for its simplicity, but a savvy investor would note the geometric average (5.86%) as a more realistic measure of growth.

Example 3: Real Estate Investment

A rental property generates the following annual returns based on rental income and appreciation:

Year 1: 8%
Year 2: 6%
Year 3: -2%

Arithmetic Average: 8+6+(−2)3=123=4% \frac{8 + 6 + (-2)}{3} = \frac{12}{3} = 4\% 38+6+(−2)=312=4%

Geometric Average: [(1.08)×(1.06)×(0.98)]13−1 \left[ (1.08) \times (1.06) \times (0.98) \right]^{\frac{1}{3}} – 1 [(1.08)×(1.06)×(0.98)]31−1 [1.12224]13−1=1.0395−1=0.0395 or 3.95% \left[ 1.12224 \right]^{\frac{1}{3}} – 1 = 1.0395 – 1 = 0.0395 \text{ or } 3.95\% [1.12224]31−1=1.0395−1=0.0395 or 3.95%

Here, the slight difference between the two averages reflects the impact of the negative return in Year 3.

Limitations of Average Return

While average return is a useful metric, it has notable shortcomings:

Ignores Volatility: The arithmetic average treats a 50% gain and a 50% loss as netting out to 0%, but in reality, an investment that rises 50% then falls 50% ends up below its starting value due to compounding.
No Timing Consideration: It doesn’t account for when returns occur, which matters for cash flow or reinvestment opportunities.
Assumes Consistency: The arithmetic average assumes returns are stable, while the geometric average assumes reinvestment, neither of which may hold true in practice.
Limited Risk Insight: Average return doesn’t reflect the variability or risk of an investment, making it insufficient on its own for decision-making.

For a more comprehensive analysis, investors often pair average return with measures like standard deviation (for risk) or CAGR (for consistent growth).

Practical Applications

Average return finds its way into various financial contexts:

Portfolio Management: Investors calculate the average return of their portfolio to assess overall performance and rebalance assets.
Benchmarking: Comparing an investment’s average return to a market index (e.g., S&P 500) helps determine if it’s outperforming or underperforming.
Retirement Planning: Estimating the average return of a retirement fund helps project future savings.
Business Decisions: Companies use average return to evaluate the profitability of projects or capital investments.

Conclusion

Average return is a fundamental tool for understanding investment performance. Whether calculated as an arithmetic mean for simplicity or a geometric mean for compounding accuracy, it provides valuable insights into historical returns. However, it’s not a standalone metric—its limitations necessitate a broader analytical approach that includes risk, volatility, and compounding effects.