Arithmetic Mean Return (also known as Average Return)

The Arithmetic Mean Return, often simply called the average return, is the straightforward average of a series of returns generated over a specific period. Imagine you're calculating your average score on a series of tests; you'd add up all your scores and divide by the number of tests. The arithmetic mean return works the exact same way for investments. You sum up the returns for each period (say, each year) and then divide by the number of periods. While it's a simple and widely used metric, especially for forecasting what a single future period's return might look like, it has a crucial blind spot. It ignores the powerful effect of compounding, which is the process of earning returns on your previous returns. This omission means the arithmetic mean can often paint an overly optimistic picture of an investment's actual performance over time. For the savvy value investor, understanding this limitation is key to avoiding misleading performance claims and making more grounded decisions.

Calculating the arithmetic mean is refreshingly simple. Let's say your 'EuroInnovate' stock had the following annual returns over three years:

• Year 1: +20%
• Year 2: -10%
• Year 3: +15%

To find the arithmetic mean, you just add them up and divide by the number of years, which is 3: (20% + (-10%) + 15%) / 3 = 25% / 3 = 8.33% The formula is simply: (Sum of all periodic returns) / (Number of periods).

Here's where it gets interesting and where many investors trip up. The simplicity of the arithmetic mean is also its biggest weakness: it doesn't reflect the reality of your portfolio's growth because investment returns are multiplicative, not additive. Let's look at a classic example to see why this matters:

1. You invest $1,000.
2. In Year 1, the investment soars by 100%, so your $1,000 becomes $2,000.
3. In Year 2, the investment plummets by 50%, so your $2,000 is halved, back to $1,000.

What's your arithmetic mean return? It's (100% + (-50%)) / 2 = 25% per year! This suggests you made a handsome profit. But what's your actual return? You started with $1,000 and ended with $1,000, so your actual return is 0%. The 25% figure is completely misleading. This discrepancy is caused by volatility and is precisely why we need another tool: the geometric mean return. The geometric mean, which accounts for compounding, would correctly show a 0% return in this scenario, as it accurately reflects the investment's journey.

Think of the two means as different tools for different jobs.

Use this when you want to estimate the expected return for the next single period (e.g., next year). It’s a forward-looking statistical forecast and represents the most likely outcome for any given year in isolation. It's often used as an input in financial models like the Capital Asset Pricing Model (CAPM).

Use this when you want to measure the actual, historical, compound rate of growth of your investment over several periods. It tells you what you really earned year after year, on average, to get from your starting capital to your ending capital. It's the most accurate representation of past performance.

For a value investor, whose horizon is measured in years, not minutes, this distinction is paramount. Always be skeptical of performance figures that boast high 'average' returns without specifying the calculation method. The arithmetic mean will almost always be higher than the geometric mean (unless returns are identical every year), and the difference grows along with volatility. Relying on the arithmetic mean to project your long-term wealth can lead to bitter disappointment. When you're assessing the track record of a company, a fund, or your own portfolio, the geometric mean is your trusted friend. It cuts through the statistical noise and tells you the true story of wealth creation—or destruction. As the saying goes, “You can't eat arithmetic returns.” Always look for the number that reflects the money that actually ended up in your pocket.