Average Investment Return Calculator

Average investment return and portfolio growth explained

Understanding how your investments have really performed over time is essential for long-term financial planning. This calculator helps you translate a sequence of yearly returns into clear metrics, including final value, total gain, arithmetic average return, geometric average return (CAGR), and real performance after inflation.

Arithmetic average return versus geometric average return

The simplest way to describe performance is the arithmetic average return. It is calculated by summing all yearly returns and dividing by the number of years:

\[ \bar{r} = \frac{1}{n} \sum_{i=1}^{n} r_i \]

This measure is easy to understand, but it does not capture the compounding effect of gains and losses. For long-term investors, the geometric average return is usually more informative. It reflects the constant rate that would turn your initial investment into the final value:

\[ r_{\mathrm{geo}} = \left( \frac{FV}{PV} \right)^{\frac{1}{n}} - 1 \]

Here, \( PV \) is the initial investment, \( FV \) is the final value, and \( n \) is the number of years. The geometric average is directly linked to the real growth of capital in your account.

How yearly returns compound into a final portfolio value

When you enter a sequence of yearly returns, the calculator applies each return to the previous year’s ending balance. If your initial investment is \( PV \) and the yearly returns are \( r_1, r_2, \ldots, r_n \), the final value is:

\[ FV = PV \times \prod_{i=1}^{n} (1 + r_i) \]

A year with a negative return reduces the balance and makes it harder for later gains to fully recover the loss. This is why volatility matters: the order and size of returns can significantly affect the final outcome, even if the arithmetic average is the same.

Nominal versus real returns after inflation

Nominal returns describe how much your money has grown in absolute currency terms. However, what really matters is purchasing power. Inflation gradually erodes the value of money, so a seemingly high nominal return can translate into a much lower real return.

If the nominal average return is \( r_{\mathrm{nom}} \) and the average inflation rate is \( \pi \), the real average return can be approximated by:

\[ 1 + r_{\mathrm{real}} = \frac{1 + r_{\mathrm{nom}}}{1 + \pi} \]

The calculator applies this relationship to both yearly returns and the geometric average, giving you a clearer view of how much your purchasing power has really improved over time.

Interpreting the year-by-year breakdown table

The year-by-year table shows how your portfolio evolves over the entire period. Each row includes the starting balance, that year’s return, the gain or loss, the ending balance, and the cumulative gain compared with the initial investment. Years with negative returns are visually highlighted so that periods of stress are easy to identify.

By comparing the arithmetic average, geometric average, and real average, you can quickly assess whether your investment strategy has been stable, volatile, or heavily influenced by inflation. This helps you decide whether you are taking the right level of risk and whether your long-term goals remain realistic.

Using the calculator to analyze different scenarios

You can test alternative sequences of returns to see how timing and volatility affect outcomes. For example, entering the same set of returns in a different order can produce very different final values, even when the arithmetic average is unchanged. This demonstrates the importance of sequence risk for investors who regularly contribute or withdraw funds.

Combine the detailed breakdown with your own financial plan to decide whether you need to adjust your asset allocation, contribution levels, or risk profile. A clear understanding of average investment returns can make your long-term planning more robust and data driven.