Understanding Average Return

What is the average return?

The average return (arithmetic average) is the simple mean of a series of investment returns over a specified period. It shows past performance by summing periodic returns and dividing by the number of periods. Unlike annualized or geometric measures, the arithmetic average does not account for compounding.

Arithmetic average formula
– Average return = (Sum of periodic returns) / (Number of periods)

Example: If annual returns over five years are 10%, 15%, 10%, 0%, and 5%, the arithmetic average is (10 + 15 + 10 + 0 + 5) / 5 = 8%.

How to calculate single-period growth

When you want the simple growth rate from a beginning value (BV) to an ending value (EV):

• Growth rate = (EV − BV) / BV

Example: A stock rises from $50 to $100. The return = (100 − 50) / 50 = 100%. If you invested $10,000 at $50 per share, you would have $20,000.

Limitations of the arithmetic average

• It ignores compounding and the sequence of returns.
• It can overstate expected long-term performance when returns vary significantly.
• It treats each period equally regardless of portfolio size or cash flows.

More accurate alternatives

Geometric average (compound annual growth rate / time-weighted rate of return)
– Formula: Geometric mean = (∏(1 + Ri))^(1/n) − 1, where Ri are periodic returns and n is the number of periods.
– It reflects compounding and gives a better measure of long-term growth.
– Example (five returns: 10%, 15%, 10%, 0%, 5%):
– Product = 1.10 × 1.15 × 1.10 × 1.00 × 1.05 ≈ 1.460075
– Geometric mean ≈ 1.460075^(1/5) − 1 ≈ 7.9% (vs. arithmetic 8%)

Money-weighted rate of return (MWRR / internal rate of return)
– MWRR accounts for the size and timing of cash flows (deposits, withdrawals, dividends).
– It is equivalent to the internal rate of return (IRR): the discount rate that makes the net present value of cash flows equal to zero.
– Use MWRR when investor cash flows materially affect performance (e.g., large contributions or withdrawals).

When to use each measure

• Arithmetic average: quick, simple snapshot of past periodic returns; useful for short-term or academic comparisons but not for projecting compounded returns.
• Geometric average (CAGR/TWR): preferred for long-term, compounded performance and comparing investments over different periods.
• MWRR/IRR: best when the timing and size of cash flows matter (portfolio with frequent contributions/withdrawals).

Key takeaways

• The average return is the arithmetic mean of periodic returns and does not reflect compounding.
• For long-term or compounded performance, use the geometric average (CAGR or time-weighted return).
• For portfolios with significant cash flows, use the money-weighted rate of return (IRR).
• Use multiple metrics together to get a fuller picture of investment performance.