Which statement best describes arithmetic returns versus geometric returns?

• A. Arithmetic return is the simple average of periodic returns; geometric return is the compounded rate of return across multiple periods.
• B. Arithmetic return is the compounded rate of return; geometric return is the simple average.
• C. Arithmetic and geometric returns are identical in all cases.
• D. Arithmetic return accounts for reinvestment; geometric return ignores it.

Answer: (A)

The key idea here is how these two measures handle compounding. Arithmetic return is the simple average of periodic returns: r̄ = (r1 + r2 + ... + rn) / n. It smooths the returns and ignores how those period returns build on each other over time.

Geometric return, by contrast, captures the effect of reinvestment and compounding. It reflects the actual growth rate across multiple periods. For total return over several periods, you multiply the growth factors: Total geometric return = (1 + r1)(1 + r2)...(1 + rn) − 1. If you want an annualized figure, you take the nth root of that product and subtract 1: [(1 + r1)(1 + r2)...(1 + rn)]^(1/n) − 1. This shows why, when returns vary from year to year, the geometric measure often differs from the simple arithmetic average and generally provides a lower, more accurate picture of long-run growth when reinvestment is involved.

So the statement that arithmetic return is the simple average of periodic returns and geometric return is the compounded rate across multiple periods is the correct description.