Sharpe ratio versus CAGR: which measures wealth growth?

CAGR measures how wealth compounded; the Sharpe ratio measures average return above a benchmark per unit of fluctuation. They answer different questions, and can rank the same portfolios differently without either calculation being wrong.

The main Sharpe guide explains the ratio and its limits. This comparison supplies exact return paths so the difference can be checked without relying on an assumed relationship between volatility and compound growth.

Key takeaways

• CAGR annualises a compounded wealth ratio; Sharpe compares average excess returns with their variability.
• Two investments can rank differently on the two measures.
• Historical CAGR is not expected log growth: the latter requires a probability distribution for future returns.

Keep arithmetic averages separate from multiplication

For periodic investment returns r, the arithmetic mean is their sum divided by the number of observations. It describes the average return in one observation, not the rate applied repeatedly to initial wealth.

For n annual observations, compound growth is:

CAGR = [product of (1 + r)]^(1/n) − 1

The historical annual Sharpe ratio in our example is:

mean(annual investment return − annual cash return) ÷ sample standard deviation of those differences

We use the sample denominator with n − 1, not the population denominator. With a constant cash return, the standard deviation of the differences equals investment-return volatility. There is no monthly annualisation in this first example because the observations are already annual.

Three portfolios with fully disclosed paths

Assume ten hypothetical years, starting with $10,000, no contributions or withdrawals, and a constant 2% annual cash benchmark. All investment returns are nominal US-dollar total returns, before fees and tax. Each two-year pair below repeats five times:

• A: +14%, then +2%.
• B: +30%, then −5%.
• C: +26%, then −10%.

These are teaching sequences, not forecasts or historical portfolio performances.

After ten years, A ends at $21,258, B at $28,730, and C at $18,753. Original calculations are in the summary CSV, with every annual input separately downloadable.

A's sample annual volatility is 6.32%, versus 18.45% for B. A earns more excess return per unit of that volatility, but B earns a sufficiently higher average return to finish with more wealth. A higher ratio therefore does not establish the highest compound return at the actual portfolio size.

Equal arithmetic means still leave a compounding gap

A and C have the same 8% arithmetic mean. Their two-year wealth multipliers are different:

A: 1.14 × 1.02 = 1.1628

C: 1.26 × 0.90 = 1.1340

Repeating those products explains why C ends $2,505 behind A. This is the exact arithmetic behind “volatility drag” in these particular sequences. It does not mean every higher-volatility asset has a lower CAGR: B is the counterexample because its mean is higher.

Reordering a given set of returns leaves final wealth unchanged when there are no intervening cash flows. With withdrawals, contributions or a strategy that changes exposure along the way, order can matter. The hedge-payout example shows how a cash-flow decision changes subsequent exposure.

The same distinction appears in historical data

For January 1973–August 2026, our 644 monthly observations of the US value-weighted stock market produce an annualised arithmetic mean of 11.90%, calculated as 12 times the monthly mean. The same monthly total returns compound at 11.17% a year.

Those are nominal USD calculations from the Kenneth French Data Library, not the S&P 500. The historical calculation CSV records the period and definitions. The annualised monthly mean is not the arithmetic mean of calendar-year returns.

Geometric growth is the outcome; Sharpe is a diagnostic

For comparing realised wealth growth without external cash flows, the outcome is net compounded wealth or its annualised CAGR. For a forward-looking model, expected log growth E[ln(1 + R)] requires positive wealth factors and a specified distribution; it is not log(1 + E[R]). A historical CAGR estimates neither that distribution nor a future optimum.

Sharpe, loss experience and exposure help describe the result, but are not substitutes for it. Scaling a strategy or financing it changes what the investor experiences; a historical ratio alone cannot identify an optimal size or eliminate rare-loss risk. The negative-Sharpe analysis demonstrates another ranking limitation.