Which fund is actually better?

A fund that returns more isn't automatically the better one — not if it lurches twice as hard to get there. The Sharpe ratioWilliam Sharpe's 1966 measure of risk-adjusted return: excess return (above the risk-free rate) divided by volatility. It answers 'how much reward am I getting for each unit of risk?' — the slope of the line from cash to the investment. scores the return you earn above cash against the volatility you stomach for it. Once you can borrow or hold cash, the highest-Sharpe choice wins — which is why sizing the bet starts from reward-per-risk, not return alone.

Fund Areturns% a year with% swingsVolatility — the standard deviation of yearly returns. Roughly, the fund spends about two years in three within ± this much of its average. Bigger means a wilder ride..
Fund Breturns% a year with% swings.
Cash earns% risk-freeThe risk-free rate — what your money earns with no risk, e.g. short-term government bills. Sharpe measures return above this, since you could always just hold cash instead., on aportfolio.
Fund Bwins · 0.56 vs 0.44 Sharpe

Fund B returns 7% to Fund A's 10% — yet it's the better buy. Per unit of risk it earns 0.56 against 0.44. Borrow to lever Fund B up to Fund A's 18% swings and it returns 12% — more than Fund A, at the same risk. Higher headline return isn't the same as higher reward for risk.

Fund AFund B
cash · 2%AB5%10%15%
0% risk10%20%24.3% volatility

Each fund's Sharpe ratio is the slope of its line from cash. The steeper line is the better deal at every level of risk: pick the volatility you want along the x-axis and the higher line always sits above the lower one. That's why the steeper fund wins even when its dot sits lower — borrow against it (slide right) or hold some cash (slide left) and you ride its line to whatever risk you like.

FundReturnVolatility± swing / yrSharpe
Fund A10%18%±€18k0.44
Fund Bwins7%9%±€9k0.56

Matched to the same risk, the winner pulls ahead on return too. Lever Fund B by 2.00× to Fund A's 18% volatility and it returns 12% — the gap is the free lunch a higher Sharpe buys. Volatility shown as ±1 standard deviation on your €100k portfolio.

Sharpe = (return − risk-free) ÷ volatility · see the Sharpe ratio