The Sharpe ratio

Raw returns are meaningless without the risk taken to earn them. The Sharpe ratio, devised by William Sharpe, is the most widely used way to put the two together.

The idea

It asks: for each unit of risk, how much return did you earn above the risk-free rate?

Sharpe ratio = (portfolio return minus risk-free rate) / portfolio volatility

The numerator is the excess return — what you earned beyond a no-risk parking spot. The denominator is the volatility you endured to get it.

A comparison

Fund A: 12 percent return, 20 percent volatility, risk-free 2 percent
    Sharpe = (12 - 2) / 20 = 0.50
Fund B: 9 percent return, 10 percent volatility, risk-free 2 percent
    Sharpe = (9 - 2) / 10 = 0.70

Fund A earned more in absolute terms, but Fund B was far more efficient per unit of risk. A risk-aware investor prefers B and can use leverage to match A's return at lower risk.

Reading the number

Roughly, a Sharpe above 1 is good, above 2 is excellent, and below 0.5 is unremarkable — though these depend heavily on the period and asset class. The ratio is also the slope of the Capital Market Line from the previous chapter, which is why the tangency portfolio is precisely the maximum-Sharpe portfolio.

Limitations

The Sharpe ratio penalizes upside volatility just as much as downside, which feels wrong — nobody complains about big gains. It also assumes returns are roughly normal, so it flatters strategies that quietly accumulate small gains while risking rare large losses. The next lesson's Sortino ratio addresses the first complaint directly.