Sharpe Ratio Calculator
Compute the Sharpe ratio from portfolio return, the risk-free rate, and volatility. See the excess return per unit of risk, with optional annualizing.
Enter a portfolio’s return, the risk-free rate, and the volatility (standard deviation) of its returns. You get the Sharpe ratio — the excess return earned per unit of risk taken.填入组合的收益率、无风险利率，以及收益的波动率（标准差），即可得到夏普比率——每承担一单位风险所换来的超额收益。
Fill in return, risk-free rate and σ to see the Sharpe ratio.填入收益率、无风险利率与 σ 即可得到夏普比率。
- Excess return超额收益
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- Per unit of risk每单位风险
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- Annualized Sharpe年化夏普
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The Sharpe ratio is your excess return divided by its volatility. Excess return is what the portfolio earned above a risk-free rate — the return you could have had for taking no risk at all; volatility is the standard deviation of those returns. Dividing one by the other answers a single question: how much return did each unit of risk actually buy?夏普比率就是超额收益除以其波动率。超额收益是组合在无风险利率之上多赚的部分——无风险利率是你不承担任何风险也能拿到的回报；波动率则是这些收益的标准差。两者相除回答的是同一个问题：每一单位风险，究竟换来了多少收益？
01The formula公式
Sharpe = ( Rp − Rf ) ÷ σ夏普 = ( Rp − Rf ) ÷ σ
Annualized = Sharpe × √k年化 = 夏普 × √k (k = periods per year: 12 monthly, 252 daily)（k = 每年周期数：月度 12、日度 252）
The ratio is unit-free: a Sharpe of 0.60 means the portfolio earned 0.60 units of excess return for every unit of volatility. The optional √k step rescales a ratio measured over short periods — monthly or daily returns — up to an annual figure so it can be compared with others quoted per year. σ must be greater than zero; a portfolio with no variation in its returns has no risk to divide by.该比率没有单位：夏普为 0.60，意味着每一单位波动率带来 0.60 单位的超额收益。可选的 √k 步骤，把按短周期（月度或日度）测得的比率放大到年度口径，以便与他人按年报出的数字比较。σ 必须大于零；收益毫无波动的组合，没有可供相除的风险。
02A worked example一个算例
Suppose a portfolio returned 12% over a year while cash (the risk-free rate) paid 3%. The standard deviation of its returns was 15%.假设某组合一年收益 12%，同期现金（无风险利率）为 3%，其收益的标准差为 15%。
- Excess return = 12 − 3 = 9%超额收益 = 12 − 3 = 9%
- Sharpe = 9 ÷ 15 = 0.60夏普 = 9 ÷ 15 = 0.60
A Sharpe of 0.60 says the portfolio was paid 0.60 units of excess return for each unit of risk it carried. A second portfolio that also returned 12% but swung twice as hard — σ of 30% — would score just 0.30. Same headline return, half the risk-adjusted quality. That is the whole point: the Sharpe ratio refuses to reward a return that was bought with outsized volatility.夏普 0.60 表示：组合每承担一单位风险，就获得 0.60 单位的超额收益。另一个同样收益 12%、但波动大一倍——σ 为 30%——的组合，只能得 0.30。名义收益相同，风险调整后的质量却减半。这正是关键所在：夏普比率不会奖励一份靠过大波动换来的收益。
03The common trap常见陷阱
A Sharpe ratio computed from monthly returns is not comparable to one computed from annual returns — the monthly figure is roughly √12 smaller. Before you rank two funds by Sharpe, make sure both are on the same clock. That is what the annualize step is for: convert the short-period ratio up by √k so like sits next to like. Quoting a raw monthly Sharpe as if it were annual quietly flatters or punishes the number by a factor of more than three.用月度收益算出的夏普比率，与用年度收益算出的并不可比——月度数字大约要小 √12 倍。在按夏普给两只基金排名之前，先确认两者用的是同一把尺子。年化步骤正是为此而设：把短周期比率乘以 √k 放大，让同类与同类相比。把原始月度夏普当作年度口径引用，会悄悄地把这个数字美化或贬低三倍以上。
04Where this breaks它的局限
The Sharpe ratio is a convention, not a law — a useful summary with real blind spots. As a rough reading: below 1 is often called subpar, 1 to 2 good, above 2 very good — but those bands are habit, not truth, and they shift with the market regime and the measurement window. A few honest limits:夏普比率是一种惯例，而非定律——它是有用的概括，却有实实在在的盲点。作为粗略参照：低于 1 常被称为一般，1 到 2 为良好，2 以上为优秀——但这些区间是习惯，不是真理，会随市场环境与测量窗口而变。几点诚实的局限：
- It penalizes upside volatility. Standard deviation counts a big up-month as “risk” exactly like a big down-month. A portfolio that mostly surprises to the upside is scored as if those surprises were dangerous. The Sortino ratio, which divides by downside deviation only, was built to address this.它惩罚向上的波动。标准差把一个大涨月与一个大跌月同样算作「风险」。一个多为向上惊喜的组合，会被当作那些惊喜很危险来打分。索提诺比率——只用下行标准差相除——正是为解决这一点而生。
- It assumes returns are roughly normal. Real returns have fat tails and skew; strategies that sell options or carry hidden crash risk can post a lovely Sharpe for years and then give it all back in a week. A high ratio built on a short, calm sample can be a mirage.它假设收益大致服从正态分布。真实收益有肥尾与偏度；卖出期权、或暗藏崩盘风险的策略，可能连续多年报出漂亮的夏普，然后在一周内悉数吐回。建立在短暂平静样本上的高比率，可能只是海市蜃楼。
- The risk-free rate and window are choices. Which cash rate you subtract, and how long a window you measure, both move the number. Two honest analysts can compute different Sharpe ratios for the same fund. Treat it as one lens among several, not a verdict.无风险利率与窗口都是选择。你减去哪个现金利率、测量多长的窗口，都会改变结果。两位诚实的分析师，可能为同一只基金算出不同的夏普比率。把它当作众多视角之一，而非最终定论。
A high return means little until you know what volatility it cost. The Sharpe ratio prices that trade-off — but read it beside the shape of the returns, not on its own.在你知道一份收益付出了多少波动之前，高收益本身意义有限。夏普比率为这一取舍定价——但要把它与收益的分布形态放在一起读，而非孤立地看。
Turn a raw gain into an annual rate with the 用 CAGR calculatorCAGR 计算器, or size a single trade by risk with the 把原始收益换算成年化利率，或用 position size calculator仓位计算器. 按风险为单笔交易定仓。