风险与回报统计

从概率情景或历史回报数据中计算 E(r)、σ²、σ、夏普、偏度、峰度。专为无需任何设置的快速问题求解而设计。

Statistics Lab

Probabilistic scenarios + historical return series — every step shown

Enter scenarios with probabilities (must sum to 1.00) and returns. The Lab computes E(r), σ², and σ in real time, with every step shown.

Scenario	Probability (p)	p × r	(r − E(r))²	p × (r − E(r))²
		0.0900	0.03610	0.01083
		0.0500	0.00010	0.00005
		-0.0300	0.06760	0.01352
Total	1.00	E(r) = 0.1100		σ² = 0.02440

E(r)

11.00%

σ²

0.02440

15.62%

Sharpe

0.448

r_f = 4.0%

Step 1: E(r) = Σ p × r

Step 2: σ² = Σ p × (r − E(r))²

Step 3: σ = √σ²

Step 4: Sharpe = (E(r) − r_f) / σ

Want the full lesson? Visit Week 4 of the Investment Management course for the formulas, derivations, and a 5-question quiz with worked solutions.

Every investment can be summarized by two headline numbers: how much it returns on average and how much it bounces around. The first is expected return, the second is volatility. From those two, plus higher moments like skew and kurtosis, you can compute Sharpe and decide whether the bet is worth it.

每个实验室都基于标准教科书数学（Bodie / Kane / Marcus、Fabozzi、Tandelilin）。 Read the full methodology in the How It Works panel above.

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Scenario

Probability (p)

Return (r)

p × r

(r − E(r))²

p × (r − E(r))²

0.0900

0.03610

0.01083

0.0500

0.00010

0.00005

-0.0300

0.06760

0.01352

Total

1.00

E(r) = 0.1100

σ² = 0.02440