リスク・リターン統計

確率的シナリオまたは過去のリターン系列から E(r)、σ²、σ、シャープ、歪度、尖度を計算。セットアップ不要の素早い問題解決のために設計。

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.

すべてのラボは標準的な教科書の数学に基づいています（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