जोखिम और रिटर्न आँकड़े

संभाव्यता परिदृश्यों या ऐतिहासिक रिटर्न डेटा से E(r), σ², σ, Sharpe, तिरछापन, कुर्तोसिस की गणना करें। बिना किसी सेटअप के त्वरित समस्या-समाधान के लिए डिज़ाइन किया गया।

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.

प्रत्येक लैब मानक पाठ्यपुस्तक गणित पर आधारित है (Bodie / Kane / Marcus, Fabozzi, Tandelilin)। Read the full methodology in the How It Works panel above.

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जोखिम और रिटर्न आँकड़े

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