σμimplied vol · KKmax(S−K,0)udβρᵢⱼfat tailsPnL · drawdownyield · TdSₜ = μSₜ dt + σSₜ dWₜC = S·N(d₁) − K·e⁻ʳᵀ·N(d₂)σₚ² = wᵀΣwd₁ = [ln(S/K) + (r + σ²⁄2)T] ⁄ σ√T∂V/∂t + ½σ²S²·∂²V/∂S² + rS·∂V/∂S − rV = 0Sharpe = (Rₚ − R_f) ⁄ σₚVaR₉₉ = μ − 2.33σρ = Cov(X,Y) ⁄ σₓσᵧE[Rₚ] = Σ wᵢ·E[Rᵢ]φ(x) = e^(−x²/2) ⁄ √2πE[Rᵢ] = R_f + βᵢ(E[Rₘ] − R_f)dXₜ = θ(μ − Xₜ)dt + σ dWₜσ²ₜ = ω + α·ε²ₜ₋₁ + β·σ²ₜ₋₁C − P = S − K·e⁻ʳᵀΔ = ∂V/∂S Γ = ∂²V/∂S²p = (e^(rΔt) − d) ⁄ (u − d)rₜ = ln(Pₜ ⁄ Pₜ₋₁)E[Xₜ₊₁ | ℱₜ] = Xₜf* = (bp − q) ⁄ bz = (x − μ) ⁄ σP(N=k) = λᵏe^(−λ) ⁄ k!Θ = −∂V/∂Tν = S·φ(d₁)·√Tmin wᵀΣw s.t. wᵀμ = μ*∫Σ∂∞λ
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σμimplied vol · KKmax(S−K,0)udβρᵢⱼfat tailsPnL · drawdownyield · TdSₜ = μSₜ dt + σSₜ dWₜC = S·N(d₁) − K·e⁻ʳᵀ·N(d₂)σₚ² = wᵀΣwd₁ = [ln(S/K) + (r + σ²⁄2)T] ⁄ σ√T∂V/∂t + ½σ²S²·∂²V/∂S² + rS·∂V/∂S − rV = 0Sharpe = (Rₚ − R_f) ⁄ σₚVaR₉₉ = μ − 2.33σρ = Cov(X,Y) ⁄ σₓσᵧE[Rₚ] = Σ wᵢ·E[Rᵢ]φ(x) = e^(−x²/2) ⁄ √2πE[Rᵢ] = R_f + βᵢ(E[Rₘ] − R_f)dXₜ = θ(μ − Xₜ)dt + σ dWₜσ²ₜ = ω + α·ε²ₜ₋₁ + β·σ²ₜ₋₁C − P = S − K·e⁻ʳᵀΔ = ∂V/∂S Γ = ∂²V/∂S²p = (e^(rΔt) − d) ⁄ (u − d)rₜ = ln(Pₜ ⁄ Pₜ₋₁)E[Xₜ₊₁ | ℱₜ] = Xₜf* = (bp − q) ⁄ bz = (x − μ) ⁄ σP(N=k) = λᵏe^(−λ) ⁄ k!Θ = −∂V/∂Tν = S·φ(d₁)·√Tmin wᵀΣw s.t. wᵀμ = μ*∫Σ∂∞λ
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Skills›Statistics
S

Statistics Skill

LiveStart here

Finance is full of noise, and a backtest that looks good is usually luck. This skill teaches the tools that tell signal from noise, with short checks (numbers you compute, steps you order, concepts you match) and finance examples: why the median beats the mean on returns, how wide an interval really is, why the best of a hundred strategies proves little, and how to cross-validate without looking into the future. It ends with a code lab that tests a momentum anomaly on real prices with a bootstrap and a multiple-testing correction.

4 modules12 graded labs~11 hoursBeginner → Advanced
Start skill

Syllabus

12 topics · open any topic, in any order
  1. 1Descriptive statistics and robust estimatorsNot started40 minStart
  2. 2Sampling distributionsNot started45 minStart
  3. 3Confidence intervals and the bootstrapNot started55 minStart
  1. 4Hypothesis tests: the t-testNot startedRequires Python45 minStart
  2. 5Multiple testing and false discoveriesNot started55 minStart
  1. 6Maximum likelihoodNot started55 minStart
  2. 7Linear regression (OLS)Not startedRequires Python55 minStart
  3. 8Heteroskedasticity and robust errorsNot started50 minStart
  4. 9Multicollinearity and regularisationNot started50 minStart
  1. 10Cross-validation and overfittingNot started55 minStart
  2. 11The deflated Sharpe ratio and backtest overfittingNot started1 hrStart
  3. 12Capstone: is this anomaly real?Not started1 hr 40 minStart

Prerequisites

Probability helps, and the two Python topics inside this skill are part of the syllabus, but you can start with high-school maths.

  • PProbability

What you'll learn

  • Summarise returns with robust statistics and understand sampling distributions and standard errors
  • Build confidence intervals, including the bootstrap for statistics without a formula
  • Run tests honestly: correct for multiple testing and control false discoveries
  • Fit models by maximum likelihood and regression, and handle heteroskedasticity, collinearity and regularisation
  • Validate without leaking the future, deflate a Sharpe ratio for the number of trials and test an anomaly end to end

Tools you'll use

PythonNumPypandaspytest

Completion

Pass all 12 labs with a score of 70+ to complete the skill and earn the Statistics for Quants badge on your profile.

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