Return Distributions

Click any bar to see the conditional distribution of the next return given the selected z-score range. Click multiple bars to aggregate. Returns beyond ±6σ are clipped from the histogram; conditional distributions use a 20×20 transition matrix.

Reference Distributions

Each reference curve is fitted from the sample moments of the selected ticker and timeframe. All are scaled to match the histogram's total area so they are directly comparable to the empirical bar heights.

Normal   N(μ, σ²)

f(z) = (1 / √2π) exp(−z2 / 2)   where z = (x − μ) / σ

Student-t   t_ν(μ, σ ⋅ √(ν−2)/ν)

Degrees of freedom estimated from excess kurtosis κ: ν = 4 + 6 / κ, clamped to [2.2, ∞). This captures heavy tails without an extra parameter.

f(z) = Γ((ν+1)/2) / (Γ(ν/2) √νπ) ⋅ (1 + z2/ν)−(ν+1)/2

Laplace   Laplace(μ, b = σ / √2)

f(z) = (1 / 2b) exp(−|x − μ| / b)

Cauchy   Cauchy(μ, γ = σ)

f(z) = 1 / (πγ (1 + ((x − μ) / γ)2))