Analytical Compounded Return Explorer

Inputs

Mean annual expected return μ (% per year) Example: 7 means 7% expected annual arithmetic return.

Volatility σ (% per year) [for charts] Chart inputs; the table grid uses ranges below.

Time horizon T (years)

μ max (%)

μ step (%)

σ max (%)

σ step (%)

Compounding discretization Charts use the selected compounding model; core stats remain analytical.

Median total multiplier (T)

—

Mean total multiplier (T)

—

Prob gain (>0%)

—

Prob lose half (≤ -50%)

—

Prob > arithmetic mean

—

Zero-σ annual r (comp.)

—

Zero-σ annual r (simple)

—

Multiplier threshold at 80%

—

Annual return PDF (Normal)

Total multiplier PDF (Lognormal GBM)

Kelly Criterion analysis

Kelly fraction f*

—

Median (K vs 100%)

—

Mean (K vs 100%)

—

Prob gain (K vs 100%)

—

Prob ≤ −50% (K vs 100%)

—

P80 threshold (K vs 100%)

—

Expected log-growth/yr (K vs 100%)

—

Portfolio multiplier PDF: Kelly vs 100% risky (r=0)

Grid KPI Max Kelly fraction