Return Calculations

When you need to explain why a fund's 8% time-weighted return translates to a negative money-weighted return for an investor who deposited right before a drawdown, this is the skill to load. It covers the full spectrum from simple holding period returns through CAGR, TWR, MWR/IRR, and the math behind geometric versus arithmetic means. The worked examples are solid, showing exactly how cash flow timing creates divergence between what the manager earned and what the investor experienced. It's Layer 0 math, so expect formulas and precision rather than high-level commentary. Use it when someone asks about portfolio performance, linking sub-period returns, or why their actual return feels different from what their advisor reported.

skills.sh installs: 745
GitHub stars: 224
last updated: Aug 21, 2026

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Install

$ npx -y skills add joellewis/finance_skills --skill return-calculations --agent claude-code

Installs into .claude/skills of the current project.

Files

Return Calculations

Core Concepts

Simple (Holding Period) Return

$$R = \frac{V_{end} - V_{begin} + D}{V_{begin}}$$

where D = distributions (dividends, interest) received during the period. If V_end already reflects reinvested distributions, do not add D again.

Mean and Log Return Conventions

Arithmetic mean R_a = (1/n) * sum(R_i) — unbiased estimate of the expected single-period return (use for forward-looking inputs, e.g., mean-variance optimization). Always >= geometric mean; overstates realized compound growth.
Geometric mean R_g = [prod(1 + R_i)]^(1/n) - 1 — the correct measure of realized multi-period compound growth. The gap below the arithmetic mean approximates sigma^2 / 2 (volatility drag).
Log return r = ln(V_end / V_begin) — time-additive (r_total = r_1 + ... + r_n), so preferred for statistical modeling and multi-period aggregation. Convert with R_simple = e^r - 1 and r = ln(1 + R_simple). Log returns are additive across time but NOT across assets.