core

Compute and compare investment return metrics including TWR, MWR (dollar-weighted IRR on portfolio cash flows), CAGR, and annualized returns. Use when the user asks about portfolio performance calculation, comparing manager returns, linking sub-period returns, understanding why different return methods give different numbers, converting returns across time periods, or computing the IRR of an investor's own contributions and withdrawals. Also trigger when users mention 'how much did I make', 'annual return', 'compound growth', 'dollar-weighted vs time-weighted', 'what was my rate of return', 'geometric vs arithmetic mean', 'log returns', or ask about the effect of cash flows on reported returns. For project or loan IRR, NPV, and generic 'solve for the rate' problems, use time-value-of-money instead.

Apply statistical methods to financial data including descriptive statistics, covariance estimation, regression, hypothesis testing, and resampling. Use when the user asks about return distributions, correlation between assets, building a covariance matrix, running a CAPM regression, testing whether alpha is significant, checking if returns are normal, or estimating confidence intervals. Also trigger when users mention 'volatility', 'how correlated are these', 'fat tails', 'skewness', 'R-squared', 'beta of a fund', 'bootstrap a Sharpe ratio', 'shrinkage estimator', 'Ledoit-Wolf', or ask why their optimizer produces unstable weights.

Calculate present value, future value, NPV, IRR for projects and loans, loan payments, and amortization schedules across all compounding conventions. Use when the user asks about discounting cash flows, valuing an annuity or perpetuity, comparing investments with different timing, building a mortgage amortization table, evaluating whether a project is worth pursuing, or solving for the rate that equates cash flows (project IRR, loan IRR, yield on an investment). Also trigger when users mention 'what is it worth today', 'how much will I have in 20 years', 'monthly payment on a loan', 'discount rate', 'Gordon growth model', 'effective annual rate', 'continuous compounding', or ask how to compare a lump sum versus a stream of payments. For portfolio money-weighted return (dollar-weighted IRR on an investor's contributions and withdrawals), use return-calculations instead.