Bonds, the time value of money, discounted cash flow, portfolios, options, risk, leverage and backtests — computed, then explained. Every screen prints the formula it evaluated and draws the exhibit that argues it, so you can check the answer instead of trusting it.
Trading at a premium
P(y) = d(y)ᵀc d_k = (1 + y/m)^(−k)
Price and yield to maturity, then duration and convexity — and the exhibit that shows exactly where duration alone stops telling the truth.
price · ytm · macaulay · modified · convexity · dv01
Annuities, the level payment and the full amortization schedule, with NPV and IRR — including the month the loan turns the corner, which on a 30-year mortgage is month 176 of 360.
pv · annuities · amortization · npv · irr · payback
Free cash flow to the firm, WACC, terminal value and the equity bridge — with a sensitivity grid that shows how fragile a single valuation really is.
fcff · wacc · gordon tv · equity bridge · sensitivity
The efficient frontier solved exactly, drawn over four thousand random portfolios that never cross it — plus the tangency portfolio, shrinkage and CAPM beta.
frontier · gmv · tangency · shrinkage · capm β
Black–Scholes and a binomial lattice priced side by side. The lattice does not converge from one side — it oscillates, and watching it settle is the lesson.
bsm · greeks · crr lattice · implied vol · payoffs
VaR and expected shortfall computed historically and parametrically on one histogram, so you can see two estimates of the same tail disagree — then GARCH, which rescales the tail to today's volatility.
var · es · historical · parametric · garch · fhs · drawdown
What a small move does to your margin, what the spread and overnight financing cost before you earn anything, and why leverage cannot create an edge — only multiply the one you have, and the bill with it.
margin · carry · break-even · sharpe · kelly
Try enough strategies and the best one looks good by luck alone. The probabilistic and deflated Sharpe ratios say how much of your backtest is skill — and how many tries it takes for chance to match it.
psr · deflated sharpe · min track record · trials
At 20× leverage a 0.2% move is a 4% return on your margin. That is the arithmetic that makes margin trading look easy, and it runs the other way just as fast: a 5% move against you takes the whole deposit.
Costs are charged on the exposure, not on your margin. A one-basis-point spread and five nights of financing at 8.1% mean the price has to move 12 basis points before you earn anything, and leverage does not lower that bar. It only multiplies what clearing it, or failing to, does to your account.
A backtest with a Sharpe ratio of 1.0 over five years looks like proof. If it was the best of 70 variants, it is more likely luck than skill: chance alone reaches that number after about 45 tries. The Leverage and Backtest labs put these numbers in front of you before a trade does.
Most calculators hand you a number and stop. hedqe prints the formula it evaluated and draws an exhibit with a caption explaining what the curve actually means — why convexity matters at 200 basis points but not at 25, why a DCF near its terminal-growth asymptote should never be quoted as one number.
Where two methods should agree, both are shown. The binomial lattice is drawn converging on the closed form; the random portfolios are drawn never crossing the frontier. Two engines meeting is a stronger claim than either number alone.
The mathematics is bundled with the app rather than fetched, so every lab works with the network off — on the bus, in an exam room, anywhere. Nothing you type is sent anywhere, because there is nowhere for it to go. It is free, and it stays free: no account, no trial, no upgrade screen.
The same six labs on iPhone, iPad and Android. Free, no account, works offline.
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hedqe is an educational and analytical tool. Nothing in it is investment advice, a recommendation, or a solicitation. All inputs are your own; no market data is supplied.