Investing Math

Compare equal periodic buys (dollar-cost averaging) with one lump sum on the first date, over a list of prices.

Dividend yield, yearly income, and yield on cost and total dividends after years of dividend growth.

Gain needed to recover a percentage loss, or the maximum drawdown and recovery gain from a list of period returns.

The price range implied by volatility over a number of days: one and two standard deviations, from implied or historical vol.

Financial-independence number from yearly spending and a withdrawal rate, and years to reach it from savings and contributions.

What an amount costs or is worth after years of steady inflation, plus the real return after inflation for a nominal return.

Margin call price for shares bought on margin: your cash, the loan, the maintenance requirement and the trigger price.

Expiry profit and loss for a long or short call or put: break-even, maximum gain and loss, and a payoff table.

Return and volatility of a two-asset mix from each asset's return, volatility and correlation, plus the lowest-risk weight.

Position size from account size, risk percent, entry and stop: units to buy, dollars at risk, cost and R-multiple targets.

Performance stats from period returns: average, volatility, Sharpe, Sortino, compound growth and max drawdown.

Reward-to-risk ratio from entry, stop and target, the win rate needed to break even, and expectancy at your win rate.