🧮Calculators

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Bond Accrued Interest

Computes the accrued interest of a fixed-income bond, the slice of coupon that has built up since the last coupon payment up to the settlement date. It uses the linear (actual-days) convention, proportional to elapsed days: interest = face value × (coupon rate ÷ frequency) × (days elapsed ÷ days in period). This is the amount the buyer pays the seller on top of the price, because the whole coupon goes to whoever holds the bond on the payment date. Enter the face value, the annual coupon rate, the number of coupons per year, the days since the last coupon and the days in the period.

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Bond Dirty Price

Computes the dirty price of a bond: the clean price plus the interest accrued since the last coupon. The clean price is what shows up in quotes, but what actually changes hands at settlement is the dirty price, because the buyer has to reimburse the seller for the interest already run up. The tool works out the accrued interest on a linear basis and adds it to the clean price, returning both parts. Enter the clean price, the face value, the annual coupon rate, the coupon frequency, the days since the last coupon and the days in the period.

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Option Color (Gamma Decay)

Computes the color of an option, the third-order Greek that shows how much the gamma changes with each passing day, all else equal. Since gamma measures how fast the delta moves, color tells you whether that speed is accelerating or slowing as expiry approaches, handy for anyone managing gamma positions near the exercise date, where an at-the-money option's gamma spikes. The result comes per year and per day, computed for a call with no dividends. Enter the spot price, the strike, the interest rate, the term in years and the volatility.

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Option Veta (Vega Decay)

Computes the veta of an option, the Greek that measures how much the vega changes with each passing day. Since vega captures the premium's sensitivity to volatility, veta shows whether that sensitivity is shrinking over time, and it does: near expiry vega tends to zero, so a call's veta is usually negative. It's a second-order Greek that helps anticipate how the volatility exposure will behave. The result comes per year and per day, for a call with no dividends. Enter the spot price, the strike, the interest rate, the term in years and the volatility.

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Call Dual Delta

Computes the dual delta of a call option: the premium's sensitivity to the strike price, that is, dC/dK. While ordinary delta measures the reaction to the underlying's price, dual delta measures how much the option would change if the strike were slightly different. For a call it equals −e^(−rT)·N(d2) and has a practical reading: in absolute terms it approximates the risk-neutral probability of the option finishing in the money. Enter the spot price, the strike, the interest rate, the term in years and the volatility.

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Option Lambda (Elasticity)

Computes the lambda of a call option, also called omega or elasticity: the percentage change in the premium for each one-percent change in the underlying's price. It's the delta times S/C, and it measures the leverage built into the option. A lambda of 6, for instance, means the option moves, in percentage terms, about six times faster than the stock, which is why options amplify gains and losses. Enter the spot price, the strike, the interest rate, the term in years and the volatility.

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Garman-Kohlhagen FX Put Price

Prices an FX put option with the Garman-Kohlhagen model, the currency-market version of Black-Scholes. As with the call, the foreign interest rate enters as a continuous dividend on the base currency: the premium is K·e^(−rd·T)·N(−d2) − S·e^(−rf·T)·N(−d1). The strike term is discounted by the domestic rate and the spot term by the foreign one. It's used to hedge against a currency falling or to speculate in that direction. Enter the spot rate, the strike, the domestic and foreign rates, the term in years and the volatility.

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Option Epsilon (Dividend Sensitivity)

Computes the epsilon of a call option, also called psi: the premium's sensitivity to the asset's continuous dividend yield, that is, dV/dq. The larger the expected dividend, the lower the call's value, because part of the asset's return leaks to whoever holds the stock rather than the option. That's why a call's epsilon is negative and equals −S·T·e^(−qT)·N(d1). It's the Greek that ties pricing to the dividend yield. Enter the spot price, the strike, the interest rate, the term in years and the volatility.

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Option Vera (DvegaDrho)

Computes the vera of an option, also called rhova: a second-order cross Greek that measures how much the vega changes when the interest rate moves, that is, the derivative of vega with respect to r. It's an obscure sensitivity, used by desks that need to understand how volatility exposure interacts with rate changes. The closed form is −vega·√T·d1/σ, and it's easy to get wrong: the correct version uses d1, not the product d1·d2. Enter the spot price, the strike, the interest rate, the term in years and the volatility.

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Parametric Expected Shortfall (CVaR)

Computes the Expected Shortfall (ES), also known as CVaR, by the parametric Gaussian method. While VaR answers what the minimum loss is in the worst cases, ES goes further and answers what the average loss is when the worst happens, summing what lies in the tail beyond the VaR. The formula is −μ + σ·φ(Φ⁻¹(c))/(1−c), with Φ⁻¹ the inverse normal. It's a coherent risk measure, required under Basel, precisely because it captures the severity of extreme losses. Enter the mean return, the standard deviation of returns and the confidence level.

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Bond Equivalent Yield (BEY)

Computes the Bond Equivalent Yield (BEY) of a discount instrument, such as a treasury bill sold below face value. The formula annualizes the percentage gain on the price paid on a 365-day basis: BEY = ((F − P)/P)·(365/t). It lets you compare, on the same ruler, a discount instrument with a coupon-paying bond. Be careful not to confuse it with the bank discount yield, which divides by face value and uses 360 days. Enter the face value, the purchase price and the days to maturity.

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Probability of Touch

Estimates the probability that an asset's price touches a given level (a barrier) before expiry, using the reflection-principle approximation: roughly twice the probability of finishing beyond the barrier, 2·N(−|d|), with d = ln(H/S)/(σ√T). It's the back-of-the-envelope calculation traders use for barrier options and for judging the chance of a stop being hit. It assumes zero drift; with high interest rates the real probability is a little higher. Enter the spot price, the barrier level, the volatility and the term.

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Long Call Butterfly Spread

Computes the outcome of a long call butterfly: buy one low-strike call, sell two middle-strike calls and buy one high-strike call, with equally spaced strikes. It's a bet that the asset will sit near the middle strike at expiry. The tool returns the net cost (debit), the maximum profit, the maximum loss (capped at the debit) and the two breakeven points. Enter the three strikes and the three call premiums.

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Long Straddle

Computes the cost and breakevens of a long straddle: buying a call and a put at the same strike and expiry. It's the classic volatility bet — you profit if the asset moves a lot in either direction, regardless of which way, and lose at most the premium paid if it stays put. The tool sums the two premiums and works out how far from the strike the asset must move to break even. Enter the strike and the call and put premiums.

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Long Strangle

Computes the cost and breakevens of a long strangle: buying a lower-strike put and a higher-strike call, both out of the money. It's a cheaper volatility bet than the straddle, because out-of-the-money premiums cost less — in exchange, the asset has to move further to turn a profit. The tool sums the premiums and works out the two breakeven points. Enter the put and call strikes and their premiums.

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FRA Settlement (Forward Rate Agreement)

Computes the settlement amount of an FRA (Forward Rate Agreement), the contract that locks in today an interest rate for a future period. At fixing, the contracted rate is compared with the market reference rate, and the difference is paid at the start of the period — which is why it's discounted: N·(L − R)·(d/B)/(1 + L·d/B). When the market rate exceeds the contracted one, the party who locked in gains. It's used to hedge loans and deposits against rate moves. Enter the notional, the contracted rate, the reference rate, the days in the period and the day-count basis.

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Modified Dietz Return

Computes a portfolio's return with the Modified Dietz method, which adjusts the result for deposits and withdrawals made mid-period. Instead of ignoring the cash that came in and out, it weights each flow by the time it stayed invested: R = (ending value − beginning value − flow)/(beginning value + flow·weight). It's an approximation of the time-weighted return widely used by managers before the era of daily calculation. Enter the beginning value, the ending value, the net flow and the flow's weight in the period.

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Breakeven Inflation Rate

Computes the breakeven inflation embedded in the gap between a nominal bond and an inflation-linked bond, using the exact Fisher equation: (1 + nominal)/(1 + real) − 1. It's the inflation rate that would equalize the return of the two instruments — above it, the linker wins; below it, the nominal one. The exact version avoids the error of the simple approximation (nominal − real), which overstates inflation by a few basis points. Enter the nominal yield and the real yield.

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Long Call Condor

Computes the outcome of a long call condor: buy one low-strike call, sell two middle-strike calls and buy one high-strike call. It's a cousin of the butterfly with a wider profit zone: you bet the asset will stay within a range rather than land exactly on a point. The tool returns the net cost, the maximum profit, the maximum loss and the two breakeven points. Enter the four strikes and the four call premiums.

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Iron Condor

Computes the outcome of an iron condor: selling a put spread and a call spread at the same time, collecting a net credit. It's the classic strategy for betting the asset will trade sideways while pocketing the premium with limited risk. The tool uses the credit received and the four strikes to return the maximum profit (the credit itself), the maximum loss and the two breakeven points. Enter the four strikes and the net credit received.

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Collar (Protective Collar)

Computes the outcome of a collar: holding a stock, buying a put as a protective floor and selling a call as a ceiling, using the call premium to fund the put. It's the cheap way to protect a gain without closing the position — in exchange, you give up the upside above the ceiling. The tool returns the net option cost, the maximum profit, the maximum loss and the breakeven. Enter the stock price, the put and call strikes and the two premiums.

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Covered Call

Computes the outcome of a covered call: holding a stock and selling a call on it to collect the premium. It's the most popular income strategy in the options market: you earn the premium now in exchange for capping your profit at the strike. The tool returns the maximum profit (if the stock is called away), the percentage return in that case, the breakeven and the maximum loss. Enter the stock price, the strike of the call sold and the premium received.

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Protective Put

Computes the outcome of a protective put: holding a stock and buying a put as insurance against a fall. The put sets a floor on the loss but costs the premium, which raises the breakeven. It's the most direct insurance for a long position: the upside stays unlimited, the downside is capped. The tool returns the maximum loss and the breakeven. Enter the stock price, the put strike and the premium paid.

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Effective Convexity (Numerical)

Computes the effective convexity of a bond by finite differences, repricing the instrument for an up and a down yield move: (V− + V+ − 2·V0)/(V0·Δy²). Unlike analytical convexity, the effective version works even for bonds with uncertain cash flows, such as those with embedded options, because it only needs the three prices. It complements duration to better estimate the price change in large rate moves. Enter the three prices and the yield change used.

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Iron Butterfly

Computes the outcome of an iron butterfly: selling a call and a put at the same central strike (the body) and buying a further-out call and put (the wings), collecting a net credit. It's a strong bet that the asset will finish right at the central strike, with a bigger credit than an iron condor but a narrower profit range. The tool returns the maximum profit, the maximum loss and the two breakeven points. Enter the central strike, the wing width and the credit received.

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Bear Put Spread

Computes the outcome of a bear put spread: buying a higher-strike put and selling a lower-strike put, paying a debit. It's a bearish bet with limited risk and cost — cheaper than buying the put alone, in exchange for a capped profit. The tool returns the cost (debit), the maximum profit, the maximum loss and the breakeven. Enter the two strikes and the respective put premiums.

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Bull Put Spread

Computes the outcome of a bull put spread: selling a higher-strike put and buying a lower-strike put, collecting a credit. It's a bullish (or neutral) bet that pockets the premium with risk capped by the bought put. The tool returns the credit received (maximum profit), the maximum loss and the breakeven. Enter the two strikes and the respective put premiums.

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Risk Reversal

Computes the net premium of a risk reversal: buying a higher-strike call and selling a lower-strike put, building a synthetic long position in the asset. Depending on the premium gap, the structure comes out as a debit (you pay) or a credit (you receive) — and when the two cancel, it becomes the classic zero-cost reversal. In FX, it also gauges the slope of the volatility smile. Enter the put and call strikes and the two premiums.

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Bond Price from YTM

Computes the price of a coupon bond from its yield to maturity, discounting all future coupons and the face value to present: P = C·[1 − (1+i)^(−n)]/i + F·(1+i)^(−n). It's the inverse of computing the YTM and the foundation of fixed-income pricing. When the coupon exceeds the YTM, the bond trades at a premium; when below, at a discount. The calculation divides coupon and yield by the payment frequency. Enter the face value, the coupon rate, the YTM, the years and the coupons per year.

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Box Spread (Arbitrage)

Computes the fair value and arbitrage of a box spread: combining a call spread and a put spread at the same strikes, creating a fixed payoff of (Kh − Kl) at expiry, equivalent to a riskless bond. The fair value is that payoff discounted: (Kh − Kl)·e^(−rT). If you set up the box for less than that, you lock in a risk-free profit. The tool returns the payoff, the fair value and the arbitrage against the cost you enter. Enter the two strikes, the rate, the term and the cost.

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Spread Duration (Numerical)

Computes the spread duration of a bond by finite differences, repricing the instrument for an up and a down move in the credit spread: (V− − V+)/(2·V0·Δs). While duration measures sensitivity to changes in the risk-free rate, spread duration isolates sensitivity to the credit spread, the premium the market charges for issuer risk. It's essential for managing credit portfolios, where spread risk often dominates. Enter the base price, the prices with higher and lower spread and the spread change used.

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G-Spread (Government Spread)

Computes the G-spread, the difference between a bond's yield and the yield of a government bond of comparable maturity. It's the most direct measure of a bond's credit risk premium: how much extra the market demands to lend to a corporate issuer instead of the treasury. The result comes in basis points, the standard unit of the credit market. Enter the bond's yield and the reference government bond's yield.

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I-Spread (Swap Spread)

Computes the I-spread, the difference between a bond's yield and the interpolated swap rate of the same maturity. It measures the bond's credit premium against the swap curve, which many consider a better reference than government bonds for pricing credit. The result comes in basis points. It's a cousin of the G-spread, but uses the swap rather than the government as the comparison base. Enter the bond's yield and the swap rate of the same maturity.

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Calendar Spread

Computes the net debit of a calendar spread, also called a horizontal spread: selling a short-dated option and buying a longer-dated one at the same strike. The strategy exploits the fact that the short option loses value to time (theta) faster than the longer one. The result is the cost of setting up the position. Enter the premium of the short option sold and that of the long option bought.

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Synthetic Forward (Put-Call Parity)

Computes the synthetic forward price implied by the prices of a European call and put with the same strike and expiry, via put-call parity: F = (C − P)·e^(rT) + K. Instead of starting from the spot price and cost of carry, it extracts the forward directly from the options market, which is useful for checking arbitrage between the two markets. Enter the call and put premiums, the strike, the interest rate and the term.

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Realized Yield with Reinvestment

Computes the realized compound (horizon) yield of a bond held to maturity, taking into account the actual reinvestment rate of the coupons. Unlike YTM, which assumes coupons earn the bond's own rate, this calculation uses the rate you can actually get when reinvesting — hence the concept of reinvestment risk. It adds the future value of reinvested coupons to the principal and returns the annualized yield (BEY and effective annual). Enter the face, the coupon per period, the reinvestment rate, the periods, the purchase price and the periods per year.

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Margin of Safety (Investing)

Computes the margin of safety of an investment: how far the market price sits below the estimated intrinsic value, as a percentage. It's the core concept of Benjamin Graham's value investing — buying an asset for well less than it's worth to build in protection against estimation errors and surprises. The larger the margin, the more comfortable the purchase. A negative margin means the price already exceeds the estimated value. Enter the intrinsic value and the market price.

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Equity Risk Premium (ERP)

Computes the equity risk premium: the extra return expected from investing in stocks rather than the risk-free rate. It's simply the expected market return minus the risk-free rate, and it serves as the central building block of the CAPM, multiplied by beta to estimate an asset's required return. The larger the premium, the more the market charges to take on equity risk. Enter the expected market return and the risk-free rate.

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Bid-Ask Spread

Computes the bid-ask spread of an asset: the difference between the ask (sell) price and the bid (buy) price, the midpoint between them and the spread as a percentage of that midpoint. The spread is the invisible cost of trading and a direct measure of liquidity: liquid instruments have a tight spread, illiquid ones a wide spread. As a percentage, it lets you compare the cost across assets of different prices. Enter the bid and ask prices.

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Breakeven Tax Rate (Tax-Free vs Taxable)

Computes the breakeven tax rate between a tax-free bond and a taxable one: the rate at which the after-tax return of the two becomes equal, t* = 1 − (tax-free yield / taxable yield). Above that rate, the tax-free bond (like a municipal) pays off more; below it, the taxable one is worth it even after tax. It's the calculation that decides between the two based on your tax bracket. Enter the yields of the tax-free and taxable bonds.

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Cost of Preferred Stock

Computes the cost of capital of a preferred stock: the fixed annual dividend divided by the stock's market price, as a percentage. Since preferred stock usually pays a constant dividend, it behaves like a perpetuity, and its cost is the yield on that dividend. This figure goes into the WACC calculation as the cost of the preferred-capital slice. Enter the annual dividend and the preferred stock's price.

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Capital Gains Yield

Computes the capital gains yield of an asset: the percentage price appreciation between the start and end of the period, (P1 − P0)/P0. It's the part of the total return that comes from the price change, not counting dividends — added to the dividend yield, it gives the stock's total return. It serves to separate how much of the gain came from appreciation and how much from income. Enter the starting price and the ending price.

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Effective Spread (Microstructure)

Computes the effective spread of a trade: twice the distance between the price at which the trade actually executed and the midpoint between the best bid and best ask at that moment. Unlike the quoted spread, which measures the bid-ask difference, the effective spread captures the real cost the investor paid, accounting for where the order actually filled in the book. The result comes in absolute value and as a percentage of the midpoint. Enter the trade price and the midpoint.

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Portfolio Turnover Ratio

Computes the turnover ratio of a portfolio or fund: the lesser of total purchases and total sales over the period, divided by average net assets, as a percentage. It's the standard measure of how much a portfolio is traded — a turnover of 100% means that, on average, the whole portfolio was swapped once in the year. High turnover usually signals more transaction costs and taxes. Enter total purchases, total sales and average net assets.

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Appraisal Ratio (Treynor-Black)

Computes the Treynor-Black appraisal ratio: a manager's alpha divided by the standard deviation of residual risk, the part not explained by the market. It measures the quality of security selection per unit of specific risk taken, and is the central metric for deciding how much to allocate to an active strategy. The higher it is, the better the manager extracts abnormal return without taking on too much diversifiable risk. Enter the alpha and the residual standard deviation.

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Cost of Equity (Bond Yield Plus Premium)

Estimates the cost of equity using the bond yield plus risk premium method: it adds to the company's own long-term debt yield a risk premium for the gap between stocks and bonds. It's a quick alternative to the CAPM, useful when you lack a reliable beta: if the company pays 8% on its debt and the typical equity-over-debt premium is 4%, the cost of equity comes to around 12%. Enter the debt yield and the risk premium.

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Sterling Ratio

Computes the Sterling ratio, a drawdown-adjusted performance measure. It divides return by a measure of how much the portfolio typically falls from peak to trough, rewarding strategies that deliver return without big drops. The tool shows two versions: the modern one, using excess return over the risk-free rate divided by the average drawdown, and the original Deane Sterling Jones form, which adds a ten percent constant to the denominator. Enter the annualized return, the risk-free rate and the average annual maximum drawdown.

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Implementation Shortfall

Computes the implementation shortfall of a buy order, André Perold's concept that measures the gap between the return of a paper portfolio executed instantly at the decision price and that of the actually executed portfolio with all costs. It separates the execution cost (price impact and commissions) from the opportunity cost of the shares that went unfilled. The result comes in money, percentage and basis points, always as a cost (positive is worse). Enter the decision price, the execution price, the quantities, the commissions and the final price.

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VWAP (Volume-Weighted Average Price)

Computes the VWAP, the volume-weighted average price of a sequence of trades: the sum of price times volume divided by the sum of volumes. Unlike a simple average, the VWAP gives more weight to prices where more trading happened, reflecting the real average price paid over the period. Traders use it as an execution benchmark — buying below the VWAP is considered a good entry. Enter the lists of prices and corresponding volumes, separated by commas.

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Maximum Drawdown from Series

Computes the maximum drawdown of a series of values or prices: the largest percentage fall from a peak to the following trough across the whole history. It's the most intuitive measure of a strategy's risk — how much, at the worst moment, the investor would have seen their capital shrink from the top. Unlike the two-point version, this one scans the entire series and finds the worst stretch automatically. Enter the series of values separated by commas.

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Pain Index

Computes the pain index of a series: the average depth underwater, that is, the mean of all point-by-point drawdowns across the history. While the maximum drawdown looks only at the worst moment, the pain index measures the average suffering — how long and how deep the portfolio stayed below its peaks. It's a cousin of the ulcer index, which uses the root mean square instead of the simple average. Enter the series of values separated by commas.

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Batting Average

Computes a manager's batting average: the percentage of periods in which the portfolio's return beat the benchmark's. Borrowed from baseball, the concept measures consistency, not magnitude — a manager who beats the index in seven of ten months has a 70% batting average. It's useful for telling apart those who win often from those who depend on a few exceptional months. Enter the lists of portfolio and benchmark returns, in the same order.

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Market Value Added (MVA)

Computes the Market Value Added (MVA): the difference between a company's total market value and the capital investors put into it. It measures how much wealth management has created (or destroyed) above the money invested — a positive MVA means the market values the company at more than it cost to build. It's the long-run counterpart of EVA, which measures value creation year by year. Enter the market value and the invested capital.

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Residual Income

Computes a company's residual income: net income minus a charge for the use of equity capital, equal to the capital times the required cost of capital. The idea is that accounting profit doesn't tell the whole story — value is only created when earnings exceed what shareholders could earn elsewhere at the same risk. A positive residual income signals a return above the cost of capital. Enter the net income, the equity capital and the cost of equity.

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Tracking Error

Computes a portfolio's tracking error: the standard deviation of the differences between the portfolio's returns and the benchmark's, period by period. It measures how much the portfolio diverges from its reference index — an index fund aims for tracking error near zero, while an active fund has a higher one, reflecting its bets. It's the denominator of the information ratio. Enter the lists of portfolio and benchmark returns, in the same order, separated by commas.

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Information Coefficient (IC)

Computes the information coefficient (IC): the correlation between the returns (or rankings) predicted by a model and those actually realized. It's the measure of predictive skill at the heart of the fundamental law of active management — an IC of zero means worthless forecasts, and the closer to one, the better the signal anticipates the future. In practice, real ICs tend to be low, around 0.05 to 0.15. Enter the lists of predicted and realized values, in the same order.

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Tail Ratio

Computes the tail ratio of a return series: the absolute value of the 95th percentile divided by that of the 5th percentile. It compares the size of extreme gains with extreme losses — a tail ratio above one means the right tail (gains) is larger than the left (losses), a desirable asymmetric profile. Below one, extreme losses dominate. It's a quick snapshot of the asymmetry at the ends of the distribution. Enter the list of returns separated by commas.

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Roll Spread Estimator

Computes Roll's effective spread estimator from a price series: 2 times the square root of the negative serial covariance between consecutive price changes. The intuition, from Richard Roll in 1984, is that the back-and-forth between buying and selling (the bid-ask bounce) creates a negative correlation in very short-term returns, and the size of that correlation reveals the implied spread. When the covariance isn't negative, the estimator is undefined and returns zero. Enter the price series.

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Burke Ratio

Computes the Burke ratio: the excess return over the risk-free rate divided by the square root of the sum of squared drawdowns. Unlike the Sharpe ratio, which penalizes all volatility, Burke focuses only on the falls, and by squaring each drawdown it punishes deep falls more than shallow ones. It's one of the tail-risk-adjusted performance metrics. Enter the portfolio return, the risk-free rate and the list of drawdowns in percent.

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Martin Ratio (UPI)

Computes the Martin ratio, also called the Ulcer Performance Index (UPI): the excess return over the risk-free rate divided by the ulcer index. The ulcer index is the root mean square of drawdowns, a measure of how deep and how long the portfolio stays below its peaks. The Martin ratio thus rewards the return earned per unit of that tail pain. Enter the portfolio return, the risk-free rate and the ulcer index, all in percent.