Course A · Introduction to Quant Finance

Glossary

5

5-standard-deviation day: a day 5 or more standard deviations from the average, either way; a bell puts about 0.57 days in a million there, about once in 6,922 years of 252 trading days A6 Fat tails

A

Account line: the account after each trade (traders call it the equity curve) A21 What is a backtest?
Annualised volatility: volatility per year: daily volatility × √252 A8 Volatility: how wide is luck?
Arithmetic mean: the plain average of the returns A14 Compounding and the asymmetry of losses
Ask: the lowest price a waiting seller accepts: what you pay to buy now A12 Markets and prices
Average win / average loss: the size of a typical winning / losing trade A1 Expectancy: why win rate isn't the point

B

Backtest: a trading rule run over past prices to see what it would have done, trade by trade A1 Expectancy: why win rate isn't the pointalso in A4, A21
Band: the range that holds the middle 95 in 100 samples' results A10 Sample size: why 10 trades say little
Best bid / best ask: the highest price a buyer is offering / the lowest price a seller is asking A13 Orders: market, limit and stop
Beta: how far one series tends to move for each 1% the other moves: the steepness of the line, which the correlation leaves out A11 Correlation and diversificationalso in A22
Bid: the highest price a waiting buyer pays: what you get to sell now A12 Markets and prices
Birthday problem: the chance that at least two people in a group share a birthday A25 Getting in, and what to learn next
Bond: a loan that can be bought and sold, with fixed payments promised by the borrower A15 Time value, interest rates and bonds
Break-even cost: the cost that leaves the average trade at $0; it equals the gross edge A16 Costs
Break-even win rate: the win rate at which the average trade makes nothing: an expectancy of zero A1 Expectancy: why win rate isn't the pointalso in A16

C

Call / put: the right, not the duty, to buy / to sell the underlying at the strike at expiry A23 Forwards, futures and options
Candle (OHLC bar): one window's open (first trade), high, low and close (last trade); body from open to close, wicks to the high and the low; empty if it closed higher, filled if lower A12 Markets and prices
Chance (probability): how often something happens if you repeat it many times, from 0 (never) to 1 (always) A4 Probability with coins
Commission: the broker's fee for each trade A16 Costs
Compounding: each return multiplies the account, so returns multiply over time rather than add up A14 Compounding and the asymmetry of lossesalso in A15
Confounder: a third series that moves two others, giving them a correlation though neither moves the other A11 Correlation and diversificationalso in A22
Correlation: the covariance divided by both standard deviations: from −1 to +1, the strength of a straight-line link only, for that sample A11 Correlation and diversification
Costs: fees and worse-than-shown prices, taken off each trade's result A21 What is a backtest?
Coupon: a bond's regular interest payment A15 Time value, interest rates and bonds
Covariance: the average product of two series' distances from their averages, dividing by n − 1; positive when they tend to land on the same side of their averages together A11 Correlation and diversification

D

Daily loss limit: a risk limit on one day's loss, measured from the value when the day began A20 Rules as risk limits
Derivative: a contract whose value depends on the price of something else, its underlying A23 Forwards, futures and options
Development: building the systems: data, backtests and the programs that send orders A3 What quants do
Discounting: working from a later amount back to its present value, by dividing by (1 + rate) once for every year A15 Time value, interest rates and bonds
Distribution: where results land, and how often A5 The bell curve
Diversification: lowering risk by mixing things that don't move as one; for a 50/50 mix it is largest at a correlation of −1 and gone at 1, if the correlation is the same throughout A11 Correlation and diversification
Down day / up day: a day the price ends lower / higher than the day before A21 What is a backtest?
Drawdown: how far an account is below its peak, as a percent of the peak; 0% at a new peak A17 Drawdown
Duration: a measure of how strongly a bond's price moves when rates change; longer when its payments come later A15 Time value, interest rates and bonds

E

Edge: what each 1R staked makes on average; a fair coin has none A19 Ruin: why doubling down goes broke
Edge (gross): the average profit of one trade before costs A16 Costs
Evaluation (challenge): a paid test sold by a prop firm (a company selling trading evaluations to individual traders): an account the firm provides, often simulated, traded under fixed rules A20 Rules as risk limits
Excess kurtosis: the average fourth power of the z-scores, minus 3: 0 for a bell, above 0 for fatter tails; driven by the few most extreme days, so it varies widely on short samples A6 Fat tails
Expectancy (expected value): the average result per trade A1 Expectancy: why win rate isn't the point
Expected value after costs: the average result per trade once the cost of every trade is taken off A3 What quants do
Expected waiting time: the average number of tries until something happens, over very many rounds A25 Getting in, and what to learn next

F

Face value: the amount borrowed, paid back with a bond's last coupon A15 Time value, interest rates and bonds
Fair coin: heads and tails equally likely: ½ each A4 Probability with coins
Fat tails: more days far from the average than a bell curve with the same standard deviation has A6 Fat tails
Fill: an order turning into a trade, and the price it traded at A13 Orders: market, limit and stop
First-step analysis: one equation per state: one try, plus each outcome's chance times the average wait from where it lands A25 Getting in, and what to learn next
Fixed amount: risking the same money on every trade A18 Position sizing
Fixed fraction (fixed-fractional sizing): risking the same share of the account on every trade, so the money at risk shrinks after losses and grows after gains A18 Position sizing
Forward contract: a promise to buy or sell later at a price agreed today A23 Forwards, futures and options
Future value: what an amount today grows to by a later date at a given rate A15 Time value, interest rates and bonds
Futures contract: a forward with standard terms, traded on an exchange, settled every day A23 Forwards, futures and options

G

Gambler's fallacy: expecting a streak to end (or go on) because of the results before it A4 Probability with coins
Gambler's ruin: the chance of reaching a target before going broke, betting a fixed amount on each flip A25 Getting in, and what to learn next
Gambler's ruin problem: which an account reaches first, a set gain or a set loss A20 Rules as risk limits
Gap: a jump in price with no trades in between, often from one day's close to the next open A13 Orders: market, limit and stop
Geometric mean: the steady return per period that reaches the same end: the growth you actually got (also: compound growth rate) A14 Compounding and the asymmetry of losses
Growth factor: new ÷ old: what the account is multiplied by (1.5 for +50%) A7 Returns, three ways

H

Hedging / speculating: taking a contract that cancels a price risk you already have / taking the price risk on purpose A23 Forwards, futures and options
Held-out data: prices kept aside while a system is adjusted, to check it on prices it never used (lesson B9) A24 Capstone: read a strategy claim

I

Independent: one result doesn't change the chance of the next A4 Probability with coins
Independent steps: each step ignores the ones before it, like a fair coin A2 Random walks: can prices be predicted?
Interest rate: what a borrower pays for one year's use of money, as a percent of the amount A15 Time value, interest rates and bonds

L

Law of large numbers: as trades add up, the average result per trade settles toward the expectancy A1 Expectancy: why win rate isn't the pointalso in A10
Least squares: fitting a line by making the sum of its squared misses as small as possible A22 Regression
Length of a drawdown: how many values in a row (months, trades) sat below its peak A17 Drawdown
Leverage: controlling more than the money put down, so gains and losses on that money are a multiple of the price's move A23 Forwards, futures and options
Limit order: fills only at its limit price or better; may never fill A13 Orders: market, limit and stop
Linear regression: fitting a least-squares line: one input, or several, each with its own slope A22 Regression
ln and eˣ: the natural logarithm, which turns multiplying into adding, and the key that undoes it A7 Returns, three ways
Log return: ln of the growth factor; log returns add up over time A7 Returns, three ways
log₂ n: the power of 2 that gives n; about the longest streak in n fair flips A4 Probability with coins
Long / short: the side that agreed to buy / to sell A23 Forwards, futures and options
Look-ahead bias: a backtest using something not yet known when a trade was made (lesson B2) A24 Capstone: read a strategy claim

M

Margin: money each side of a futures contract deposits with the exchange; the daily gains and losses are paid from it A23 Forwards, futures and options
Margin of error: how far either side of the true value the results of about 95 samples in 100 land; for a win rate, about 100 ÷ √n points A10 Sample size: why 10 trades say little
Market: a place where buyers and sellers trade the same thing A12 Markets and pricesalso in A21
Market order: fills now, at the other side's best price A13 Orders: market, limit and stop
Martingale: double the stake after every loss, back to 1R after a win A19 Ruin: why doubling down goes broke
Maturity: the time left until a bond's last payment A15 Time value, interest rates and bonds
Maximum drawdown: the deepest drawdown in an account's history: the largest fall from a peak to a later trough A17 Drawdown
Maximum loss: a risk limit on the whole account: at its line the account stops for good A20 Rules as risk limits
Mean (μ): the average result, the middle of the bell; 0 with no edge A5 The bell curve
Mid: halfway between the bid and the ask A12 Markets and prices
Model: the made-up world a simulation plays out: its rules and their chances A9 Monte Carlo: answer a question by simulating it
Model risk: the risk of acting on a model that is wrong; in this lesson's simulation a bell-based model was most wrong about the rarest, largest days A6 Fat tails
Monte Carlo simulation: answering a question by playing out a model many times with random numbers and counting what comes out A9 Monte Carlo: answer a question by simulating it
Multiplication rule: for independent events, the chance that all happen is the product of their chances A4 Probability with coins

N

Net: what is left after costs A16 Costs
Normal distribution: the bell curve; the shape of a total of many small, separate random effects (the central limit theorem) A5 The bell curve

O

Order book: the orders waiting to trade: bids (to buy) and asks (to sell), with prices and sizes A13 Orders: market, limit and stop
Overfitting: a fit that matches noise in the data used, so it looks better there than on new data A22 Regression

P

Payoff: what a contract pays at its end, worked out from the price then A23 Forwards, futures and options
Peak: the highest value an account has reached so far, its starting value included A17 Drawdown
Percent return: the change as a share of where the period started A14 Compounding and the asymmetry of losses
Percent-risk position sizing: choosing the number of shares so that a sale at the stop loses a set share of the account A18 Position sizing
Percentage point: the gap between two percentages: from 51.8% to 52.0% is 0.2 points A9 Monte Carlo: answer a question by simulating it
Percentage return: P_sell ÷ P_buy − 1: the price move as a share of the buy price A21 What is a backtest?
Point: one percentage point: 40% to 50% is 10 points A10 Sample size: why 10 trades say little
Position size: what a trade's shares cost: shares × the price paid for one A18 Position sizingalso in A21
Position sizing: deciding how much each trade buys, and so how much it risks A18 Position sizing
Present value: what an amount paid later is worth today at a given rate A15 Time value, interest rates and bonds
Price: the price of the last trade A12 Markets and prices
Pricing: working out what a contract, such as an option, is worth A3 What quants do
Proprietary trading firm: a firm that trades only its own money, with no outside clients; not the retail “prop firm” evaluations A3 What quants do
Put–call parity (payoff form): at expiry, a call's payoff minus a put's, same strike, equals the price minus the strike A23 Forwards, futures and options

Q

Quant: short for quantitative analyst: someone who uses numbers, statistics and code to make decisions about prices and risk A3 What quants doalso in A25

R

R: a fixed amount of money, the same on every trade; results are counted in it A1 Expectancy: why win rate isn't the point
R (R-multiple): a result in units of its risk: result ÷ risk A7 Returns, three ways
Random walk: a running total of random steps: the price is the start plus every step so far A2 Random walks: can prices be predicted?also in A9
Record: a value more extreme than every one before it, such as a new deepest drawdown A17 Drawdown
Research and trading: finding patterns in data and testing whether they are worth acting on after costs A3 What quants do
Risk: measuring how much a firm's holdings could lose, and setting limits on it A3 What quants doalso in A7
Risk limit (cap): a line set before trading starts: when losses reach it, trading stops; reaching it is a breach A20 Rules as risk limits
Round: from a 1R stake to its first win (won, 1R up) or to broke; lost if the ladder ran out A19 Ruin: why doubling down goes broke
Round trip: a buy and the sell that undoes it; at once, it costs the spread on every share A12 Markets and prices
Ruin: losing the whole account: a broke account can't trade again A19 Ruin: why doubling down goes broke
Ruined: an account that falls to 0R: it stops trading A1 Expectancy: why win rate isn't the point
Run: one play of the model: one game of four rolls, one simulated year, one account A9 Monte Carlo: answer a question by simulating it
Rung: one doubling of the stake; the account pays for only so many A19 Ruin: why doubling down goes broke
R²: the share of y's spread (squared distances from its average) the line removes, on the data it was fitted to; not a measure of cause A22 Regression

S

Sample: the trades you happened to get, standing in for all the trades a strategy could make A10 Sample size: why 10 trades say little
Sample size (n): the number of trades in a sample A10 Sample size: why 10 trades say little
Sample standard deviation (s): the standard deviation with the sum divided by n − 1 instead of n, for a few numbers standing in for many A8 Volatility: how wide is luck?
Scatter plot: a chart of pairs, one dot each: across for one series, up for the other A11 Correlation and diversification
Sell side / buy side: firms that make, sell and trade financial products for clients (mostly banks) / firms that invest money (asset managers, hedge funds) A3 What quants do
Set of markets: every market the rule ran on, read together A21 What is a backtest?
Simple (percent) return: the change as a share of the start: new ÷ old − 1 A7 Returns, three ways
Slippage: getting a different price from the one you planned: fill − intended price (for a buy a positive number is the worse price; for a sell, a negative one) A13 Orders: market, limit and stopalso in A16
Slope / intercept: how far the line rises for each 1 that x moves / the line's value where x is 0 A22 Regression
Spread: the ask minus the bid A12 Markets and pricesalso in A13, A16
Square root (√): the number that, multiplied by itself, gives the number: √400 = 20 A2 Random walks: can prices be predicted?
Square-root rule: with independent, same-size steps that average 0, the typical distance grows with √steps A2 Random walks: can prices be predicted?
Stake: what you put on one trade: a win pays it, a loss takes it A19 Ruin: why doubling down goes broke
Standard deviation (σ): how far a typical result lands from the mean: the width of the bell (precisely, the square root of the average squared distance from the mean) A5 The bell curvealso in A8
Standard error (Monte Carlo error): how far a simulated answer typically lands from the answer endless runs of the same model would give; it measures luck in the runs, not whether the model is right A9 Monte Carlo: answer a question by simulating it
Standard error of the slope: the typical distance of a measured slope from the true one, estimated from one sample when the days are independent A22 Regression
Static limit: a maximum loss measured from the starting value; its line never moves A20 Rules as risk limits
Stop: the price, set before the buy, at which a trade sells if it goes wrong A7 Returns, three ways
Stop order (stop-loss): waits until the price reaches the stop, then becomes a market order A13 Orders: market, limit and stop
Streak (run): a run of the same result, for as long as it lasts A4 Probability with coins
Strike / expiry / premium: an option's fixed price / its last day / what its buyer pays up front A23 Forwards, futures and options
Student's t distribution: a family of hill-shaped curves set by its degrees of freedom ν: a small ν gives fat tails, a large one is close to the bell A6 Fat tails
Support: a level a price keeps falling to and bouncing up from; coin walks draw them too A2 Random walks: can prices be predicted?
Swing: how far a typical return sits from the average; its textbook name is the standard deviation (lesson A8) A14 Compounding and the asymmetry of losses

T

The research loop: question, data, test, decision; the decision raises the next question A3 What quants do
Time value of money: a euro now is worth more than a euro later, because it can earn interest meanwhile (with a positive rate) A15 Time value, interest rates and bonds
Time window: a stretch of time of fixed length: a minute, an hour, a day A12 Markets and prices
Trade: a buyer and a seller agree on a price, and the seller's shares go to the buyer at it A12 Markets and prices
Trade and result: one buy and one sell; what came back minus what went in A21 What is a backtest?
Trade list: every trade the backtest took A21 What is a backtest?also in A24
Trading rule: a fixed instruction: an entry (when to buy) and an exit (when to sell) A21 What is a backtest?
Trailing limit: a maximum loss measured from the peak; its line follows the account up, never down A20 Rules as risk limits
Transaction costs: what one trade costs, win or lose: commission, the spread and slippage A16 Costs
Trough: the lowest point of a drawdown, before the account climbs back A17 Drawdown
Typical distance: the square root of the average squared distance from the start (lesson A9 gives it its textbook name, the standard deviation) A2 Random walks: can prices be predicted?

U

Under water: below the peak so far; time under water is the share of an account's history spent there A17 Drawdown
Underwater chart: an account's drawdown drawn at every step, hanging below 0% A17 Drawdown

V

Variance (σ²): the average squared distance from the mean A8 Volatility: how wide is luck?
Volatility: the standard deviation of returns; daily volatility uses daily returns A8 Volatility: how wide is luck?
Volatility drag: the gap between the arithmetic and the geometric mean, caused by the swings A14 Compounding and the asymmetry of losses

W

Win rate / loss rate: the share of trades that win / lose; together they make 100% A1 Expectancy: why win rate isn't the point

Y

Yield: the one rate at which a bond's payments, discounted, add up to its price (in full: yield to maturity) A15 Time value, interest rates and bonds
Yield curve: the yields of one borrower's bonds plotted against their maturities: normal (rising), flat or inverted (falling) A15 Time value, interest rates and bonds

Z

z-score: a result's distance from the mean, in standard deviations A5 The bell curve