Switching From Software or Science

A share is not a claim on a company's buildings. It is a bundle of three things, a residual claim on whatever is left after everyone else is paid, a cap on your losses, and a vote, and the residual part is what makes equity behave the way it does.

An American Depositary Receipt is a US-listed claim on foreign shares held in a vault abroad, when the two prices drift apart, a depositary bank's conversion mechanism lets an arbitrageur create or cancel ADRs to pull them back together.

A stock's price drops by roughly the dividend on the ex-dividend date, a mechanical, predictable event that traders try to exploit around, and that options markets price in well before it happens.

The default way to build an index is to weight each stock by its market value, but that isn't the only choice, equal weighting and other alternative schemes trade off diversification, turnover and performance in very different ways.

An ETF tracks what it holds because a handful of large firms can always swap a basket of the underlying shares for brand-new ETF shares, or hand ETF shares back and take the basket. That swap is an arbitrage valve, and it is the whole reason an ETF is not just another closed-end fund.

An index is a rule, not a fact. The choice of which companies count and how much each one counts decides what "the market did today" means, and three sensible rules applied to the same four stocks can give three different answers.

Before an IPO prices, the underwriters spend a week collecting orders at different prices from investors, that order book, and who gets how much stock out of it, is how the offer price actually gets set.

A poorly-run public company is a standing invitation for someone else to buy it and replace management, takeover defences are the legal tools boards use to slow that down or price it up.

Every short sale starts with borrowing the stock first, a large, mostly invisible rental market where the fee is set by how scarce the shares are to borrow, not by anything happening in the price chart.

The extra return investors expect for holding stocks instead of a safe government bill. It is the single most important number in finance and nobody knows what it is, because it has to be estimated from data so noisy that a century of history still leaves the answer blurry.

When a stock is added to a major index like the S&P 500, trillions of dollars of passive money are forced to buy it on a fixed date, a predictable, price-insensitive demand shock that tends to push the price up before the buying even happens.

US stock trades used to settle two business days after the trade; since May 2024 they settle in one, a change that sounds administrative but compresses the entire window brokers, custodians and foreign investors have to move cash and shares.

Small-cap stocks often look cheap and undercovered on paper, but their thin trading volume means the cost of actually buying and later selling a meaningful position can quietly erase the edge.

A bond's price is just the present value of the cash it promises. The wrinkle is that the price you see quoted is not the price you pay, because the seller is owed the slice of the next coupon they sat through.

A repo is a short-term loan wearing the clothes of a sale. You hand over bonds, take in cash, and agree to buy the bonds back tomorrow at a slightly higher price. It is the plumbing that funds almost every leveraged bond position in the world.

The single interest rate that makes a bond's promised cash flows worth exactly its price. It is the bond market's universal comparison number, and it quietly assumes things that are almost never true.

How to turn a handful of quoted coupon bonds into a clean rate for every single future date. You solve one maturity at a time, each answer feeding the next, which is why it is called bootstrapping.

Betting that a yield curve steepens or flattens sounds like a single trade, but sizing the two legs by equal dollar notional (cash-neutral) versus equal dollar-value-of-a-basis-point (duration-neutral) produces two very different exposures to parallel rate moves.

A callable bond's cash flows change depending on where rates go, so ordinary duration, which assumes fixed cash flows, gives the wrong answer; effective duration fixes this by re-pricing the bond, option and all, at shifted rates.

A Brazilian government bond denominated in dollars and one denominated in reais can carry wildly different yields for the same issuer, because one asks you to bear only credit risk while the other stacks currency and local rates risk on top.

A bond whose cash flows come from thousands of home loans. Because every homeowner can repay early whenever they like, the investor is short a call option, and that one fact explains almost everything odd about how MBS behave.

Fit a smooth curve through a set of bond yields and the leftovers, the residuals, tell you which individual bonds are trading expensive or cheap relative to their neighbours, which is where curve relative-value trades come from.

A SOFR floating-rate loan does not know its own interest payment until the period is nearly over, because the rate is built by compounding each day's overnight rate after the fact, a genuine mechanical break from how LIBOR loans used to be set in advance.

A yield curve can be quoted three different ways, as spot rates, par yields, or forward rates, and each is a mechanical transformation of the same underlying discount factors, not a different opinion about interest rates.

Why does a ten-year bond yield more than a one-year bill? Either the market expects short rates to rise, or it is paying you to accept the risk of locking money up. Splitting the yield curve into those two pieces is one of the central problems in fixed income.

The US Treasury sells new debt through single-price auctions where every winning bidder pays the same clearing yield, and the gap between that yield and where the bond traded beforehand, the tail, is the market's own scorecard on how the auction went.

An affine term structure model builds the whole yield curve from a small number of underlying factors using a straight-line (affine) formula, which is why models like Vasicek and Nelson-Siegel can price every maturity from just two or three numbers.

Treasury market liquidity does not come from an exchange order book, it comes from dealers willing to warehouse bonds on their own balance sheets, and post-crisis capital rules mean that willingness now shrinks exactly when the market needs it most.

The expectations hypothesis says a steep yield curve should just mean rates are expected to rise, but a steep curve actually predicts positive excess returns on long bonds, evidence of a time-varying risk premium that forward rates only partly reveal.

A yield curve doesn't move as dozens of independent points, almost all of its motion decomposes into three simple shapes, level, slope and curvature, and hedging a rates book against just those three catches most of the risk with far fewer trades.

A Treasury futures contract and its cheapest-to-deliver bond are linked by a cash-and-carry trade, and the return that trade earns, the implied repo rate, tells a trader whether the futures basis is worth buying or selling against actual overnight funding costs.

There is no direct, liquid market for most currency pairs on earth. Traders instead route through the US dollar as a common intermediate step, and the price you see for an exotic pair is usually built, not quoted, from two dollar legs.

Every FX price is one currency measured in another, so the first thing you must know is which is which. Base versus quote currency, pips, big figures, and which side of the spread you are on.

When dollar funding markets freeze abroad, the Federal Reserve lends dollars directly to other central banks, who then relend them to banks in their own jurisdiction, a backstop built to stop a local shortage from becoming a global crisis.

If you can lock in every step of a round trip through another currency, the outcome has to match simply staying at home. That single no-arbitrage condition pins the forward exchange rate to the two interest rates.

Many currencies are not pegged to a single dollar rate but managed against a weighted basket of trading partners, and allowed to drift inside a band that itself moves over time.

A forward locks in an exchange rate today for settlement on a future date. Dealers do not quote the rate itself, they quote the small adjustment to spot called forward points, and that number comes from the interest-rate gap rather than from any view on the currency.

An FX swap lets you borrow one currency by posting another as collateral, and the swap points you pay back out embed an interest rate, often a cheaper or more available one than borrowing directly.

A single security can carry four different identifiers at once, a global ISIN, a US CUSIP, a UK SEDOL and a market-specific ticker, because each was built for a different purpose, and confusing them is a routine source of trade breaks.

The last trade of the day and the exchange's official closing price are usually the same number, but not always, the closing auction exists precisely because a single last print can be an outlier, and most of the money in the market marks its books to the auction price, not the last tick.

A stock is quoted in dollars, a bond in yield or price-per-hundred, a swap in a spread, and an FX pair as a ratio, the same underlying idea of "what does it cost" takes a different quoting convention in every asset class, and mixing them up is a fast way to misread a screen.

Every corporate action a company can announce sorts into one of a handful of standard categories, mandatory, voluntary or mandatory-with-choice, and knowing which category an event falls into tells you immediately what a data feed, a back office and a shareholder each have to do about it.

A CCP steps into the middle of every cleared trade so that neither original party ever has to trust the other again, the mechanism that does it, novation, is what makes modern derivatives and repo markets survivable when a large member fails.

Index providers sell licences to a set of published rules, not to the securities themselves, a business model that turns "which stocks are in the S&P 500" into a recurring revenue stream and a source of real, tradeable market impact around every reconstitution.

Clicking buy is the easy part. Behind every trade is a chain of routing, matching, clearing and settlement that takes a verbal agreement to trade and turns it into an actual, legally final change of ownership.

A custodian is the institution that actually holds a fund's securities and cash, settles trades, collects income and keeps the official books, quiet infrastructure work that almost nobody outside operations ever thinks about until it fails.

A prime broker is the bank that lends a hedge fund cash and stock, holds its collateral, clears its trades away from a single executing broker, and in the process becomes one of the fund's largest single points of failure.

Different regulators have jurisdiction over different products and different geographies, a US equity option, a US futures contract and a UK-listed stock can each answer to a different regulator, and knowing which one matters the moment something goes wrong.

A central counterparty absorbs a defaulting member's losses through a strict, pre-agreed order of resources, and the CCP's own capital is deliberately placed in that queue so it shares the pain before its members do.

Before any model tells you what an option is worth, pure logic tells you what it cannot be worth. A handful of inequalities pin every option price into a band, and a quote outside that band is free money you can collect without a forecast.

The whole option chain at one expiry contains the market's entire probability distribution for where the underlying will land, not just its average and its spread. Differentiate the call price twice with respect to strike and the distribution falls out.

An option's bent payoff can be manufactured out of shares and cash, provided you keep adjusting the mix as the price moves and never add or remove money along the way. The cost of setting that machine running on day one is the option's fair price.

A set of prices contains no free money if and only if you can find a set of made-up probabilities that reprices everything as a fair bet. That equivalence is the theorem the whole derivatives industry stands on, and a second half tells you when those probabilities are unique.

Black-Scholes assumes you can rehedge continuously for free. In reality every rehedge costs money, so a trader has to pick how often to touch the hedge, too rarely and the hedge tracks poorly, too often and fees eat the position alive.

A hedge you set up once and never touch again is a static hedge; one you have to keep rebalancing as the market moves is dynamic. The choice between them is a trade-off between transaction costs and model risk, not a question of which is 'better.'

A trading book's profit or loss on any given day is one number. PnL attribution splits that number into the pieces the Greeks predicted, delta, gamma, theta, vega, plus whatever is left over, which is the part nobody can explain yet.

A pricing model has knobs you cannot observe directly, like volatility. Calibration is the act of turning those knobs until the model's prices match the market's prices, so you can then use the model to price the things the market doesn't quote.

Hold an option and short exactly the right number of shares and the randomness cancels out. What is left cannot earn more than a bank deposit without creating free money, and writing that sentence down gives you the Black-Scholes equation.

Black-Scholes turns a volatility guess into a price, but the market only ever gives you a price. Getting volatility back out means solving the formula backwards, and there is no algebra that does it, only iteration.

Monte Carlo runs forward in time, but an early-exercise decision needs to know the value of waiting, which lives in the future. Longstaff-Schwartz breaks the deadlock by regressing what actually happened on simulated paths to estimate that value of waiting.

Every pricing model is wrong in some specific, knowable way, and the risk that this particular wrongness costs you real money, not the risk that the market moves, is model risk.

A Monte Carlo price wobbles, and brute force is an expensive cure, four times the paths only halves the error. Variance reduction buys the same accuracy from far fewer paths by pairing random draws and borrowing quantities whose true value you already know.

The matching engine is the only place a trade actually happens. It is a deterministic, single-threaded loop that takes messages in a fixed sequence, applies each one to an in-memory book, and emits the fills and quote updates the whole market then sees.

A passive order is a race between two clocks, the queue in front of you draining, and the price walking away. Estimating who wins is what decides whether you post or cross.

The mid-price sits halfway between the bid and the ask no matter how lopsided the book is. The microprice weights it by queue sizes, giving a fair value that leans toward the thin side, which is the side about to be eaten.

A fill that looks profitable against the spread can still be a loser once you check where the price went in the seconds after, a markout tracks exactly that, and it's the single most honest number a market maker has.

A market maker's daily P&L is one number, but it comes from at least four different sources that behave nothing alike, spread capture, rebates, inventory mark-to-market, and adverse selection, and lumping them together hides which part of the business is actually working.

A market maker sitting on unwanted inventory doesn't just wait it out, it nudges both quotes in the direction that encourages the market to take that inventory off its hands, accepting a worse expected price in exchange for less risk.

A market maker's revenue is the spread earned on fills, and the cost is inventory risk plus getting picked off by better-informed traders. The business only works if spread capture, repeated thousands of times a day, outruns those two costs.

The quoted spread is what you see; the effective spread is what a trade actually paid; the realised spread is what the liquidity provider actually kept once the price moved on afterward. The gap between effective and realised spread is a direct measure of price impact.

When a large order moves the price, part of that move sticks and part of it fades. Splitting the two tells you how much you paid for speed versus how much information you leaked.

Before an order is sent, a desk estimates what it will cost to trade, spread, impact, and the risk of prices moving while you wait, and uses that estimate to pick how fast to trade.

The same trade can be scored as a 22 bps loss or a 40 bps win depending on what you compare it to. Picking the benchmark is not a reporting decision, it is an instruction to the algo about what to optimise.

Every child order you send is evidence. If your slices are the same size, on the same venue, at the same cadence, other people work out what you are doing and the price moves before you get there. Leakage is the part of your cost that never comes back.

Every order is a trade-off between paying the spread now for a guaranteed fill (aggressive) and waiting in the queue for a better price that might never come (passive). The right choice depends on urgency and how likely you are to actually get filled.

You cannot backtest an execution algorithm the way you backtest a signal, your own order changes the very book you're trading against. Simulating execution means modelling queue position, fill probability, and impact, not just replaying historical prices.

Trading depresses the price, and then the book heals, new liquidity slowly refills the levels you just ate. Obizhaeva-Wang models that healing explicitly, which is what lets it say something Almgren-Chriss can't: trading fast and then pausing is different from trading slowly and steadily.

Once you can also hold cash, the whole efficient frontier collapses to a single best mix of risky assets plus a dial. That one mix is the tangency portfolio, and the straight line running through it is the capital market line.

If you can rebalance continuously and your appetite for risk does not change with how rich you are, the optimal fraction of your wealth to hold in a risky asset is a single constant, edge divided by risk aversion times variance, no matter your horizon or your bank balance.

The best portfolio to hold and the best portfolio to trade into are different things. Putting trading costs inside the optimizer, rather than subtracting them afterwards, produces a no-trade region and a partial-adjustment rule instead of a chase.

The diversification you counted on when you built the portfolio is measured in calm markets, and calm-market correlations are not the correlations that show up when everything actually goes wrong at once.

Instead of assuming a shape for tomorrow's losses, replay the last few hundred real market days through today's positions, sort the results, and read off the loss you exceed only rarely. Simple, popular, and quietly full of assumptions.

A trading book holds thousands of different instruments, but their risk comes from a few dozen shared drivers. Mapping is the translation step that rewrites every position as a set of sensitivities to those drivers, so the whole book can be aggregated and measured.

A VaR model makes a promise you can check: losses should breach the number on 1% of days and no more. Backtesting counts the breaches, and Kupiec's test decides whether the gap between promised and observed is ordinary bad luck or a broken model.

A precise way to answer "how much of the portfolio's total risk does this one position actually cause," using a mathematical property that guarantees the pieces add up exactly to the whole.

A statistical theory for the worst days specifically, built from the idea that the shape of extremes doesn't have to match the shape of the everyday, and that you can estimate a 1-in-1000-day loss from a lot fewer than 1000 bad days.

Instead of assuming everyone holds the market portfolio, this theory asks a weaker question, what expected returns must hold so that no combination of assets creates a free lunch, and gets a multi-factor pricing model out of that question alone.

The commercial template nearly every equity risk desk actually runs, style factors like value and momentum plus an industry classification, estimated fresh every day from a huge cross-sectional regression, turned into a full stock-by-stock covariance matrix.

Factor models shrink a huge stock-by-stock covariance problem down to a small factor-by-factor one, but that small matrix is still noisy, still time-varying, and still needs its own careful, separate estimation before you can trust any risk number built on top of it.

Two entirely different ways to build a factor model, one where you decide the factors first and let the data supply the exposures, the other where you let the data decide the factors and hope you can name them afterward.

Hundreds of "factors" claiming to predict stock returns have been published, more than any economic story can plausibly justify. This is the portfolio-construction side of that problem, what it means for anyone actually building a factor portfolio, not just for the academics arguing about it.

A hedge fund trades other people's money under a fee arrangement designed to align the manager's incentives with investor returns, understanding that arrangement explains most of how these firms actually behave.

Base salary, bonus, and P&L-linked pay work very differently across prop firms, hedge funds, and banks, the mix tells you as much about a firm's incentives as the headline number does.

Prop trading firms, hedge funds, banks, and asset managers all hire quants, but they pay for different skills, take different risks, and feel very different to work inside, a map of who's who before you specialize your prep.

Prop firms trade only their own capital, mostly in liquid exchange-traded products, and their whole hiring and culture model, fast, meritocratic, high-variance, follows from that one fact.