Every concept, endless questions
Each concept is a small financial model. Read how it works, then draw a real interview question from it: forwards, backwards or what-if, with fresh numbers and a worked solution every time.
Forward runs a concept the usual way. Inverse runs it backwards, which is what separates understanding from memorizing.
Market Making
4 conceptsEdge capture on the spread
A market maker earns the spread only in theory. Each fill is worth half the spread against the mid at that instant — but fills are not random. You get lifted just before the price goes up and hit just before it goes down, because the people trading with you sometimes know something. The average move against you after a fill is adverse selection, and it comes straight out of the half-spread. What is left, plus any exchange rebate, is the edge you actually keep. That is why a tighter spread can still make more money if it wins enough volume — and why it can also turn every fill into a loss.
Skewing a quote for inventory
A market maker wants to earn the spread, not hold a position. When fills pile up on one side, the desk leans its quotes: long inventory means moving both the bid and the offer down, so the offer becomes the most attractive in the market (buyers come to you) and the bid becomes the least attractive (sellers go elsewhere). Short inventory is the mirror image. Skewing gives up a little edge on each unwinding trade in exchange for getting flat without crossing the spread. The bigger the position, the harder the lean — until the quote on the exit side reaches fair value and the desk is paying the whole edge to get out.
Adverse selection
A market maker cannot tell an informed trader from an uninformed one, so it prices every order as if it might be informed. A buy order is a small piece of evidence that the stock is worth more, so the break-even offer is the expected value given that someone wants to buy — above the mid. The more of the flow that is informed, and the bigger the news they know about, the wider the spread must be. The uninformed pay that spread and the informed collect it: the market maker is just the conduit. That is why spreads blow out before earnings, and why retail order flow, which is almost never informed, is valuable enough for wholesalers to pay for.
Inventory risk and position limits
Every share a market maker holds overnight is a bet it did not choose to make. The desk limits that risk in dollars of value at risk, so the position it can carry shrinks when the stock is expensive, when volatility rises, or when the limit is cut. The subtler point is liquidity: a position you cannot sell in a day is exposed for as many days as it takes to sell, and that horizon itself grows with the size of the position. Risk then rises faster than size — with the power 1.5 — so halving a large, illiquid position removes much more than half its risk.
Bond Math
6 conceptsPrice from yield, yield from price
A bond is a fixed set of cash flows, so its price is just those cash flows discounted at the market yield — and its yield is whatever rate makes that discounting land on the price. Because the cash flows never change, price and yield move in opposite directions: a higher discount rate makes the same payments worth less. When the coupon is above the yield the bond pays more than the market requires, so it trades above par; when it is below, below par. A zero-coupon bond is the cleanest case — one payment, so the yield can be read straight off the price.
Duration
Duration answers two questions that turn out to be the same. Macaulay duration is the average time you wait for your money, each cash flow weighted by its share of the price. Modified duration is how many percent the price moves for a one-point move in yield. They are linked because a cash flow far in the future is discounted many times over, so it is the most sensitive to the rate. A zero has one cash flow, so its duration is its maturity; coupons pay some money back early and pull the average — and the rate sensitivity — below maturity.
DV01 and hedging
Traders do not think in duration; they think in dollars per basis point. DV01 turns a bond’s rate sensitivity into the number that matters on a risk report: how much the position makes or loses when yields move one basis point. It is also what makes hedging work. A 2-year note moves far less per dollar of face than a 10-year bond, so hedging one with the other face-for-face leaves most of the risk on. Match the DV01s instead and a parallel move in yields cancels — but a move that is not parallel does not, which is why a duration-hedged position is really a bet on the shape of the curve.
Convexity
Duration draws a straight line through a curve. The true price-yield relationship bends: as yields rise, each extra basis point costs a little less, because the price it is working on has already shrunk; as yields fall, each basis point earns a little more. That bend is convexity. It makes a long bond position win more on a rally than it loses on an equal sell-off, so it is worth paying for — and the market does charge for it, with a lower yield. For small moves it hardly matters; for the 100–200 bp moves that happen in a bad year it is the difference between a good estimate and a bad one.
Carry and roll-down
A bond position earns money even if nothing happens, in two separate ways. Carry is the coupon you collect less the cost of financing the bond in repo. Roll-down is the price gain from ageing: on an upward-sloping curve, a 10-year bond becomes a 9-year bond a year later, and 9-year yields are lower, so the same bond is worth more. Together they are the return from standing still — and they set how far yields can move against you before the trade loses money. On an inverted curve roll-down turns into a cost, and when repo is above the coupon, so does carry.
Bond futures
A bond future is a promise to deliver a government bond at a fixed price later. The short can choose from a basket of bonds, so the exchange scales each one by a conversion factor to make them roughly comparable — and whichever is still cheapest after scaling gets delivered. Owning the cash bond and selling the future locks in a return: you pay the cash price, earn the coupon, and get the invoice price at delivery. That return is the implied repo rate. If it beats the rate you can borrow at, the future is rich; the bond that offers the highest implied repo is the cheapest to deliver, and the future trades off it.
FX & Rates
5 conceptsCross rates
Almost every currency trades against the dollar, so a rate between two other currencies — euro against yen, euro against sterling — is built by going through the dollar. If one euro buys 1.08 dollars and one dollar buys 147 yen, one euro buys 1.08 × 147 yen. Whether you multiply or divide depends on which side of each quote the dollar sits. The cost of that route is that you cross two spreads, always on the side that hurts you, which is why a cross is quoted wider than either of the dollar pairs it is made from.
Forward points
An FX forward is not a forecast. Anyone can manufacture one today: borrow dollars, buy euros, deposit them, and the amounts you owe and own at the end fix the rate. So the forward is spot adjusted for the interest rate gap, and nothing else. The currency with the higher interest rate trades at a forward discount — you are paid interest for holding it, and give that back through a worse forward rate. Forward points are simply that adjustment in pips. If a bank quotes a forward away from parity, the same borrow-convert-deposit trade locks in a risk-free profit.
Quoting conventions
An FX quote is a price for one unit of the first currency, paid in the second. That one sentence settles most confusion: in USD/JPY the dollar is the thing being bought and sold, in EUR/USD it is the money. The dealer’s bid is where it buys the first currency and its offer where it sells, so a client always buys at the higher number and sells at the lower. A pip is the smallest standard price step, and because the quote currency is the money, a pip’s value is naturally in that currency — which is why a USD/JPY pip is worth a different number of dollars every day and a EUR/USD pip is not.
Swap rates
An interest rate swap exchanges a fixed rate for a floating one on a notional that never changes hands. At inception it is worth nothing to either side, which pins the fixed rate: the par swap rate is the coupon that makes a fixed stream worth the same as the floating stream, and the floating stream is worth par. That turns the swap rate into a weighted average of the forward rates along the curve. Once rates move, the swap is no longer free: whoever pays a fixed rate below the new market rate holds something valuable. The annuity — the sum of discount factors — converts every basis point of rate difference into dollars.
Curve trades
Most rate views are not "rates will go up" but "the curve will change shape": short yields will fall faster than long ones when the central bank cuts, or rise faster when it hikes. A curve trade isolates that view. Buy one maturity, sell another, and size the legs so their DV01s match: a parallel move then makes nothing and loses nothing, and the P&L depends only on the spread between them. Get the sizing wrong — equal face amounts, say — and the "curve trade" is mostly an outright bet on the longer bond, because a 10-year note carries several times the rate risk of a 2-year.
Mental Math
2 conceptsFast percentages and fractions
On a trading floor, percentages are done in your head and fast, and the trick is never to compute what you can recognize. 12.5% is an eighth; 17.5% is 10 plus 5 plus 2.5; a 25% rise needs a 20% fall to undo, because the fall is measured from a bigger number. Basis points are just hundredths of a percent. Knowing a handful of fractions cold — sevenths, ninths, elevenths, sixteenths — turns most of these into recall rather than arithmetic, and leaves your attention for the actual question.
Rule of 72 and quick compounding
Compounding is hard to do in your head and easy to count in doublings. Money growing at r percent a year doubles in about 72 ÷ r years, because ln 2 is 0.693 and ln(1 + r) is a little under r — 72 rounds the gap and has lots of divisors. Once you think in doublings, "8% for 27 years" becomes "three doublings, so eight times". The rule is best around 8%; it runs slightly long for low rates and slightly short for high ones, which is worth knowing before you quote it to a client.