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.
Long / Short Equity
5 conceptsBeta-hedged pair trade attribution
A pair trade is a bet on one stock against another with the market taken out. The long earns its own return plus beta times the market; the short costs its own return plus beta times the market. Size the short so the two beta-dollar exposures cancel and whatever the market does washes out; what is left is the difference in the two stocks’ own returns — the alpha. A dollar-neutral hedge is the lazy version: it only cancels the market if the two betas happen to be equal. Attribution afterwards asks one question: how much of the P&L was the market you did not mean to own, and how much was the view you did?
Gross and net exposure
Two numbers describe a long/short book. Gross exposure — longs plus shorts over capital — says how much is at work and therefore how levered the fund is and how much it can lose if both sides go wrong at once. Net exposure — longs minus shorts — says which way the fund is leaning and roughly how much of the market it owns. Neither is complete without beta: a book that is net flat in dollars but long high-beta names against low-beta shorts is long the market. Beta-adjusted net is the number the risk desk actually watches.
Short rebate and the cost of carry
A short position is not free to hold. The cash raised from selling borrowed stock sits at the prime broker and earns interest — the rebate — but the broker charges a fee to borrow the stock, and if the company pays a dividend the short must pay it to the lender. Net those and you have the carry: positive when rates are high and the stock is easy to borrow, negative — sometimes brutally — when the name is hard to borrow or pays a fat dividend. Carry sets the bar: the stock must fall by at least the negative carry over the holding period for the short to break even, before any thought of being right.
Sizing to a contribution-to-risk target
Position size is not a measure of conviction; it is a risk budget. A pod is told how much volatility it may contribute to the fund, and each idea is sized so that its own share of that budget — its weight times its volatility times how much it moves with the rest of the book — fits inside the allowance. A second rule sits alongside: how far the stock can fall before the thesis is wrong, times the weight, must not exceed what the desk is willing to lose. Whichever rule gives the smaller position wins. Volatile, correlated, far-from-stop names get small; quiet, diversifying, close-to-stop names get big — regardless of how much the analyst loves them.
Crowding and factor overlap
Two things make a stock-picker’s position riskier than its volatility suggests. Crowding: if many funds hold the same name, the exit is through the same door at the same time, and the measure of that is how many days of normal volume it takes to get out. Factor overlap: if most of a stock’s movement is explained by a factor — the market, momentum, its sector — the position is a factor bet the fund did not mean to make, and the part that is genuinely the analyst’s view is smaller than the position size implies. Both are invisible in the P&L until the day everyone runs for the same exit.
Valuation Multiples
5 conceptsEV/EBITDA versus P/E
EV/EBITDA prices the whole business before anyone is paid — lenders, the tax authority, the depreciation of the assets. P/E prices what is left for shareholders after all of them. Two companies on the same EV/EBITDA can sit on very different P/Es if one carries more debt, depreciates more, or pays a different tax rate — and two on the same P/E can be worth very different multiples of EBITDA. Neither is "right". EV/EBITDA compares businesses; P/E compares what an equity holder gets. An analyst who can walk from one to the other, and say why they differ, understands the capital structure.
Free cash flow yield
Earnings are an opinion; cash is a fact. Free cash flow yield asks what the business actually throws off, after the capex it needs and the interest and tax it must pay, as a percentage of what you pay for the equity. It is the number to set against a bond yield: a 9% FCF yield in a stable business is a 9% coupon that can grow, and if the company spends it buying back its own shares, it retires 9% of the share count a year. The unlevered version — cash before interest, over enterprise value — compares businesses across capital structures, just as EV/EBITDA does for earnings.
PEG and growth-adjusted multiples
A P/E on its own says nothing about whether a stock is cheap, because a high multiple on fast growth can be a better deal than a low multiple on none. The PEG ratio divides the P/E by the growth rate to put the two on the same footing: a stock on 30x growing 30% a year is on a PEG of 1.0, the same as one on 10x growing 10%. The rule of thumb says below 1 is cheap and above 2 is dear. It is crude — it ignores how long the growth lasts, how risky it is and whether any cash comes back — but it is the fastest way to compare a growth stock with a value stock, and it is the first number a PM will ask for.
Sum of the parts
When a company runs two businesses that the market values differently, one multiple for the whole is wrong for both. A sum-of-the-parts values each segment at the multiple its own peers trade on, subtracts the head-office costs that belong to neither (capitalized, because they recur), subtracts the net debt, and compares the answer with the share price. The gap is the conglomerate discount — the market’s charge for complexity, for the chance the good business subsidises the bad one, and for management that may never separate them. An activist’s pitch is usually just a SOTP with a plan to close the gap.
The multiple bridge: where a stock’s return comes from
A share price is earnings times a multiple, so a return has to come from one of three places: the earnings grew, the multiple changed, or you were paid a dividend while waiting. The bridge separates them. Earnings growth is the company’s work; multiple change is the market’s mood; the dividend is cash. Run it forward and it tells you what a stock can return if the multiple does nothing. Run it backwards and it tells you what multiple the stock must exit on to hit a target return — which is the honest way to see how much of a pitch is a bet on re-rating.
Event-Driven
4 conceptsMerger arbitrage spread
When a deal is announced the target does not jump all the way to the offer. The gap that remains — the spread — is what the market charges for the chance the deal breaks and for the wait until it closes. Buy the target, collect the spread at closing; that is the trade. Judged on its own the spread looks small, so arbs annualize it: a 3% spread over four months is 9% a year. In a stock deal the payment is acquirer shares, so the arb shorts the acquirer in the exchange ratio to lock the spread in and take the acquirer’s price out of the bet. Either way the arb is selling insurance against the deal failing, and the spread is the premium.
Deal break price
The spread is what you earn if the deal closes; the break price is what you are left holding if it does not. Start from where the stock traded before the deal leaked, move it with the sector since — the world has changed in the meantime — and take something off for the damage: a company that was for sale and was not bought is worth less than one that never was. The gap from today’s price down to that number is the downside; the gap up to the offer is the upside. Merger arb is the business of comparing the two and deciding whether the odds the market implies are the odds you believe.
Probability-weighted expected value
A merger arb position is a bet with two outcomes and known payoffs, so it can be priced like one. Weight the offer by the chance the deal closes and the break price by the chance it does not, and you have the expected value of the stock. Set that equal to the market price and solve, and you have the probability the market is implying — the number every arb compares with their own. If you think the deal is more likely to close than the price says, you are being paid to take the position; if less, you are not, however wide the spread looks. Add a third outcome — a bumped offer — and the same arithmetic tells you what a competing bid is worth.
Rights issue dilution
A rights issue sells new shares to existing holders at a discount. The discount is not a gift: after the issue every share, old and new, is worth the same blended price — the theoretical ex-rights price — which sits between the old price and the subscription price. A holder who takes up their rights ends up with more shares at that lower price and is exactly as wealthy as before; one who sells the rights pockets their value and is also exactly as wealthy as before. The only way to lose is to do nothing. What the issue does change is the company: more shares, more cash, less debt — and that, not the headline discount, is what the event-driven investor is pricing.
Portfolio Risk
5 conceptsTwo-asset portfolio volatility
Risk does not add. Two positions with 30% volatility each do not make a 30% portfolio unless they move together perfectly; if they move independently the combination is far calmer, and if they move against each other it can be calmer still. The correlation is the whole story: it decides how much of each asset’s risk survives the combination. Every hedge, every pair trade and every diversified book is an application of this one formula, and the number that matters most in a crisis — when correlations go to one — is the one that is hardest to estimate.
Beta hedge ratio
A long book has a beta, and the beta is a market position the manager may not want. The cheapest way to remove it is to short index futures: each contract carries a fixed dollar exposure to the market, so the number of contracts is just the beta-dollars you want to shed divided by the beta-dollars per contract. Hedge to zero and the book’s P&L becomes pure stock selection; hedge to a target beta and you keep a chosen amount of market. The hedge is only as good as the beta estimate — and betas move, so the hedge is re-struck, not set.
Sizing under a drawdown limit
A hedge fund’s real risk limit is the drawdown at which its capital gets cut — by the platform, by the prime broker or by redeeming investors. Everything else is sized backwards from that. Start with the cushion between where the fund is and where it dies, decide how bad a bad day can be in units of volatility, and the maximum gross exposure falls out. The arithmetic has a cruel corner: after a loss the cushion is smaller, so the book must shrink just when the manager most wants to press — and the gain needed to recover grows faster than the loss that caused it.
Sharpe ratio and leverage
Sharpe measures return per unit of risk, and leverage is the dial that turns one into the other. A strategy that earns a little with very little risk can be levered into one that earns a lot with a lot of risk, and — if borrowing were free — the Sharpe would not move: both the excess return and the volatility scale by the same factor. Borrowing is not free, so each turn of leverage costs the financing spread and the Sharpe erodes a little. That is why allocators compare strategies on Sharpe and then choose how much to lever, and why a high Sharpe at low volatility is worth more than the same return at high volatility.
Contribution to risk versus contribution to capital
Half the capital is not half the risk. A volatile position in a 50/50 book can account for eighty percent of the portfolio’s volatility while the quiet one accounts for twenty. The contribution to risk is what each position adds to the portfolio’s volatility, counting how it moves with the rest of the book, and the contributions add up to the total exactly. Risk parity is the idea of sizing so that they are equal — which for two assets simply means giving the quieter one proportionally more capital. Whether or not a fund runs risk parity, the gap between the capital split and the risk split is the first thing a risk manager looks at.
Credit
5 conceptsYield to maturity and yield to worst
A bond’s coupon is what it pays; its yield is what you earn, and the two differ whenever the price is not par. Yield to maturity is the single rate that discounts every coupon and the principal back to the price you pay. If the bond can be called early, the issuer will call it when that is cheaper for them — which is exactly when it is worse for you — so a callable bond trading above par should be valued to the call, not to maturity. Yield to worst takes the lower of the two, and it is the number a credit desk quotes, because it is the return you can actually count on.
Recovery analysis
When a company cannot pay, what each creditor gets depends on two things: what the business is worth in distress, and where the creditor stands in the queue. Value flows down the capital structure in strict order — secured lenders are paid in full before the unsecured see a cent, and the unsecured are paid before equity — so the same enterprise value can mean a full recovery for one class and pennies for the next. A distressed investor’s work is to estimate that value, find the class where it runs out, and compare what the bonds will recover with what they cost today.
Credit spread decomposition
A bond’s spread over the risk-free rate is compensation for two things. The first is the loss you should expect: the chance the issuer defaults in a year, times what you lose when it does. The second is everything else — being paid to bear the uncertainty, to hold something illiquid, to take the risk that the defaults cluster. Split the spread and you can see how much of it is a fair price for the losses and how much is a premium. Run it backwards and you get the default rate the market is pricing in, which is the number to argue with.
Loan to own and the fulcrum security
In a restructuring, value runs down the capital structure until it runs out. The class where it runs out — paid partly but not fully — is the fulcrum. Everyone above is made whole; everyone below is wiped out; the fulcrum gets the company. That makes it the most interesting security in the structure: buy enough of it at a distressed price and you are not buying a bond, you are buying the reorganised equity at a discount, with a seat at the table when the plan is written. Loan to own is the strategy of finding the fulcrum before the market does and paying bond prices for equity.
Covenant breach: what it takes and what the lender gets
A maintenance covenant is a tripwire the lender sets so that it gets to the table before the money is gone. Two wires are common: leverage must not rise above a ceiling, and interest coverage must not fall below a floor. Both are ratios of EBITDA, so both are tests of how far EBITDA can fall — and one of them is always closer than the other. When the wire trips, the borrower has three ways out: a sponsor writes a check to cure it, the lender waives it for a fee and a higher coupon, or the loan is renegotiated. For a credit investor the covenant is not the risk; it is the moment the risk gets priced.