Foundations · 12 lessons

Revision sheet

Every Foundations lesson’s essentials, formula and takeaway on one page. Each heading opens the full lesson.

F1The map of markets

Asset classes: Families of similar risk: rates (government bonds), credit (company debt), equities (shares), FX (currencies) and commodities. What you buy decides which risk you carry.
Primary and secondary markets: In the an issuer sells new bonds or shares and receives the cash. After that, investors trade them with each other in the , where most trading happens.
Buy side and sell side: The (pension funds, insurers, fund managers, hedge funds) invests. The (banks) quotes prices, takes the other side of client trades and holds the risk until it can pass it on.
Cash and derivatives: A cash trade buys the asset itself. A is a contract whose value comes from something else, such as an agreement today on the price of oil delivered in three months. Futures, swaps and options are derivatives.
Exchange and over the counter: Standard contracts that many people trade, such as shares and futures, are listed on an exchange with public prices. Tailored deals, including most bonds, swaps and currency trades, are agreed directly with a bank: .
Leverage: Holding more assets than your own money pays for, by borrowing. At 20× , every 1% move in the assets is 20% of your capital, and a 5% fall wipes it out.

Leverage and the wipe-out move

L = E ÷ C; wipe-out move = C ÷ E = 1 ÷ L

L: leverage, as a multiple
E: exposure: the value of all positions held
C: capital: the investor’s own money at risk

Remember: Wipe-out move = 1 ÷ leverage. At 20× leverage a 5% fall loses all the capital, which is why levered investors are forced to sell into falling markets.

F2Inside a trading floor

Desks and FICC: A trading floor is split into desks by asset class: rates, FX, credit, commodities and equities. The first four are often grouped as : fixed income, currencies and commodities. Each desk is judged on its P&L.
Who does what: Sales looks after clients and brings in their orders; traders set prices and manage the risk; structurers design products for one client; quants build pricing models; research writes forecasts and trade ideas.
Bid, offer and spread: A dealer buys at its bid and sells at its offer; the gap is the . A quoted 99.96–100.04 is 8 cents wide per 100: sold to the dealer at 99.96, bought from it at 100.04.
What a market maker earns: A earns about half the spread per trade when client buying and selling balance: £10,000 on £25m at 8 cents wide. A move on what it holds can wipe that out: 0.10 on £50m is £50,000.
Flow and structured: Flow products (currencies, government bonds, plain swaps) trade in volume at thin spreads, much of it priced by algorithms. products are built for one client: more profit per trade, harder to hedge.

Dealer revenue from the spread

Revenue ≈ n × size × spread ÷ 2

n: number of client trades
size: notional of each trade
spread: bid–offer spread as a fraction of price: 8 cents per 100 is 0.0008

Remember: Revenue ≈ trades × size × half-spread. A market maker earns about half the spread on each trade, as long as prices don’t move against its inventory in between.

F3Market making, inventory and the balance sheet

Inventory and the axe: Inventory is what a dealer has bought from clients and not yet sold, or sold and not yet bought back. The side it wants to trade out of is its : long bonds, it is axed to sell and prices that side keenly.
Skewing the quote: Moving bid and offer the same way to work off inventory: down when long, to attract buyers; up when short. At 0.01 per £1m held, being long £3m moves a 100.00 middle price to 99.97.
Two parts of a dealer’s profit: The spread captured on each trade, small and fairly certain, and the gain or loss on inventory while it is held, usually larger. Buying £20m 0.05 below mid captures £10,000; a 0.20 fall then loses £40,000.
Capital and risk weights: Capital is the bank’s own money and takes losses first. Riskier assets carry higher risk weights and need more: £100m at a 50% weight, with capital set at 10% of , uses £5m.
Market making and proprietary trading: Market making serves clients and earns the spread; bets the bank’s own money on a view. The US bans most of it at deposit-taking banks.

Skewed quote and capital used

new mid = mid − skew × inventory; capital = size × risk weight × capital rule

skew: how far the middle price moves for each unit held
inventory: what you hold: positive if long, negative if short
capital rule: the share of risk-weighted assets held as capital, such as 10%

Remember: Capital = exposure × risk weight × ratio. A dealer earns a small spread but carries a larger inventory risk, and every position it holds uses scarce capital.

F4Time value of money and day counts

Time value of money: Money today is worth more than the same sum later, because it can earn interest meanwhile. At 5%, £100 grows to £105 in a year and £110.25 in two, as interest earns interest: compounding.
Present value: What a future sum is worth today, after discounting at the interest rate for each year of waiting. The further away and the higher the rate, the less it is worth: at 5%, £1 due in ten years is worth about 61p.
Net present value (NPV): The present value of everything an investment pays, minus its cost today. Positive means it beats the discount rate: paying £1,000 for £400 a year over three years has an NPV of about +£31 at 8%.
Internal rate of return (IRR): The discount rate at which NPV is exactly zero: the return the investment earns. £1,000 for £400 a year over three years has an IRR of about 9.7%, so it clears an 8% hurdle.
Day counts: Money-market interest is paid for the days a loan runs. Sterling counts a 365-day year, dollars and euros 360, so 4% for 91 days pays £99,726 on £10m but $101,111 on $10m.

Present value

PV = CF ÷ (1 + r)ⁿ

CF: the cash received in n years
r: the interest rate per year, as a decimal (5% = 0.05)
n: the number of years you wait

Remember: PV = CF ÷ (1 + r)^n. The higher the rate and the further away the cash, the less it is worth today; NPV is positive when the IRR beats the discount rate.

F5Returns, risk and portfolios

Volatility: The typical size of an asset’s moves: the standard deviation of its returns, usually quoted per year. A share that moves 3% on a typical day is riskier than one that moves 1%.
Square root of time: Risk grows with the square root of time, because up and down days partly cancel. A year has about 252 trading days and √252 ≈ 16, so 1% a day is about 16% a year: the .
Value at risk (VaR): The loss a position should exceed only on a set share of days. £10m with 1% daily volatility has a 95% one-day of about £165,000. It says nothing about how big losses beyond it get.
Correlation and diversification: runs from −1 to +1. Below +1, a mix swings less than the average of its parts. Correlations change: in 2022, rising interest rates hit shares and bonds together.
Sharpe ratio: Return above cash divided by volatility: the return earned for each unit of risk. A 9% return with cash at 4% and 10% volatility gives 0.5; higher is better.
Beta: How far a share moves with the market. A beta of 1.3 means about 1.3% for each 1% move in the index, so £10m of the shares behaves like £13m of the index.

Volatility and value at risk

σ_year = σ_day × √252; 95% VaR ≈ 1.65 × σ_day × V

σ: volatility: the typical size of moves (standard deviation of returns)
√252: about 16: the square root of the trading days in a year
V: the value of the position

Remember: σ_year ≈ σ_day × 16. Risk grows with the square root of time, and diversification works only while correlations stay low.

F6Growth and the business cycle

GDP: is the value of everything an economy produces, usually counted by who spends: households, business investment, government, and exports minus imports. Households are more than half of UK and US GDP.
Real and nominal growth: Nominal growth includes price rises; real growth strips them out. Headline GDP growth is real: spending up 6% with prices up 4% is about 2% real growth.
Contribution to growth: A part’s effect on headline growth depends on its size as well as its pace: household spending at 60% of GDP rising 2% adds 1.2 percentage points.
Quarterly and annualised: The UK reports growth against the previous quarter; the US annualises it, as if it ran for a whole year. A UK 0.5% quarter is about 2.0% in US terms.
Recession: A broad fall in activity. The UK rule of thumb is two quarters in a row of falling real GDP; in the US a panel of economists makes the call.
PMI: A monthly survey of firms: the share reporting higher activity plus half the share reporting no change. Above 50 means growth, below 50 contraction. It measures how widespread growth is; it says nothing about its size.

Contribution to growth and annualising

contribution = share × growth; annualised = (1 + q)⁴ − 1

share: the component’s share of GDP
growth: the component’s own growth over the period
q: quarter-on-quarter growth (0.5% = 0.005)

Remember: Contribution = share × growth. Markets trade the surprise against consensus, so know each release’s units, its usual surprise and which part the central bank watches.

F7Inflation and real rates

CPI inflation: The yearly rise in the price of a typical household basket, published monthly and worked out from index levels: an index of 123.0 against 120.0 a year earlier is 2.5% inflation.
Base effects: Each month, the new monthly change enters the yearly rate and the same month last year drops out. If last year’s 1% jump is replaced by a 0.2% rise, yearly inflation falls about 0.8 points.
Core inflation: Inflation without volatile food and energy prices: a steadier guide to underlying pressure. The Bank of England aims for 2% inflation and watches core and services prices, which mostly follow wages.
Real interest rate: The interest rate minus inflation. Savings at 5% with 3% inflation earn about 2% real; at 4% with 6% inflation the real rate is −2%, so the money buys less each year.
Breakeven inflation: pay a on top of inflation. The gap to an ordinary ’s , such as 4.6% against 1.2%, is breakeven inflation: 3.4%, a market estimate plus a little for risk.

Inflation and breakevens

inflation = index now ÷ index a year ago − 1; breakeven = nominal − real

index: the price-index level, such as 123.0
nominal: yield on an ordinary bond
real: real yield on the matching inflation-linked bond

Remember: Breakeven = nominal yield − real yield. Inflation is a ratio of index levels, so the month that drops out matters as much as the one coming in.

F8Central banks and the policy rate

Mandate: The Bank of England’s main job is low, steady inflation, against a 2% target set by the government. The Fed has a : 2% inflation and maximum employment.
The policy rate: The interest rate a central bank sets: in the UK, paid on the money banks hold at the Bank of England. Other rates follow it, and a higher rate makes borrowing dearer, cooling spending and then inflation.
The MPC: Bank Rate is set by the nine-member , which meets eight times a year and publishes each member’s vote. A close split, such as 5–4, signals the next move is near.
Hawkish and dovish: leans towards higher rates, or keeping them high; leans towards cuts. A hawkish surprise usually lifts short-term interest rates and the currency.
Reading market pricing: Rate futures are quoted as 100 minus the rate, so a future at 96.25 implies 3.75%. With 10bp of a 25bp cut priced for a meeting, the market puts the chance of a cut at about 40%.
QE, QT and guidance: creates money to buy bonds, pushing longer-term rates down; runs those holdings down. moves markets by saying what the bank is likely to do next.

Reading the market’s odds

chance of a move ≈ (priced rate − current rate) ÷ size of the move

priced rate: the rate markets expect after the meeting (100 − futures price)
current rate: today’s overnight rate
size: the step being priced: +0.25% for a hike, −0.25% for a cut

Remember: P(move) ≈ priced change ÷ size of move. Markets move on the gap between what a central bank does and what was priced, so know the pricing before the decision.

F9Fiscal policy, debt and bond supply

Deficit and debt: The is one year’s gap between spending and tax revenue, covered mostly by selling bonds; the debt is all the borrowing still owed. Tax cuts and extra spending are expansionary and usually mean more borrowing.
Debt against GDP: Debt is judged against yearly output: £2,000bn of debt with GDP of £2,500bn is 80%. The is the budget before interest on past debt.
Interest rate against growth: When the average rate on the debt exceeds nominal growth, debt/GDP rises on its own: at 100% of GDP, a rate of 4% against growth of 3% adds about 1 point a year, even with a balanced primary budget.
Supply and term premium: The sells . Selling many more long-dated ones makes investors ask a higher to hold them, the , while short yields follow the .
Autumn 2022: After the September 2022 tax-cut package, 30-year gilt yields rose more than 0.8 points in two trading days. Forced selling by funds pushed them higher until the Bank of England bought long gilts from 28 September.

Debt dynamics

Δd ≈ (r − g) × d − pb

d: government debt as a share of GDP
r: average interest rate on the debt (nominal)
g: nominal GDP growth
pb: primary balance, % of GDP: a surplus is positive, a deficit negative

Remember: Δ debt/GDP ≈ (r − g) × debt − primary balance. When interest rates exceed growth, debt grows on its own, and the long end of the curve charges for the extra supply.

F10How data moves markets

Consensus and the surprise: Prices already reflect the , the average of economists’ forecasts, so markets react to the surprise: the actual figure minus consensus. A figure in line barely moves anything.
Sizing the surprise: Scale it by the release’s usual miss, then by the usual move: a 0.2 beat where misses are about 0.1 is two standard deviations, and at 6bp each that suggests about 12bp on 2-year .
Reaction function: The link from data to what the central bank is expected to do. Hot inflation lifts short-term interest rates first and most; the currency tends to rise and shares to fall.
Bad news can be good news: The sign depends on what markets fear most. With inflation the worry, weak jobs figures can lift shares by bringing rate cuts closer; with recession the worry, the same figures hurt them.
Priced in and positioning: A move everyone expects is and barely shifts prices. Crowded makes a surprise bigger, as investors holding the same bet get out together.
Read past the headline: Find the part the central bank reacts to. Inflation that beats on petrol while services inflation is soft is less hot than it looks; jobs growth that beats while earlier months are revised down is weaker.

Sizing a data surprise

z = (actual − consensus) ÷ σ; move ≈ sensitivity × z

σ: the usual size of surprises in this release (their standard deviation)
z: the surprise in standard deviations
sensitivity: the typical move per standard deviation, such as bp of 2-year yield

Remember: Move ≈ sensitivity × surprise in σ. Markets move on the surprise against consensus, filtered through what the central bank will do about it.

F11Corporate finance for traders

EBIT and EBITDA: EBIT is profit before interest and tax. Add back depreciation and amortisation, charges that use no cash, to get , a rough measure of the cash a business makes: £200m + £50m = £250m.
Free cash flow: Cash left for lenders and shareholders after tax, new equipment (capex) and the stock and customer credit a business funds: £600m of EBIT taxed at 25%, plus £200m of depreciation, less £250m of capex and £50m of working capital, is £350m.
Equity value and enterprise value: Equity value is the share price times the number of shares: 500m at £8 is £4bn. adds , debt minus cash: with £2bn of it, £6bn.
Valuation multiples: is the share price over ; a P/E of 20 is an of 5%. values the whole business, so it compares companies with different amounts of debt.
WACC: The blended cost of a company’s equity and after-tax debt, weighted by how much of each it uses: 60% equity at 10% and 40% debt at 5% gives 8%. It is the rate used to value its future cash.
Leverage and buybacks: Credit traders watch net debt ÷ EBITDA. On £0.8bn of EBITDA, a £1bn debt-funded lifts it from 2.5× to 3.75× while EV barely changes, so the tends to widen.

Enterprise value and free cash flow

EV = equity value + debt − cash; FCF = EBIT × (1 − tax) + D&A − capex − ΔWC

D&A: depreciation and amortisation: charges that use no cash this year
capex: spending on equipment and other long-lived assets
ΔWC: the rise in working capital: stock and unpaid customer bills, minus unpaid supplier bills

Remember: EV = equity value + net debt. Financing choices move value between shareholders and bondholders: credit traders watch leverage, equity traders watch earnings.

F12Regulation and market plumbing

Capital and CET1: Capital is a bank’s own money, which takes losses before depositors do. The core measure is , mostly shareholders’ equity: a bank with £5bn of it can lose £5bn before depositors are at risk.
Risk-weighted assets: Each asset is scaled by a risk weight: in a simple example, 0% for , 35% for mortgages and 100% for company loans. £5bn of CET1 against £25.5bn of is a 19.6% CET1 ratio.
Leverage ratio: A backstop that ignores risk weights, so government bonds count in full: £5bn of capital on £65bn of total assets is 7.7%. Swapping gilts for loans cuts the CET1 ratio but leaves this unchanged.
Liquidity coverage ratio (LCR): A rule that a bank holds enough liquid assets, such as government bonds, to cover 30 days of stressed outflows: at least 100%. Capital covers losses and liquidity covers runs; Silicon Valley Bank ran out of liquidity first in 2023.
From LIBOR to SONIA: rested on banks’ estimates, which were gamed. Markets moved to rates built from real overnight trades: in sterling, in dollars. Every LIBOR setting had stopped by the end of September 2024.
Settlement cycle: The business days from the trade date (T) to settlement. US shares moved to T+1 on 28 May 2024; the UK and the EU plan to follow on 11 October 2027.

Toy bank ratios

CET1 ratio = CET1 ÷ RWA; leverage ratio = capital ÷ total assets

CET1: core capital: mostly shareholders’ equity
RWA: risk-weighted assets: each asset scaled by its risk weight, then added up

Remember: CET1 ratio = CET1 ÷ risk-weighted assets. Capital absorbs losses and liquidity survives runs; a bank needs both, as Silicon Valley Bank’s collapse in 2023 showed.