Equities · 9 lessons

Revision sheet

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

E1How equity markets work

Bid, offer and spread: The bid is the most a buyer will pay; the offer is the least a seller will accept. Buying at once costs the offer and selling at once gets the bid. The gap, 1p on a 412p–413p quote, is the .
Market and limit orders: A market order trades now against the , taking worse prices as it grows: 300 shares at 100p and 500 at 101p fill 800 at 100.625p. A sets your worst price and may never fill.
Cap-weighted indices: Most indices, including the FTSE 100 and the S&P 500, weight each company by its market value. A company worth 5% of the index that rises 4% adds about 0.2%, so a few big names can drive a day’s move.
Price-weighted indices: indices, such as the Dow and the Nikkei 225, count each company by its share price, not its size. A $500 share moves the Dow ten times as much as a $50 share for the same % move.
Settlement: Shares and cash swap a set number of business days after the trade date (T): the . US shares settle on T+1; UK and EU shares settle on T+2 and move to T+1 on 11 October 2027.

An index move from its members

Index % move ≈ Σ weight × the company’s % move

weight: the company’s share of the index, by free-float market value
Σ: add up over every company that moved

Remember: Index % ≈ Σ weight × move. An index weighted by size moves with its biggest companies, so a few large stocks can explain most of the day’s move.

E2Valuation for traders: P/E, yields and rates

P/E ratio: Share price divided by : how many years of profit you pay for. A share at £30 earning £1.50 a year trades on a of 20.
Trailing and forward P/E: A trailing P/E uses last year’s earnings; a forward P/E uses analysts’ forecast for next year. A trailing P/E of 30 against a forward P/E of 20 means profits are expected to rise by about half.
Earnings yield: The P/E turned upside down: the profit you buy for each £1 you pay. A P/E of 20 is an of 5%, which can be set directly against a bond’s .
Equity risk premium: The extra return for owning shares rather than safe bonds. A rough estimate is the earnings yield minus the on inflation-linked government bonds: 5% against 1.5% leaves about 3.5%.
Why rates hit growth stocks hardest: Higher bond yields raise the return investors require, so share values fall. With growth 2 points below that return, a one-point rise in yields cuts the value by a third; with growth 6 points below, by a seventh.

The dividend growth model

P = D ÷ (r − g)

P: the share’s value today
D: next year’s dividend per share
r: the return investors require: the government bond yield plus the equity risk premium
g: how fast dividends grow each year, for ever

Remember: Earnings yield = 1 ÷ P/E; P = D ÷ (r − g). When growth sits close to the return investors require, the P/E is high and a rise in yields cuts it hardest.

E3Earnings and events

Beat or miss: Results are judged against the , the average analyst forecast, not against last year. Earnings of 52p against a consensus of 50p is a 4% beat; the surprise, not the growth, moves the shares.
Guidance and quality: The company’s own forecast, its , often matters more than the result: a beat paired with a cut to next year’s forecast usually sends the shares down. So can a beat built on one-offs, or one after a rally into results.
Implied move: A pays on a move either way, so its price divided by the share price is the . A 120p straddle on a 2,000p share implies about 6%, to set against the stock’s past moves on results.
Index inclusion: In an , trackers must buy a joining company: tracker assets × its weight, mostly at the close before the change. £200 billion tracking and a 0.5% weight make £1 billion of buying.
Merger arbitrage: Buying a takeover target below the cash offer to collect the gap when the deal completes: 490p against 500p is 2%, about 6% a year over four months. If the deal breaks, the target can fall back to its pre-bid price.

The move options expect

Implied move ≈ straddle price ÷ share price

straddle: a pair of options that pays the size of the move, up or down, expiring just after the results

Remember: Implied move ≈ straddle ÷ share price. A share moves on the surprise against what was expected, so read the guidance and the implied move, not just the headline beat.

E4Short selling and securities lending

Short selling: Selling borrowed shares and buying them back later, to profit from a fall. The most a short can make is 100%, if the share goes to zero; the loss has no limit, because the price can keep rising.
Securities lending: Long-term holders such as pension and index funds lend shares for a fee and hold cash or bonds as . The lender can recall the shares at any time, which can force a short to close at a bad moment.
The cost of a short: The borrow fee, quoted as a % a year of the value borrowed, plus every dividend paid while short. Large companies cost well under 1% a year to borrow; shares many people want to short can cost 10% or more.
Short interest and days to cover: is the shares sold short and not yet bought back, often given as a % of the . Over daily volume it gives : 30 million against 4 million a day is 7.5.
Short squeeze: A needs crowding plus a trigger, such as good news, a bid or recalls: shorts buy into a rising price and push it higher. A rising borrow fee is an early warning that lendable shares are running out.

Cost and crowding of a short

Borrow cost = fee × value × days ÷ 365

fee: the yearly borrow fee, in %
value: the value of the shares borrowed
days: how long the short is open

Remember: Days to cover = short interest ÷ daily volume. A short pays borrow and dividends every day it is open, and the more crowded it is, the harder it is to get out.

E5Equity forwards and futures

Index future: An agreement to buy or sell an index on a set date at a price fixed today, settled in cash. The FTSE 100 future is worth £10 a point (the E-mini S&P 500, $50), and gains and losses are paid daily as .
Fair value: The index plus the interest saved by not buying the shares, minus the dividends missed. An index at 10,000 with interest at 4% and dividends at 3% gives a one-year of 10,100.
Basis: The gap between the future and the index. When dividends outweigh interest the future sits below the index: at 2% interest and 3% dividends, a one-year future on 10,000 is worth 9,900. The shrinks to zero at expiry.
Index arbitrage: If the future trades above fair value, traders buy the shares and sell the future to lock in the gap; below it, they do the reverse. This keeps futures within a band set by trading costs.
Hedging with futures: Selling futures removes a portfolio’s market risk: £9m with a of 1.2 needs 120 FTSE 100 contracts at 9,000. Stocks that do worse than the index are left unhedged: that is .

Index future fair value

F = S × (1 + (r − d) × t)

S: the index level now
r: the interest rate, % a year
d: the index’s dividend yield, % a year
t: time to expiry in years (days ÷ 365)

Remember: F = S × (1 + (r − d) × t). A future is the index plus interest minus dividends; when dividends outweigh interest, it trades below the index.

E6Delta one: swaps, CFDs and ETFs

Total return swaps and CFDs: A pays one side a share’s price change plus dividends in return for interest on the notional: the result of owning the shares without buying them. A is the same deal in a standard form.
The two legs: The performance leg pays the price change plus dividends; the financing leg charges an overnight rate, such as in sterling, plus a spread. Paying 5% a year on £10m for 73 days costs £100,000.
Why use a swap: A swap needs only a deposit, which gives . It lets a fund go short without borrowing stock and reach hard-to-trade markets, and in the UK it avoids the 0.5% on buying shares.
Delta one: Products that move one for one with the shares underneath, such as swaps, CFDs and futures. A desk hedges what it gives clients, so it earns from financing and trading, not from direction.
ETFs and NAV: An is a fund whose units trade on an exchange all day; is its holdings’ value per unit. create or redeem units, keeping the price within their costs of NAV.

Net payment on a total return swap

Net = N × R − N × (rate + spread) × days ÷ 365

N: the amount the swap is on (the notional)
R: the shares’ return over the period: price change plus dividends
rate: the overnight interest rate, such as SONIA
spread: the bank’s extra charge for financing

Remember: TRS net = N × return − N × (rate + spread) × t. Delta one products copy owning the shares; the money is made on financing and trading, not on direction.

E7Convertible bonds

Convertible bond: A bond the holder can swap for a fixed number of shares, the conversion ratio: £100 converting into 20 shares sets a conversion price of £5. Because that right has value, it pays less interest than a plain bond.
Parity and premium: is the bond’s value as shares: 20 shares at £4.20 is 84 per £100. A convertible at 98 trades at a of 16.7% over that.
Bond floor: The convertible’s value as a plain bond, ignoring the right to convert: where it heads if the shares collapse. It is not fixed: if the company’s credit weakens, the falls.
Equity-like or debt-like: With the shares far above the conversion price, the premium is small and a convertible moves almost one for one with them; near the floor it moves with the company’s credit. Bigger expected share swings raise its value.
Convertible arbitrage: Buying the convertible and shorting its × the shares it converts into: £10m of bonds at 20 shares per £100 with a delta of 0.55 means shorting 1.1 million. That shorting is why shares often dip at launch.

Parity and conversion premium

Premium = (price − parity) ÷ parity, where parity = ratio × share price

price: the convertible’s price per £100 of bond
ratio: shares received for each £100 of bond
parity: the bond’s value as shares, per £100

Remember: Premium = (price − parity) ÷ parity. A convertible is a bond plus the right to swap into shares: near its floor it trades like a bond, close to parity it trades like the shares.

E8Structured products and dealer flows

Capital-protected note: A note that returns at least the capital at maturity plus a share of any rise in an index. It is a that grows back to £100, plus a bought with what is left.
Participation: The share of the index’s rise the note pays: 16 left after the bond and fees, with calls at 20, gives 80%, so a 30% rise pays £124 per £100. The protection is only as good as the bank that issued the note.
Rates and participation: Lower rates make the zero-coupon bond dearer, leaving less for the option: at 1% a year for five years it costs about £95. Issuers then cap the upside with a call spread, lengthen the term or protect less.
Reverse convertibles and autocallables: A pays a high coupon but repays in shares if the stock ends below its start: the investor has sold a put. An repays early if the index is at or above its start on a check date.
What the bank keeps: The bank holds the other side of every option. Protected notes leave it short calls, so ; reverse convertibles and autocallables leave it owning puts, so long volatility. All leave it long dividends.

Participation on a capital-protected note

Participation = (N − zero − fees) ÷ call cost

N: the capital protected, such as £100
zero: price of a zero-coupon bond paying N at the end: N ÷ (1 + r)^years
call cost: price of a call on the index for the same term

Remember: Participation = (N − zero − fees) ÷ call cost. A structured note is a bond plus options; whatever the investor buys or sells, the bank holds the other side and must hedge it.

E9Hedging an equity portfolio

Hedging with futures: A hedge is a second trade that gains when the portfolio loses. Selling index futures is the quickest, with no premium, but gives up the upside: £20m that tracks the FTSE 100 needs about 222 contracts at 9,000 (£10 a point).
Beta and basis risk: A portfolio with a of 1.5 moves 1.5% for each 1% in the index, so it needs 1.5 times as many futures. Stocks that fall further than the index are left uncovered: that is .
Buying puts: A pays below its strike and keeps all the upside, for a premium paid up front: a 95% put costing 2% on £20m costs £400,000. Protection is dearest when is already high.
Collars and put spreads: A zero-cost buys a put and sells a call that pays for it: a floor and a cap, with no premium. A put spread sells a lower put to cut the cost and covers only falls between the strikes: 95/85 covers 5% to 15%.
Matching the hedge to the fear: Puts suit fear of a crash while keeping the upside; a put spread, a moderate fall at low cost; a collar, no premium in return for capped gains; futures, getting out of the market fast.

Futures to hedge a portfolio

Contracts = portfolio value × beta ÷ (futures price × £ per point)

beta: how much the portfolio moves for each 1% move in the index
£ per point: the contract’s size: £10 a point on the FTSE 100 future

Remember: Contracts = value × beta ÷ (futures price × £ per point). Every hedge trades cost against protection: futures cost nothing but take the upside, puts keep it for a premium, and collars and spreads sit between.