CFA Level I · CFA Level I Exam

Equity Issuance and Trading: formula sheet

Full chapter guide

Key formulas

Primary vs secondary test: Primary: new shares issued, cash goes to issuer. Secondary: existing shares change hands, cash goes to the selling investor; Use this first to classify any transaction.
Rights issue: theoretical ex-rights price: Ex-rights price = (N × P + n × S) ÷ (N + n); N = existing shares, P = price before the issue, n = new shares issued, S = subscription price. Assumes the issue proceeds are valued fairly and no other news.
Value of one right: Value of a right = cum-rights price − ex-rights price = (P − S) ÷ (N_old + 1); P is the cum-rights price, S is the subscription price, and N_old is the number of existing shares (rights) needed to buy one new share. Example: 5 rights buy 1 new share, so (20 − 14) ÷ (5 + 1) = $1.00, which matches 20 − 19.
Net proceeds to issuer: Net proceeds = shares sold × offer price − underwriting spread − other issue costs; In a firm commitment deal the underwriter pays the issuer the offer price less the spread.
IPO first-day return (underpricing): Underpricing = (first-day close − offer price) ÷ offer price; A positive value means the shares were underpriced relative to the first trading price.
Value of non-convertible, non-callable preferred share: V = D ÷ r; Treats the fixed dividend D as a perpetuity. r is the required return. Use annual D with annual r.
Conversion value of convertible preferred: Conversion value = conversion ratio × market price of common share; If conversion value exceeds the preferred's own value, conversion is attractive to the holder.
Claim priority in liquidation: Creditors > preferred shares > common shares; Common shareholders are residual claimants and rank last.
Cumulative preferred dividend owed: Owed = dividend rate × par × years missed (plus current dividend); Applies only to cumulative preferred. Non-cumulative missed dividends are not owed.
Call market: Orders collected → one price at a set time (call auction); Single clearing price, all orders executed together. Lots of liquidity at one moment.
Continuous market: Trades happen whenever bid and ask orders can be matched during trading hours; Prices can differ from trade to trade.
Quote-driven (dealer) market: Dealers post bid and ask; dealer earns the spread; You trade against the dealer. Typical: FX, bonds.
Order-driven market: Public orders matched by rules: order precedence + trade-pricing rule; Typical: electronic limit order book on an exchange.
Brokered market: Broker finds a counterparty for hard-to-trade or large trades; Used for block trades, illiquid assets, unique assets.
ATS and dark pool: ATS = non-exchange matching venue; dark pool = ATS with no pre-trade transparency; All dark pools are ATSs or similar; not all ATSs are dark.
Buy limit order: Executes at limit price or lower; A resting buy limit is placed below the market. If set at or above the best ask, it is marketable and fills immediately.
Sell limit order: Executes at limit price or higher; Placed above the market when resting.
Sell stop order: Triggers when trade price ≤ stop price; then becomes a market order; Stop price sits below the current market. Used to protect a long position.
Buy stop order: Triggers when trade price ≥ stop price; then becomes a market order; Stop price sits above the current market. Used to protect a short position.
Stop-limit order: Trigger at stop price; then becomes a limit order at the limit price; May not fill if the price moves through the limit.
Order priority: Price priority first, then time precedence; Highest bid and lowest offer go first; ties go to the earliest order.
Fill-or-kill vs immediate-or-cancel: FOK: full quantity now or cancel. IOC: fill what you can now, cancel the rest; Day orders expire at close; GTC orders persist until filled or cancelled.
Leverage ratio: Leverage = Position value ÷ Equity = 1 ÷ Initial margin %; A 50% initial margin gives leverage of 2.
Equity and loan at purchase (long): Equity = Initial margin % × P0 × N; Loan = P0 × N − Equity; P0 is the purchase price and N is the number of shares.
Margin percentage (long): Margin % = (Market value of shares − Loan) ÷ Market value of shares; A margin call occurs when this falls below the maintenance margin.
Margin call price (long): Margin call price = P0 × (1 − Initial margin) ÷ (1 − Maintenance margin); Assumes no interest or costs added to the loan. Price must fall to this level.
Margin call price (short): Margin call price = P0 × (1 + Initial margin) ÷ (1 + Maintenance margin); Short sellers get the call when price rises. Equity as a percentage is measured against the market value of the shares owed.
Return on equity (long): Return = [(P1 − P0) × N + Dividends − Interest − Commissions] ÷ Equity; Divide by your own equity, not by the position value.
Return on equity (short): Return = [(P0 − P1) × N − Dividends paid − Costs] ÷ Equity; Add interest earned on proceeds only if the question says so.
Leveraged return: R equity = R asset + (Loan ÷ Equity) × (R asset − borrowing rate); Useful when the question gives percentage returns instead of prices.
Weak form: Prices reflect all past market data (prices, volume); Technical analysis should not earn excess returns. Fundamental analysis and insider information might.
Semi-strong form: Prices reflect all public information (past data plus public news and filings); Fundamental analysis should not earn excess returns. Insider information might.
Strong form: Prices reflect all information, public and private; No one earns excess returns, including insiders. Evidence that insiders can earn abnormal returns generally rejects this form.
Nesting of forms: Strong ⇒ Semi-strong ⇒ Weak; Strong form efficiency implies semi-strong and weak form efficiency. So rejecting a lower form rejects all higher forms: rejecting weak form rejects all three. Rejecting strong form is consistent with weak and semi-strong forms still holding, but it does not prove them.
Informational vs operational efficiency: Informational: prices reflect information. Operational: low trading costs and efficient execution; A market can be operationally efficient yet informationally inefficient, and the reverse.
Price-weighted index value: Index = Σ prices of constituents ÷ divisor; Initial divisor is usually the number of stocks. Each stock's weight = its price ÷ sum of all prices.
Divisor after a split or constituent change: New divisor = Σ new prices ÷ index value before the change; Keeps the index value unchanged at the moment of the change. A split into more shares lowers the divisor.
Market-cap weight: Weight of stock i = (price × shares outstanding)i ÷ Σ (price × shares outstanding); Use float shares (shares available to the public) for a float-adjusted index.
Market-cap-weighted index value: Index = (Σ current market caps ÷ base-period market cap) × base value; Index return equals the weighted average of constituent returns using beginning weights.
Equal-weighted index return: Return = (1 ÷ N) × Σ constituent returns; Holds when you start the period at equal weights. Weights drift, so rebalancing is needed.
Index return from weights: Index return = Σ (beginning weight × return) for any weighting method; Works for price, cap, equal or fundamental weights, as long as you use beginning-of-period weights.

Quick revision

Primary market: the issuer receives the money. Secondary market: investors trade among themselves and the issuer does not receive proceeds.
An IPO is the first public sale of shares. A seasoned (follow-on) offering is a further sale by a listed company.
A private placement sells shares to a small group of qualified investors, not to the public.
Preferred shares usually rank ahead of common shares for dividends and in liquidation but typically carry limited or no voting rights.
A market order prioritises execution. A limit order prioritises price.
A buy stop order is placed above the current price. A sell stop order is placed below it.
Leverage ratio on margin = position value ÷ equity. Initial margin of 40% means leverage of 2.5.
Margin call price (long) = purchase price × (1 − initial margin) ÷ (1 − maintenance margin).
Margin call price (short) = short sale price × (1 + initial margin) ÷ (1 + maintenance margin).
Weak-form efficiency: past prices and volume cannot be used to earn abnormal returns.
Semi-strong form: all public information is already in prices. Strong form: private information too.
Anomalies are patterns that appear to contradict efficiency, but they may reflect risk, data mining or costs.
Index weighting matters: price-weighted, equal-weighted and market-cap-weighted indices respond differently to the same price moves.

Common mistakes

Saying the issuer receives cash when shares trade on an exchange. Fix: Only a primary market sale gives the issuer cash. Exchange trading after listing is secondary and moves money between investors.
Treating an IPO and a follow-on offering as the same thing. Fix: An IPO is the first public sale by a private company. A follow-on is by a company already public, also called a seasoned equity offering.
Saying preferred shareholders normally have full voting rights. Fix: Remember that preferred usually has no voting rights or limited ones, in exchange for priority in dividends and liquidation.
Mixing up cumulative and participating. Fix: Cumulative protects against missed dividends. Participating gives extra dividends or liquidation proceeds beyond the stated amount.
Saying a call market trades continuously through the day. Fix: Link call with auction: orders pile up, then one price at one time.
Treating all dark pools and ATSs as the same thing. Fix: An ATS is the broad category. A dark pool is an ATS (or similar venue) with no pre-trade transparency.
Saying a stop order guarantees the stop price. Fix: A triggered stop becomes a market order, so the fill can be worse than the stop price. Only a limit fixes a price.
Placing a sell stop above the market. Fix: A sell stop sits below the market and a buy stop above it. A sell limit sits above the market.
Using maintenance margin as the loan percentage, for example price × (1 − MM) as the call price. Fix: Keep the loan fixed in currency. Solve (P × N − Loan) ÷ (P × N) = MM for P.
Calculating return on the position value instead of on equity. Fix: Divide the total gain or loss, after interest and dividends, by your initial equity.

Exam tips

Start every classification question with 'does the issuer receive the cash?' It removes two options quickly.
Learn the exact vocabulary: seasoned equity offering equals follow-on offering, and both mean new shares from an already listed company.
A private placement is still primary. Do not rule it out because it is not public.
For rights issue maths, check that your ex-rights price lies between the subscription price and the old price. If not, you made an error.
With no penalty for wrong answers, always answer, but guess only after eliminating options that fail the primary or secondary test.
Match the feature to the beneficiary: callable favours the issuer, putable and convertible favour the holder.
Remember that questions on DRs usually test sponsored versus unsponsored and currency risk, not detailed listing rules.
For preferred valuation, check for conversion or call features before using V = D ÷ r.