CFA Level I · CFA Level I Exam

Fixed-Income Issuance and Trading: formula sheet

Full chapter guide

Key formulas

Source-of-repayment rule: Issuer type → source of repayment → credit risk; Sovereign: taxes and borrowing. General obligation: taxing power. Revenue bond: project income. Corporate: firm cash flow. Securitized: asset pool.
Municipal bond split (US): Municipal bonds = general obligation bonds + revenue bonds; General obligation bonds rely on the issuer's taxing power. Revenue bonds rely on a specific project's revenue.
Support hierarchy for agencies: Explicit guarantee > implied support > no support; A stronger government link generally means lower credit risk, but check the guarantor's own rating.
Supranational ownership: Supranational = owned by multiple sovereign member countries; Not owned by one country, so not a sovereign or an agency of one state.
Underwritten offering risk: Underwritten: issuer gets fixed proceeds; dealer bears unsold-bond risk; Also called firm commitment. The dealer earns the spread between purchase price and resale price.
Best-efforts offering risk: Best-efforts: dealer acts as agent; issuer bears unsold-bond risk; No guarantee of amount sold or proceeds.
Underwriter spread: Underwriting spread = resale (offer) price − price paid to issuer; Per bond, then multiply by the number of bonds for total gross spread.
Shelf registration: Register once, issue in tranches over time; Gives timing flexibility. Not a separate way of pricing, only a registration approach.
Private placement: No public registration, limited investors, less liquidity; Faster and cheaper, but resale is restricted.
Bid-ask spread: Spread = Ask price − Bid price; The dealer buys at the bid and sells at the ask. You, the client, sell at the bid and buy at the ask.
Full (invoice) price: Full price = Clean price + Accrued interest; The buyer pays the full price at settlement. Quotes are clean prices.
Accrued interest: AI = Coupon per period × (days since last coupon ÷ days in coupon period); Counted from the last coupon date up to the settlement date. The day-count convention (for example 30/360 or actual/actual) depends on the bond.
Spread as percent of price: Relative spread = (Ask − Bid) ÷ Mid price, where Mid = (Bid + Ask) ÷ 2; Use this to compare liquidity across bonds with different prices.
Repurchase price: Repurchase price = Sale price × (1 + repo rate × days ÷ 360); Uses simple interest. Use the day-count the question gives (commonly 360 for USD).
Repo interest: Interest = Repurchase price − Sale price; This is what the cash borrower pays the cash lender.
Repo rate from prices: Repo rate = (Repurchase price ÷ Sale price − 1) × (360 ÷ days); Annualized simple rate.
Loan amount with haircut: Loan = Collateral market value × (1 − haircut); Haircut is a percentage of collateral value, not of the loan.
Haircut from loan: Haircut = (Collateral value − Loan) ÷ Collateral value; Equivalent to 1 − loan ÷ collateral.
Commercial paper discount price: Price = Face value × (1 − discount rate × days ÷ 360); Discount rate is quoted on face value. Actual yield on price is higher than the discount rate.

Quick revision

Issuers include sovereigns, non-sovereign government and quasi-government entities, agencies, supranationals, corporates and securitisation vehicles; know the typical credit and purpose of each.
Primary market means new issuance; secondary market means trading of bonds already issued.
In an underwritten offering the investment bank takes on the risk of selling the issue; in best efforts it does not guarantee the sale.
A private placement is sold to a small group of investors, usually without full public registration.
A shelf registration lets an issuer register once and sell in portions later.
Government bonds are often sold by auction.
Most bonds trade over the counter through dealers, not on exchanges.
Dealers quote a bid price (where they buy) and an ask price (where they sell); the difference is the spread.
A repo is a sale of securities with an agreement to repurchase them at a set later date and price; the seller is borrowing cash and the buyer is lending it.
The repo rate is the implied interest on the cash lent; the haircut is the initial margin, so the collateral's value exceeds the cash advanced.
Variation margin is the adjustment made as the collateral's value changes, so the lender stays protected.
Commercial paper is short-term, usually unsecured, and issued by creditworthy firms to fund working capital.
Reverse repo is the same trade seen from the cash lender's side.

Common mistakes

Treating all government-related issuers as sovereign. Fix: Only the national government itself is sovereign. States and cities are non-sovereign. Agencies are quasi-government entities. Supranationals belong to several countries.
Assuming agency bonds always carry an explicit government guarantee. Fix: Check the stem. Many agencies have only implied support, which is weaker than an explicit guarantee.
Saying the issuer bears unsold-bond risk in an underwritten offering. Fix: Underwritten means the dealer buys the whole issue, so the dealer bears the risk. Best-efforts leaves it with the issuer.
Treating shelf registration as a type of selling method like auction. Fix: Shelf registration is a registration approach. It allows later sales in tranches, which may themselves be underwritten or sold otherwise.
Saying most bonds trade on exchanges like shares. Fix: Remember that most bond trading is OTC through dealers because of the huge number of distinct issues. Exchange trading exists but is the smaller share.
Reversing bid and ask from the client's perspective. Fix: The dealer bids (buys from you) and offers (sells to you). You sell at the bid and buy at the ask. The ask is the higher price.
Treating repo and reverse repo as different trades. Fix: Remember they are one trade. The cash borrower does a repo. The cash lender does a reverse repo.
Applying the haircut to the loan instead of to collateral value. Fix: Loan = collateral value × (1 − haircut). The haircut is a share of collateral value.

Exam tips

Most items test classification. Find the owner and the source of repayment before looking at the options.
Watch for explicit versus implied government support. The stem usually gives a clue.
Remember that questions use three options and no combined answers, so one option is usually a mislabelled issuer type. Eliminate it first.
Do not assume the highest-rated issuer is always sovereign. Read for currency and country strength.
If the stem mentions member countries and development lending, think supranational immediately.
Expect standalone three-option questions that test one clue: who bears the unsold risk, or what shelf registration allows.
Remove options that reverse the risk holder. This usually eliminates two choices fast.
If a calculation appears, it is simple multiplication. Use the price paid to the issuer for proceeds and the price difference for the spread.