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What is a bond?
Answer: A debt instrument in which the issuer (borrower) promises to pay the bondholder (lender) periodic coupon interest and return the principal (par value) at maturity.
Bonds are contractual claims; equity represents residual ownership. The contract terms are set out in the bond indenture.
What is par value (face value) of a bond?
Answer: The principal amount the issuer promises to repay at maturity; coupon payments are calculated as a percentage of par value.
Example: a bond with $1,000 par value and 5% annual coupon pays $50/year regardless of its market price.
What is a zero-coupon bond?
Answer: A bond that pays no periodic coupons and is sold at a discount to par, with the investor's return coming entirely from price appreciation to par at maturity.
Price = Face value / (1+y)^N, so all return is implicit in the discount.
What is a floating-rate note (FRN)?
Answer: A bond whose coupon rate resets periodically based on a reference rate (e.g., SOFR) plus a fixed spread.
FRNs have low interest rate risk because the coupon adjusts with market rates, keeping price close to par between reset dates.
Callable bond vs putable bond — who holds the option?
Answer: Callable: issuer has the right to redeem the bond early (benefits issuer when rates fall). Putable: investor has the right to sell the bond back early (benefits investor when rates rise).
Callable bonds trade at lower prices/higher yields than otherwise-identical option-free bonds; putable bonds trade at higher prices/lower yields.
What is a convertible bond?
Answer: A bond that gives the holder the right to convert it into a specified number of shares of the issuer's common stock.
Convertibles combine a straight bond with an embedded equity call option, so they typically offer a lower coupon than a comparable non-convertible bond.
Current yield formula
Answer: Current yield = Annual coupon payment / Current market price of the bond
Example: a bond with $60 annual coupon trading at $1,050 has a current yield of 60/1,050 = 5.71%. It ignores capital gains/losses and the time value of money.
Yield to maturity (YTM) — definition and pricing formula
Answer: YTM is the internal rate of return that equates the bond's discounted cash flows to its current price: Price = Σ [C/(1+YTM)^t] for t=1…N + F/(1+YTM)^N
C = periodic coupon payment, F = face value, N = number of periods. YTM assumes coupons are reinvested at the YTM itself and the bond is held to maturity.
What is a spot rate, and how is it used to price a bond?
Answer: A spot rate z_t is the yield on a zero-coupon bond maturing at time t. A bond's arbitrage-free price is: Price = Σ [CF_t / (1+z_t)^t] for t=1…N
Unlike YTM (one discount rate for all cash flows), spot-rate pricing discounts each cash flow at the rate matching its own maturity.
What is a forward rate, and how does it relate to spot rates?
Answer: A forward rate is an interest rate for a future period implied by current spot rates, e.g.: (1+z2)^2 = (1+z1) × (1+1f1)
z1, z2 = 1- and 2-year spot rates; 1f1 = the 1-year forward rate starting one year from now. Forward rates are used to test the expectations theory of the yield curve.
Bond-equivalent yield (BEY) vs effective annual yield (EAY)
Answer: BEY annualizes a semiannual yield by simply doubling it (2 × semiannual rate); EAY compounds it: EAY = (1 + periodic rate)^(periods per year) − 1.
Example: semiannual rate of 3% gives BEY = 6% but EAY = (1.03)^2 − 1 = 6.09%. EAY is always ≥ BEY when compounding more than once a year.
Describe the price–yield relationship for a bond and sketch its shape.
Answer: Bond price and yield move inversely, and the relationship is convex (curved), not linear.
Example: as yield rises from 2% to 10%, price falls but at a decreasing rate — price declines are smaller for each additional 2% rise in yield at higher yield levels.
When does a bond trade at a premium, discount, or par?
Answer: Premium: coupon rate > market yield (price > par). Discount: coupon rate < market yield (price < par). Par: coupon rate = market yield (price = par).
As a bond approaches maturity, its price converges to par value regardless of starting premium/discount status ('pull to par').
Why is the price–yield curve convex rather than linear?
Answer: Because the price impact of a given change in yield is not symmetric: price increases from a yield decrease are larger than price decreases from an equal-size yield increase.
This asymmetry (positive convexity) is beneficial to bondholders and is the reason duration alone (a linear/tangent-line approximation) misestimates price changes for large yield moves.
What is Macaulay duration?
Answer: The weighted-average time (in years) until a bond's cash flows are received, with weights equal to the present value of each cash flow as a fraction of the bond's total price.
Macaulay duration measures a bond's interest rate exposure and 'average' time to receive cash flows; a zero-coupon bond's Macaulay duration equals its maturity.
Modified duration formula
Answer: Modified duration = Macaulay duration / (1 + y/k)
y = yield to maturity (annualized), k = number of compounding periods per year. Modified duration estimates the % price change for a 1% change in yield.
Formula for approximate % price change using duration and convexity
Answer: %ΔPrice ≈ −(ModDur × Δy) + 0.5 × Convexity × (Δy)^2
ModDur = modified duration, Δy = change in yield (decimal), Convexity = the bond's convexity measure. Example: ModDur=7, Convexity=80, Δy=+0.01 → %ΔP ≈ −7(0.01)+0.5(80)(0.0001) = −7%+0.4% = −6.6%.
What is effective duration, and when must it be used instead of modified duration?
Answer: Effective duration measures price sensitivity to yield changes using a pricing model that accounts for changes in expected cash flows, calculated as: EffDur = (P− − P+) / (2 × P0 × Δy)
P− and P+ are prices if yield falls/rises by Δy. It must be used for bonds with embedded options (callable, putable, MBS) because their cash flows change as rates change, unlike option-free bonds.
What does convexity measure, and how does it affect duration-based price estimates?
Answer: Convexity measures the curvature of the price-yield relationship; adding the convexity adjustment improves the accuracy of duration's linear price-change estimate, especially for large yield changes.
Duration alone (the tangent line) underestimates price increases and overestimates price decreases; the convexity term corrects for this gap, which widens as curvature increases.
What are the three components of credit risk?
Answer: Default risk (issuer fails to pay), spread risk (credit spread widens, lowering price), and downgrade risk (rating agency lowers the issuer's credit rating).
All three can reduce bond value even if the issuer never actually defaults.
Where is the cutoff between investment-grade and high-yield (speculative) bonds?
Answer: Investment grade: Baa3/BBB− and above (Moody's/S&P). High yield (junk): Ba1/BB+ and below.
High-yield bonds carry greater default risk and trade at higher credit spreads than investment-grade bonds.
What is a credit spread?
Answer: The difference in yield between a credit-risky bond and a benchmark risk-free bond (e.g., a government bond) of similar maturity.
Credit spreads widen when perceived default risk rises (e.g., during recessions) and narrow when credit conditions improve.
What is the term structure of interest rates, and what are its three common shapes?
Answer: The term structure (yield curve) plots yields against maturities for bonds of similar credit quality. Common shapes: normal (upward-sloping), inverted (downward-sloping), and flat.
A normal curve reflects investors demanding higher yields for longer maturities; an inverted curve often signals expectations of economic slowdown/rate cuts.
Pure expectations theory of the term structure
Answer: Long-term rates are determined by the market's expectations of future short-term rates; forward rates are unbiased predictors of future spot rates.
Under this theory alone, an upward-sloping curve implies the market expects short-term rates to rise.
Liquidity preference theory of the term structure
Answer: Investors demand a liquidity premium for holding longer-maturity bonds, so forward rates are biased estimates of future spot rates (upward-biased) even if rate expectations are flat.
This premium helps explain why yield curves are normally upward-sloping even absent expectations of rising rates.
Market segmentation theory of the term structure
Answer: Yields at different maturities are determined independently by supply and demand within separate maturity segments, because investors/issuers have preferred habitats and do not freely substitute across maturities.
This theory explains why the yield curve can have humps or irregular shapes not predicted by expectations alone.
What is securitization?
Answer: The process of pooling financial assets (e.g., mortgages, loans, receivables) and issuing securities backed by the cash flows of that pool to investors.
Securitization converts illiquid assets into tradable securities and typically involves a special purpose entity (SPE) to isolate the assets from the originator's credit risk.
What is a mortgage pass-through security, and what is its key risk?
Answer: An MBS pass-through distributes the pooled mortgage principal and interest payments to investors; its key risk is prepayment risk — borrowers repaying principal early (often when rates fall), shortening the security's life.
Prepayment risk makes pass-through cash flows uncertain, unlike a standard bond, and causes negative convexity when rates fall sharply.
Primary market vs secondary market
Answer: Primary market: where issuers sell new securities directly to investors to raise capital (e.g., IPOs, bond issuance). Secondary market: where existing securities are traded among investors (e.g., exchanges).
Only primary market transactions provide proceeds to the issuer; secondary market trading provides liquidity and price discovery.
Market order vs limit order
Answer: Market order: executes immediately at the best available current price. Limit order: executes only at a specified price or better.
Market orders guarantee execution but not price; limit orders guarantee price but not execution.
Quote-driven vs order-driven market structure
Answer: Quote-driven (dealer) markets: trades occur against prices quoted by dealers/market makers. Order-driven markets: trades are matched directly between buy and sell orders via rules (e.g., an order book), without a dedicated dealer.
Many modern exchanges use hybrid structures combining both mechanisms.
Distinguish price-weighted, market-cap-weighted, and equal-weighted equity indices.
Answer: Price-weighted: weight based on each stock's share price (e.g., DJIA). Market-cap-weighted: weight based on market capitalization (e.g., S&P 500). Equal-weighted: every constituent gets the same weight regardless of price or size.
A stock split reduces a stock's influence in a price-weighted index even though the company's value is unchanged — a key limitation of price weighting.
What are the three forms of the Efficient Market Hypothesis (EMH)?
Answer: Weak form: prices reflect all past price/volume data. Semi-strong form: prices reflect all publicly available information. Strong form: prices reflect all information, public and private (insider).
Under semi-strong efficiency, fundamental analysis of public information cannot consistently generate abnormal returns; under strong-form efficiency, even insider information cannot.
General dividend discount model (DDM) formula
Answer: V0 = Σ [D_t / (1+r)^t] for t = 1 to ∞
V0 = intrinsic value of the stock today, D_t = expected dividend in period t, r = required rate of return on equity. The model values a stock as the present value of all future expected dividends.
Gordon growth model formula
Answer: V0 = D1 / (r − g)
D1 = expected dividend next period = D0×(1+g), r = required return, g = constant perpetual dividend growth rate (r must exceed g). Example: D0=$2, g=4%, r=9% → D1=$2.08, V0 = 2.08/(0.09−0.04) = $41.60.
Name the common equity price multiples and their formulas.
Answer: P/E = Price per share / Earnings per share. P/B = Price per share / Book value per share. P/S = Price per share / Sales per share. P/CF = Price per share / Cash flow per share.
Lower multiples can indicate undervaluation (or weaker growth/quality prospects), so multiples are best compared against peers or historical norms, not used in isolation.
Enterprise value (EV) formula
Answer: EV = Market value of common equity + Market value of preferred stock + Total debt − Cash and cash equivalents
EV represents the theoretical takeover cost of a company and is used in multiples like EV/EBITDA, which are useful for comparing firms with different capital structures.
What are Porter's Five Forces used in industry analysis?
Answer: 1) Threat of new entrants, 2) Bargaining power of suppliers, 3) Bargaining power of buyers, 4) Threat of substitute products, 5) Rivalry among existing competitors.
Stronger forces (e.g., low entry barriers, high buyer power) tend to compress industry profitability, which analysts factor into competitive and valuation analysis.
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