Fixed Income Flashcards
Explain the credit valuation adjustment (CVA).
Explain the swap rate curve.
Describe the parameters that define a given CDS product.
Describe convexity.
Explain reduced form models, including assumptions, strengths, and weaknesses.
Explain a positive upfront payment.
Describe the process of calibrating a binomial interest rate tree to match a specific term structure.
Describe credit-default swap (CDS).
Describe ratchet bonds.
Calculate the value of a callable or putable bond from an interest rate tree.
Describe the relationship between forward and spot rates and the shape of the yield curve.
Explain the unbiased expectations theory.
Describe credit events.
Describe the assumptions concerning the evolution of spot rates in relation to forward rates implicit in active bond portfolio management.
A bond PM would consider the market price of a bond to be less than its value (undervalued) if expected future spot rates are less than quoted forward rates. That is, the market discounts the bonds cash flows by the higher forward rates rather than the lower expected spot rates.
Explain how changes in the level and shape of the yield curve affect the value of a callable or putable bond.
Describe the downside risk of a convertible bond.
Calculate effective duration of a callable or putable bond.
Explain a succession event.
Explain the maturity structure of yield volatilities and their effect on price volatility.
List types of callable bonds.
An American-style callable bond can be called by the issuer at any time, starting with the first call date until maturity.
A European-style callable bond can only be called by the issuer at a single date at the end of the lockout period.
A Bermudan-style callable bond can be called by the issuer on specified dates following the lockout period.
Describe the local expectations theory.
Distinguish between a physical settlement and a cash settlement.
Describe the option analogy in structural models.
Equity holders have an implied option to either pay off liabilities K at maturity by selling assets and receive AT – K or default on the issue and allow debt holders to assume ownership of assets. The choice depends on whether AT – K is positive (liquidate) or negative (default).
Describe the relationship between expected and realized returns on bonds.
Describe the use of key rate durations to evaluate the interest rate sensitivity of bonds with embedded options.
Define convertible bonds.
Describe the Libor-OIS spread.
Explain loss given default (LGD).
Compare effective durations of callable, putable, and straight bonds.
As interest rates fall, bond value decreases at a decreasing rate due to call option value increases. As the call goes into the money, price appreciation ceases.
As interest rates rise, bond value falls at a decreasing rate due to put option value increases.
Effective duration on both callable and putable bonds will therefore be less than straight-bond duration.
Describe a binomial interest rate tree framework.
Calculate and interpret the components of a convertible bond’s value.
Conversion value involves the market price of shares at conversion and the conversion ratio:
VConversion = P0 × Conversion ratio
= P0 × (#Shares ÷ Bond)
Minimum value equals the higher of conversion value or straight bond value calculated using the arbitrage-free valuation framework:
VMin = Max[Conversion; Straight]
Explain the relationships between the values of a callable or putable bond, the underlying option-free (straight) bond, and the embedded option.
Explain structural models of corporate credit risk including assumptions, strengths, and weaknesses.
Explain the liquidity preference theory.
Distinguish among level, steepness, and curvature risks that affect the shape of the yield curve.
Level – Upward or downward (parallel) shifts in the yield curve.
Steepness – Changes in yield curve slope that occur when short-term and long-term rates have different changes.
Curvature – Changes in shorter rates and longer rates are greater than changes in middle rates.
Describe the Z-spread.
Describe pathwise valuation in a binomial interest rate framework and calculate the value of a fixed-income instrument given its cash flows along each path.
Explain how a bond’s exposure to each of the factors driving the yield curve can be used to manage yield curve risks.
Describe effective duration, key rate duration, and a measure based on the factor model.
Compare the credit analysis required for securitized debt to the credit analysis of corporate debt.
Senior tranches are paid first, followed by junior tranches and with remaining cash going to equity holders. Losses are absorbed first by junior tranches and then by senior tranches.
Analysts must also consider enhancements (underlying collateral, total debt, liquidity) or other constraints that could affect spreads, and the relationship between obligor and originator. Granularity requires valuing individual assets vs homogeneity (statistical).
Describe how the arbitrage-free framework can be used to value a bond with embedded options.
Explain arbitrage-free (AF) models and how they are used.
Describe a tranche CDS.
A tranche CDS also covers a portfolio of borrowers, but only to a prespecified amount of losses (as with tranches of asset-backed securities that only cover a specific amount of losses).
Describe the use of one-sided durations to evaluate the interest rate sensitivity of bonds with embedded options.
One-sided durations separately measure price sensitivity to rate increases and rate decreases. This is especially important when the embedded option is near-the-money.
Describe sinking fund bonds and the acceleration option.
Define the preferred habitat theory and its implications for the shape of the yield curve
Calculate the value of a floored floating rate bond.
Explain determinants of the term structure of credit spreads.
Compare pricing using a zero-coupon yield curve to pricing using an arbitrage-free binomial lattice.
Describe the strategy of rolling down the yield curve.
Rolling down the yield curve involves holding a security where expected spot rates are less than quoted forward rates.
With a stable yield curve, buying a maturity greater than holding period captures return due to added duration as well as the spread between spot and forward.
Describe the use of CDS to take advantage of valuation disparities among separate markets, such as bonds, loans, equities, and equity-linked securities.
Explain how interest rate volatility affects the value of a callable or putable bond.
Compare effective convexities of callable, putable, and straight bonds.
Interpret effective duration of a callable or putable bond.
Calculate the value of a capped floating rate bond.
Distinguish an extendible bond from a putable bond.
An extendible bond offers the bondholder the right to keep the bond a number of years after maturity, possibly with a different coupon rate.
Calculate and interpret the swap spread for a given maturity.
The swap spread measures the difference between the higher swap fixed rate and “on-the-run” government securities of the same maturity/tenor as the swap.
Swap spreads indicate perceived credit and liquidity risks and increases for the tenor of the swap (time value). For default-free securities, swap spreads indicate liquidity or mispricing.
Explain the implications of traditional term structure theories for the shape of the yield curve.
Describe fixed-income securities with embedded options.
On what does duration for bonds with embedded options depend?
Define the segmented markets theory and its implications for the shape of the yield curve.
Segmented markets theory contends that yield for each maturity along the yield curve is determined independently by supply of and demand for funds at a specific maturity; yields do not reflect separate expected spot rates or liquidity premiums.
This theory is consistent with regulatory or self-imposed asset-liability management constraints.
Explain how a bond’s exposure to each of the factors driving the yield curve can be measured (1).
How is the TED spread calculated?
TED spread measures LIBOR less the yield on a T-bill with the same maturity. The TED spread indicates the perceived level of credit risk in the overall economy.
Explain expected loss given default (LGD) for any period.
Define embedded options.
Explain how interest rate volatility affects option-adjusted spreads.
Explain credit ratings.
Issuer ratings based on senior unsecured debt are used in the wholesale bond market. Priority of claims lead to “notching” the rating for specific bond issues. Agencies also issue an outlook for future ratings and indicate when a firm is “under watch” for a rating change.
Identify the options in change-of-control events.
Define option-adjusted spread (OAS).
OAS is the constant spread added to all one-period forward reference rates that equates calculated value with the market price.
[Z-spread for a risky bond is its OAS at zero volatility.]
Describe how callable and putable convertible bonds are valued.
Explain expected exposure.
Explain the upside of a convertible bond.
Describe the use of CDS to manage credit exposures.
Explain the asymmetric response problem with using effective duration.
Effective duration, an average measure of price change, does not adequately capture capped upside potential and larger loss for an in-the-money embedded call or capped loss potential and larger gain for an in-the-money embedded put.
Explain the principles underlying and factors that influence the market’s pricing of CDS.
PVProtection = Upfront payment + PVPremium
The protection leg represents expected loss given default; that is, the risk-free PV product of loss given default and hazard rate (the probability of default given that it has not occurred) at each cash flow.
PCDS = 100 − %Upfront premium
≈100 − [D(Credit spread − Fixed Coupon)]
Describe defining features of a convertible bond.
Describe how zero-coupon rates (spot rates) may be obtained from the par curve by bootstrapping.
Explain the calculation and use of option-adjusted spreads (OAS).
Calculate the arbitrage-free (AF) value of an option-free, fixed-rate coupon bond.
Identify the benefits to issuers and investors of convertible bonds.
Investors accept lower coupons on convertible bonds compared to otherwise identical straight bonds because they can participate in the upside of the issuer’s equity through the conversion mechanism.
Issuers benefit from lower coupon rates and from no longer having to repay the debt (if the bonds are converted into equity).
Interpret changes in a credit spread.
Benchmark securities provide compensation for macroeconomic factors affecting the securities market. A spread over benchmark captures taxation and compensation for liquidity risk, expected LGD, and uncertainty about LGD. If CVA varies and the spread varies more or less, it is related to variables other than credit risk.
Calculate and interpret effective duration for a callable or putable bond.
Describe the backward induction valuation methodology and calculate the value of a fixed income instrument given its cash flow at each node.
Explain credit scores.
Describe the delivery option as part of sinking fund bonds and characterize their combinations with a call option.
Calculate and interpret a convertible bond’s conversion value and the conversion premium to bondholders.
Describe a Monte Carlo method forward rate simulation.
Describe the actual probability of default (i.e., likelihood an investor will not meet its obligations on schedule).
Describe how the settlement amount is calculated.
Payout amount = Notional × Payout rate
= Notional × (1 − Recovery rate)
Payout may occur long after the credit event. The payout ratio is established after dealers submit bids for the cheapest-to-deliver defaulted debt. CDS parties accept this as the recovery rate, although actual recovery can be quite different.
Calculate the expected return on a bond given transition in its credit rating.
Describe how a convertible bond is valued in an arbitrage-free framework.
Describe the use of CDS to express views regarding changes in shape and/or level of the credit curve.
Explain how a bond’s exposure to each of the factors driving the yield curve can be measured (2).
Describe single-name and index CDS.
Interpret a term structure of credit spreads.
Explain why and how market participants use the swap rate curve in valuation.
Describe the relationship of spot rates and the yield curve.
Describe floating rate bonds (i.e., floaters).
Calculate the value of a bond and its credit spread, given assumptions about the credit risk parameters.
Describe equilibrium models of term structure and how they are used.
Equilibrium models apply regression analysis to variables assumed to affect interest rates. Cox-Ingersoll-Ross (CIR) assumes an equilibrium short-term rate r at which no one else seeks to borrow or lend with a “drift” or reversion-to-mean component and small adjustments based on the size of r. Vasicek assumes mean reversion but assumes constant volatility and suggests possible negative rates.
Explain what is meant by arbitrage-free valuation of a fixed income instrument.
Compare the risk-return characteristics of a convertible bond with the risk-return characteristics of a straight bond and of the underlying common stock.
Describe applications of a Monte Carlo method forward rate simulation.
Identify the disadvantages of convertible bonds.
The issuer’s current shareholders face earnings dilution if bondholders convert.
Issuers with unconverted bonds at maturity may face higher refunding rates. Bondholders in that scenario lose out on interest income relative to otherwise identical straight bonds.
Describe the risk-neutral probability of default (P*).
Risk-neutral probability equates the current market value of the bond to expected receipt of cash flows discounted at the risk-free rate. Risk-neutral probabilities are used because the cash flows explicitly consider risk of default.
