Twists refer to:

yield curve changes when the slope becomes either flatter or more steep. A flattening (steepening) of the yield curve means that the spread between short- and long-term rates has narrowed (widened).

parallel shift up and down of the yield curve

The usual method is to apply parallel shifts to the yield curve, use those curves to compute new sets of forward rates, and then enter each set of rates into the interest rate tree. The resulting volatility of the present value of the bond is the measure of effective duration. 

A sequential-pay CMO is structured so that each class of bond:

is retired sequentially

When there are prepayments, the principal in the first bond class (tranche) is reduced until it is fully retired, then the principal of the next bond class is retired, and so on.

The no-arbitrage price of a futures contract (formula)

S = spot rate

Annualized yield volatility (formula)

Annualized yield volatility = σ × sqrt(#trading days per yr)

where:
σ = the daily yield volatility

Key rate duration can be defined as:

the approximate percentage change in the value of a bond or bond portfolio in response to a 100 basis point change in a key rate, holding all other rates constant, where every security or portfolio has a set of key rate durations, one for each key rate maturity point.

Important considerations of the issuer’s character include (6 things):

(1) strategic direction

(2) financial philosophy

(3) conservatism

(4) track record

(5) succession planning

(6) control systems

First lien loans

secure bonds

senior subordinated debt

subordinated debt

unsecured debt

Market Conversion Price of a convertible security (formula):

Premium over straight price (formula):

market conversion price =

market price of convertible bond ÷ conversion ratio. 

POSP = (market price of bond) / (straight value) − 1

Calculate price of forward contract on Treasury bond (with coupon payment paid in x days)

The forward price is calculated as the bond price minus the present value of the coupon, times one plus the risk-free rate for the term of the forward.

(1,000 – (PMT/2)/(1+r)^x/365) (1+r)^t/12 = $1,001.84

t = length of forward contract

The liquidity theory

Forward rates reflect investors’ expectations of future rates plus a liquidity premium to compensate them for exposure to interest rate risk, and this liquidity premium is positively related to maturity. The implication of the liquidity theory is that forward rates are a biased estimate of the market’s expectation of future rates, since they include a liquidity premium.

capacity, collateral, covenants, and character

How do the risk-return characteristics of a newly issued convertible bond compare with the risk-return characteristics of ownership of the underlying common stock?

The convertible bond has __ risk and __ return potential.

All things equal, highest OAS:

Bond with (highest/lowest) price

(Call/put)able bond with (high/low)est rating

Lowest price

Callable bond with lowest rating

For many sequential-pay CMO structures, the last tranche to be paid principal also does not receive current interest until the other tranches have been paid off. This tranche is called the Z-tranche or accrual tranche, and the securities that represent a claim against its cash flows are called Z-bonds or accrual bonds. The interest that would ordinarily be paid to the accrual tranche is applied against the outstanding principal of the other tranches, in sequence. The diverted interest from the accrual tranche accrues. That is, it is added to the outstanding principal balance of the Z-tranche.

A convertible bond underperforms the underlying common stock when that stock ______ in value

Increases in value

This is because of the conversion premium which means that the bond will increase less than the increase in stock price. If the stock price falls, the convertible bond should outperform the stock because of the floor created by the straight-value. If the stock is stable, the bond is likely to outperform the stock because of the higher current yield of the bond. If the bond is upgraded, the bond should increase in value. There is no reason that upgrading the bond should lead to the bond underperforming the stock.

The historical yield volatility method uses the ______.

The implied yield volatility method uses ______

the standard deviation formula

derivative prices

Credit Analysis:

(1) Default risk

(2) Loss severity

(3) Expected loss

(4) Recovery rate

(1) Probability of default

(2) Loss given default = % lost

(3) Default risk x loss severity

(4) 1 - Expected loss

(approx.) = 

-duration * Delta(Spread) + [1/2*Convexity*Delta(Spread)²]

Theories of Term Structure:

(1) Pure (unbiased) expectations

(2) Liquidity theory

(3) Preferred habitat theory

(1) Forward rates are a function of expected future spot rates

(2) Forward rates reflects expectations of expected future spot rates plus liquidity premium

(3) Imbalance between fund supply/demand at maturity range induces lenders to shift from preferred habitats to one with opposite imbalance

Relative valuation analysis:

If benchmark is Treasuries or higher-rated bond sector:

Undervalued if ______

If bench. is issuer-specific:

Undervalued if _____

(1) Undervalued if OAS > required OAS

(2) Undervalued if OAS > 0

SMM = 1 - (1 - CPR)^1/12

Conditional prepayment rate (CPR) is assumed annual rate at which mortgage pool balance is prepaid

Single monthly mortaility (SMM) rate is % of beginning-of-month balance, less scheduled payments, prepaid during month

PSA Benchmark / 100 PSA

(finish)

Contraction risk:

Extension risk:

Occurs as rates fall, prepayments rise, average life falls

Occurs as rates rise, prepayments slow, average life rises

CMO Prepayment Risk (extension/contraction):

(1) PAC I

(2) PAC II

(3) Support

(4) IO strips

(5) PO strips

(1) Low contraction/extension risk (due to PAC collar)

(2) Somewhat higher contract/extens risk

(3) Higher contract/extens risk

(4) Value positively related to IR at low current rates

(5) Negative convexity at low rates, high IR sensitivity

ABS Credit Enhancement:

(1) External

(2) Internal

(1) Corporate guarantees, letters of credit, bond insurance

(2) Reserve funds, overcollateralization, senior/sub structure

ABS Prepayment Risks:

(1) Closed-end home equity loan

(2) Manufactured housing loan

(3) Auto loan

(4) Student loan

(5) Credit card receivable

(1) Prepayments are also affected by borrower credit traits

(2) Low PP risk, small balances, high depreciation, low borrower credit ratings

(3) Low PP risk, small balances, high depreciation

(4) Prepayments from default, loan consolidation

(5) Low PP risk, lockout period, no prepayment on CCs

Collateralized Debt Obligations (CDO):

(1) structure

(2) arbitrage-driven cash CDO

(3) Cash flow CDO

(4) Synthetic CDO

(5) Advantages of synthetic CDO

(1) senior tranche(s), mezzanine, equity

(2) Use interest rate swap

(3) actively managed, no short-term trading

(4) bondholders take on economic risks of assets but not legal ownership of them

(5) no funding, shorter ramp-up period, acquire exposure more cheaply through CDS

MBS/ABS Credit Analysis:

(1) plain-vanilla corporate

(2) callable corporate

(3) MBS

(4) credit card/auto

(5) high-quality home equity ABS

(1) use Z-spread

(2) use OAS (binomial model)

(3) use OAS (monte carlo model)

(4) use Z-spread

(5) use OAS