Fixed Income Valuations Flashcards
Chapters 54, 55, 56, 57
Yield-To-Maturity
The market discount rate appropriate for discounting a bond’s cash flows is called the bond’s yield to maturity (YTM).
It represents a single discount rate that sets the PV of cash flows of the bond equal to its market price.
If coupon rate > marker rate, coupon will trade at (Discount/Par/Premium)?
Premium
If coupon rate < market rate, coupon will trade at (Discount/Par/Premium)?
Discount
If coupon rate = market rate, coupon will trade at (Discount/Par/Premium)?
Par
Accrued Interest
If bonds are sold between the coupon dates, bond pricing has to account for the fact that the next coupon will be paid to the buyer, but a portion of it, which is the accrued interest, will be owed to the seller.
Why are bond prices quoted without accrued interest? Bond’s quoted price is also called…
This is because, holding yield constant, including accrued interest would make a bond’s price appear to increase on each day of a coupon period and drop suddenly on the coupon payment date. A bond’s quoted price is known as its f lat price (or clean price).
Flat Price = Full Price - Accrued Interest
Flat Price =/= PV of Bond at coupon date
What is a bond’s full price?
A bond’s full price (also known as its invoice price or dirty price) is the sum of its flat price and the accrued interest. However, we cannot simply calculate a f lat price and add accrued interest to it.
Full Price = PV on last coupon date x (1 + YTM/periods per year)^days since last coupon/days in coupon period
A decrease in YTM = (Increase/Decrease) in Bond Price
Increase (Inverse relationship between YTM & Bond Price)
The price of a bond with a lower coupon rate is (more/less) sensitive to a change in yield than is the price of a bond with a higher coupon rate.
More
The price of a bond with a longer maturity is (more/less) sensitive to a change in yield than is the price of a bond with a shorter maturity.
More
The percentage decrease in value when the YTM increases by a given amount is (smaller/greater) than the increase in value when the YTM decreases by the same amount
smaller (Price-Yield relationship is convex)
Relationship between Price & Maturity
Before maturity, a bond can be selling at a signif icant discount or premium to par value. However, regardless of its required yield, the price will converge to par value as maturity approaches.
Matrix Pricing
Matrix pricing is a method of estimating the required YTM (or price) of bonds that are currently not traded, or infrequently traded. The procedure is to use the YTMs of traded bonds that have credit quality very close to that of a non-traded or infrequently traded bond and are similar in maturity and coupon, to estimate the required YTM.
Periodicity of a Bond
Number of times a coupon is paid per year
Street Convention
Bond yields calculated using the stated coupon payment dates are referred to as following the street convention.
True Yield
When coupon dates fall on weekends and holidays, coupon payments will actually be made the next business day. The yield calculated using these actual coupon payment dates is referred to as the true yield. Because coupon payments will be made later when holidays and weekends are taken into account, true yields are usually slightly lower than street convention yields, if only by a few basis points.
Current Yield
AKA Income Yield, Running Yield
looks at just one source of return, which is a bond’s annual interest income—it does not consider capital gains or losses or reinvestment income.
= Annual Cash Coupon/Flat Price
Simple Yield
Takes into account amortized value of discount and premium into the yield calc
Simple yield = (annual cash coupon + Annual amortized discount or - annual amortized premium) / Flat Price
*straight line amortisation
yield-to-call
For a callable bond, an investor’s yield will depend on whether and when the bond is called. The yield to call can be calculated for each possible call date and price.
yield-to-worst
The lowest of YTM and the various yields to call is termed the yield-to-worst.
Value of Callable Bond
= Value of Straight Bond - Call Option Value
Option Adjusted Price
= Value of Callable Bond + Value of Call Option
Option Adjusted Yield
Represents the yield that the bond would be offering if it were not callable, calculated using option adjusted price
To make it comparable to a straight bond
Yield Spread
AKA Benchmark Spread
Difference between yields of a bond and the benchmark security
G-Spread
A yield spread of a bond over the government bond (in basis points)
Interpolated Spreads
AKA I-Spreads
An alternative to using government bond yields as benchmarks is to use rates for interest rate swaps in the same currency and with the same tenor as a bond. Yield spreads relative to swap rates are known as interpolated spreads or I-spreads and represent the extra return of a bond in excess of the interbank market reference
rates (MRRs) used in swap contracts. I-spreads are frequently stated for bonds denominated in euros.
If yield increases but yield spread remains constant, it most likely indicates….
Positive Macroeconomic factors
If yield increases and yield spread also increases, it most likely indicates….
Issuer specific factors like deterioration in credit quality
Spot Rates
Yields earned by individual cash lows at different maturities are referred to as spot rates.
The single YTM of a coupon-paying bond represents a weighted average of the different spot rates offered by the individual cash f lows of the bond.
Z-Spread
AKA Zero Volatility Spread
A method for deriving a bond’s yield spread to a benchmark spot yield curve that accounts for the shape of the yield curve is to add an equal amount to each benchmark spot rate and value the bond with those rates.
When we find an amount which, when added to the benchmark spot rates, produces a value equal to the market price of the bond, we have the appropriate yield curve spread. A yield spread calculated this way is known as a zero-volatility spread or Z-spread.
Option Adjusted Spread (OAS)
Difference in yields of a callable bond using its Option adjusted price and the yield of a straight bond for the government spot rate (yield) for the same maturity
OAS = Z-Spread - Option Value
*takes away the option yield from the z-spread
OAS = Z-Spread + Option Value (For Putable Bonds)
Quoted Margin
The fixed margin above the MRR actually paid in the coupon is referred to as the quoted margin (QM).
Required Margin
AKA Discount Margin
The margin required to price the FRN at par is called the required margin or the discount margin (DM).
QM = DM
FRNs are usually issued at par with the QM equal to the DM at issuance. If the credit quality of an FRN remains unchanged after issuance, the QM will remain equal to the DM and the FRN will trade at par on its coupon reset dates.
DM > QM
If the credit quality of the issuer decreases after issuance of the FRN, investors will demand a higher DM in compensation for increased credit risk. This will cause the DM to be greater than the f ixed QM, and the FRN will trade at a discount to its par value.
DM < QM
If the issuer’s credit quality improves during an FRN’s life, the DM will be less than the f ixed QM, and the FRN will sell at a premium to its par value.
Value of FRN at reset date
Use the current MRR plus the QM to estimate the future cash flows for the FRN, and discount these future cash flows at the MRR + DM.
Assuming semi annual
I/Y = (MRR + DM)/2
PMT = FV* (MRR + QM)/2
Quoted Add-on-yield
Used for money market securities
= HPY x 365/days to maturity
Quoted Discount Yield v Actual Annualised yield
Quoted Discount Yield = Actual Discount on the security x 360/days to maturity
Bond Equivalent Yield for a Money Market Security
Annualised add-on yield based on a 365 day year
Spot Rates
discount rates for a single payment to be received in the future are called spot rates and can be observed by calculating the discount rates for zero-coupon bonds (hence, spot rates AKA zero-coupon rates or zero rates or no-arbitrage rate
Usually quoted on a semi annual basis so are comparable to YTMs quoted for Government Bonds
Par Yields
Par yields ref lect the coupon rate that a hypothetical bond at each maturity would need to have to be priced at par, given a speci fic spot curve. Alternatively, they can be viewed as the YTM of a hypothetical par bond at each maturity.
Par Yields = 1-dL/sum of ds
d = discount factors
Forward Rates
A forward rate is a borrowing/lending rate for a loan to be made at some future date.
F1y2y - Forward rate one year from now for a 2 year maturity
Relation of Spots & Forwards
Ex: (1+S3)^3 = (1+S1) x (1 + F1y1y) x (1+ F2y1y)
Spot Rate Yield Curve
AKA Zero Curve or Strip Curve
Plot of Spot Rates v Maturity
Usually upward-sloping (reflects higher yield for longer maturity) AKA Normal Yield Curve
Downward Sloping (lower yield for longer maturities) AKA Inverted Yield Curve
Yield Curve for Coupon Bonds
Shows the YTMs for a similar type of actively traded coupon bonds at various maturities (e.g., U.S. Treasury bonds).
Yields are calculated for several available maturities, and yields for bonds with maturities between these are estimated by linear interpolation.
Yields are usually expressed on a semiannual bond basis.
Par Bond Yield Curve
AKA Par Curve
Hypothetical yields of bonds that would trade at par value for a specific maturity
Yields of Par Bonds v Maturity
Forward Yield Curve
A forward yield curve shows forward rates for bonds or money market securities for annual periods in the future. Typically, the forward curve would show the yields of 1-year securities for each future year, quoted on a semiannual bond basis.
Relationship between Forward Yield curve and Spot Curve
The spot rate for a given maturity is a geometric average of the forward rates that apply to each period between now and that maturity. When the forward curve is upward sloping, the spot curve is also upward sloping, but less so.
Likewise, when the forward curve is downward sloping, the spot curve will also be downward sloping, but less so.
Relationship between Spot Curve and Par Curve
a par yield at a certain maturity is a weighted average of the spot rates that apply to the individual cash flows of the bond (most heavily weighted toward the longest-dated spot rate when par payment takes place). Hence, par yields will also be upward sloping, and very close to spot rates (but slightly below them) in a normal (upward-sloping) forward curve environment.
Par yields will also be downward sloping, and close to spot rates (but slightly above them)
Flat Yield Curve
When forward rates are constant, it means that all future periodic rates are the same. This means that spot rates to all maturities will be the same—and therefore, bond yields will be the same for all maturities. We describe this as a flat yield curve environment.
STRIPS
Separately traded registered Interest principal only
Value of Coupon bearing bonds = Striped ZCBs
relationship between simple, current yield, YTM & Coupon rate
If trading at a discount = Simple > Current > YTM > Coupon
If trading at par, all equal
If trading at premium = Simple < Current < YTM < Coupon
True or False: The stated rate adjusts for the frequency of compounding.
False. The effective rate of interest adjusts for frequency of compounding
If YTC < YTM, what rate would you consider in making your purchase decision?
YTC - as more conservative
A disadvantage of G-spreads and I-spreads is that they are theoretically correct only if the
spot yield curve is:
Flat
When the company that issues the FRN has less credit risk than the institution where the
MRR was derived, the quoted margin (QM) will be:
Less than the MRR.
If the discount margin is lower than the quoted margin on a floating rate note, it’s credit quality has…
improved
As a floating-rate note (FRN) gets closer to maturity, assuming no change in credit quality
since the original issuance, the quoted margin (QM) will:
remain the same
If the yield curve is downward-sloping, the no-arbitrage value of a bond calculated using
spot rates will be:
equal to market value.
The value of a bond calculated using appropriate spot rates is its no-arbitrage value. If no
arbitrage opportunities are present, this value is equal to the market price of a bond.
To determine the full price of a corporate bond, a dealer is most likely to calculate accrued
interest based on:
30-360 convention
actuals for sovereign
Full price calculated using actuals
Quoted Price
= Flat Price = Invoice Price
The effective annual rate, not the stated rate, adjusts for the frequency of compounding. (T/F)
True
A disadvantage of G-spreads and I-spreads is that they are theoretically correct only if the
spot yield curve is:
flat
An interpolated spread (I-spread) for a bond is a yield spread relative to:
MRR or swap rates
A single yield used to discount all of a bond’s cash flows when calculating its price is most
accurately described as the bond’s:
YTM
The bonds of Grinder Corp. trade at a G-spread of 150 basis points above comparable
maturity U.S. Treasury securities. The option adjusted spread (OAS) on the Grinder bonds is
75 basis points. Using this information, and assuming that the Treasury yield curve is flat:
The option cost is the difference between the zero volatility spread and the OAS, or 150 −
75 = 75 bp. With a flat yield curve, the G-spread and zero volatility spread will be the same.
_____ is added to each spot rate on the government yield curve that will cause the
present value of the bond’s cash flows to equal its market price.
Z Spread
A yield curve for coupon bonds is composed of yields on bonds with similar:
credit quality/issuer
The Treasury spot rate yield curve is closest to which of the following curves?
zero coupon bond yields
Price appreciation creates all of the zero-coupon bond’s return. (T/F)
T
An investor buys a bond that has a Macaulay duration of 3.0 and a yield to maturity of 4.5%.
The investor plans to sell the bond after three years. If the yield curve has a parallel downward shift of 100 basis points immediately after the investor buys the bond, her annualized horizon return is most likely to be:
approx 4.5
as at MD price risk & reinvestment risk offset each other
&
All else being equal, which of the following bond characteristics most likely results in less
reinvestment risk?
A shorter maturity.
A lower Macaulay duration may reflect more or less reinvestment risk, depending on what
causes Macaulay duration to be lower. A lower Macaulay duration could result from a
shorter maturity (which reduces reinvestment risk) or a higher coupon (which increases
reinvestment risk).
Sarah Metz buys a 10-year bond at a price below par. Three years later, she sells the bond.
Her capital gain or loss is measured by comparing the price she received for the bond to its:
carrying value
An investor is concerned about rising interest rates and associated price risks. If her
investment horizon is 5.25 years, the Macaulay duration on her bond investment is likely
(higher/lower) than her horizon
higher
Price risk will dominate reinvestment risk when the investor’s duration gap is (positive or negative)?
positive
Interest rate risk (or price volatility) increases at (longer/shorter) maturities and with (higher/lower) coupons.
longer, lower
The higher the yield on a bond the lower/higher the price volatility (duration) will be.
lower
Inclusion of a call feature will increase/decrease the duration of a fixed income security.
decrease
Compared to a bond’s Macaulay duration, its modified duration:
is lower
ModD = MacD/(1+YTM)
A fixed-income portfolio manager is estimating portfolio duration based on the weighted
average of the durations of each bond in the portfolio. The manager should calculate
duration using:
parallel shifts of the benchmark yield curve.
Portfolio duration
only considers a linear approximation of the actual price-yield function for the portfolio. (T/F)
T
As interest rates fall, the bond prices….
increase at a decreasing rate
Key rate duration is best described as a measure of price sensitivity to a:
change in yield at a single maturity
Compared to general obligation (GO) bonds, revenue bonds typically (higher/lower) yields
higher
Total cash flows to investors in an ABS issue are (less than/greater than/equal to) the total interest and principal payments from the underlying asset
pool.
less than as fees are paid to the servicer
A collateralized debt obligation (CDO) in which the collateral is a pool of residential
mortgage-backed securities is most accurately described as a:
structures Finance CDO
With respect to auto-loan backed ABS (all/some/none) have some sort of credit enhancement.
all
An agency RMBS pool with a prepayment speed of 50 PSA will have a weighted average life
that is less than its weighted average maturity.
Weighted average life of a mortgage pool is less than its WAM if there are any
prepayments. “50 PSA” means the prepayment speed is assumed to be 50% of the Public
Securities Association prepayment benchmark.
The pool of loans backing a commercial mortgage-backed security consists of:
non recourse loans only
A renegotiable mortgage has a fixed interest rate that:
changes to a different fixed rate during its life.
An annualized measure of the prepayments experienced by a pool of mortgages is its:
conditional prepayment rate.
single monthly mortality rate.
The single monthly mortality rate is the percentage by which prepayments have reduced the month-end principal balance.
PSA prepayment benchmark.
The PSA prepayment benchmark is a monthly series of CPRs to which a mortgage pool’s CPR may be compared.
Support Tranche is a Planned Ammortization Class Bond
In a planned amortization class (PAC) CMO, the support tranches have more extension risk
and more contraction risk than the PAC tranches. Because of these higher risks, the
support tranches offer a higher interest rate than the PAC tranches.
