(R44) Introduction to Fixed-Income Valuation

Question 1

Calculate a bond’s price given a market discount rate

Answer 1

The price of a bond is the present value of its future cash flows, discounted at the bond’s yield-to-maturity (use time value of money keys)

Question 2

Discount or premium bond when coupon rate < YTM

Answer 2

Discount bond; premium bond is when coupon rate > YTM

Question 3

Identify relationship among bond price and discount rate

Answer 3

Bond price is inversely related to the discount rate; when price goes up, rate goes down (this is called the inverse effect)

Question 4

What is the convexity effect relationship for bond price?

Answer 4

Given the same coupon and time to maturity, the % change in price is greater when rates are decreasing compared to when rates in increases

Question 5

What is the coupon effect relationship for bond prices?

Answer 5

Lower coupon bond is more price sensitive than a higher coupon bond when rates change, given the same time to maturity

Question 6

What is the maturity effect relationship for bond prices?

Answer 6

For the same coupon rate: a longer term bond is more price sensitive than a shorter-term bond

Question 7

Spot rate and calculation of PV using spot rates

Answer 7

Spot rates are market discount rates for single payments to be made in the future (each payment in the future has a different rate); PV = [PMT/(1+S1)] + [PMT/(1+S2)] + [PMT/(1+Sn)]

Question 8

When a bond is between coupon dates, its price has two parts:

Answer 8

1) the flat price (PVflat) and 2) accrued interest (AI); the sum of these equal PVfull

Question 9

Formula to calculate accrued interest for bonds

Answer 9

Accrued interest = t/T x PMT (where t = # of days between last payment and settlement date; T = # of days between each payment)

Question 10

Two conventions to count days for calculating accrued interest and PVfull

Answer 10

30/360 (used for corporate bonds) and actual/actual (used for gov’t bonds)

Question 11

Formula for PVfull

Answer 11

PVfull = PV x (1+r)^(t/T)

Question 12

Matrix pricing

Answer 12

Matrix pricing is a method used to estimate the yield-to-maturity for bonds that are not traded or infrequently traded. The yield is estimated based on the yields of comparable bonds (i.e. similar tenor, coupons, credit quality).

Question 13

Difference between effective annual rate and semi-annual bond basis yield

Answer 13

Effective annual rate is for bonds with a periodicity of 1 (1 coupon/year); Semi-annual bond basis yield is for bonds with a periodicity of 2 (2 coupons/year).

Question 14

Relationship between periodicity and annual percentage rate

Answer 14

As periodicity increases, APR decreases

Question 15

Formula for periodicity conversions (semi to quarterly)

Answer 15

[1 + (r/2)]^2 = [1+(r/4)]^4

Question 16

Define bond yields that follow street convention and true yields.

Answer 16

Bond yields that follow street convention use the stated coupon payment dates (ignores weekend/holidays). A true yield accounts for coupon payments that are delayed by weekends or holidays and may be slightly lower than a street convention yield.

Question 17

Define yield-to-call and yield-to-worst.

Answer 17

For a callable bond, a yield-to-call may be calculated using each of its call dates and prices. The lowest of these yields and YTM is a callable bond’s yield-to-worst.

Question 18

Define government equivalent yield

Answer 18

Quoted for a corporate bond
Restates 30/360 to actual/actual
Results in a more accurate spread over benchmark measure

Question 19

Define floating rate notes

Answer 19

interest payments are not fixed. They vary from period to period depending on the current level of a reference interest rate. The reference rate is usually a short-term money market rate (i.e. Libor). Intent of FRN is to offer a security with less market price risk than a fixed-rate bond.

Question 20

Define quoted margin and required margin for floating rate notes

Answer 20

Quoted Margin: the yield spread over the reference rate; this is credit related and may be negative.
Required Margin/discount margin: spread required by investors to reflect changes in credit quality; changes usually come from changes in the issuer’s credit risk

Question 21

Describe relationship between quoted margin, required/discount margin and PV

Answer 21

PV of floating rate note is > 100 when QM>DM

Question 22

Calculate price of floating-rate note (PV)

Answer 22

Use time value of money keys: PMT=[(index + QM)/m] x 100; index is libor

Question 23

Define money market instruments

Answer 23

Money market instruments are annualized but not compounded. For money market instruments, yields may be quoted on a discount basis or an add-on basis

Question 24

Formula for two yield measures for money market instruments

Answer 24

Discount Rate => PV = FV x [1 - (days/yr) x DR]
DR = (yr./days) x (FV - PV) / FV
Add-on rates => PV = FV / [1 - (days/yr) x AOR]
AOR = (yr./days) x (FV - PV) / PV

Question 25

Define yield curve

Answer 25

A yield curve (aka maturity structure or term structure of interest rates) shows the term structure of interest rates by displaying yields for a particular cluster of bonds (Same currency, liquidity, credit risk, tax status, and coupon)

Question 26

Define spot curve

Answer 26

The spot curve includes YTMs for zero-coupon bonds for a full range of maturities (sometimes called the zero or strip curve)

Normal yield curve is upward sloping => longer maturities have higher YTMs

Question 27

Define par carve

Answer 27

Sequence of YTMs such that each bond is priced at part. Par rates are derived from spot rates

Question 28

Define a forward curve

Answer 28

A forward curve is a yield curve composed of forward rates, such as 1-year rates available at each year over a future period. Rates agreed on today, received/paid in the future; Forward curve is a mathematical result of the spot curve

Question 29

Compare the curves when looking at them on a graph

Answer 29

When all curves are upward sloping (Forward > spot > par); When all curves are downward sloping (Forward < spot < par)

Question 30

What does f(2,5) mean?

Answer 30

2 years from now, 5 year rate

Question 31

Given a spot curve, what kind of curve can be derived?

Answer 31

Forward curve

Question 32

Define forward rate and calculate the implied forward rate from a spot rate

Answer 32

Interest rate on a bond or money market instrument traded in a forward market (aka break-even rates or no-arbitrage rates). rates agreed on today but received/paid in the future

Ex: 3y1y means this begins in 3 years and lasts 1 years; f (3,1)

Spots: 3yr. = 3.615%; 4yr = 4.18%

Implied forward rates are calculated from spot rates using the following formula:

[1 + (.0418/2)]8 = [1 + (.0365/2)]6 [1 + (f(3,1)/2)2 we are solving for f(3,1)

Question 33

What is a yield spread?

Answer 33

A yield spread is the difference between a bond’s yield and a benchmark yield or yield curve.

Question 34

What is a zero-volatility spread (Z-spread)

Answer 34

A constant spread over a government spot curve (or swap curve)

Question 35

Yield measures typically are annualized and compounded if they mature when?

Answer 35

Greater than 1 year

If maturity is less than a year, then they only annualize but no compounding

Question 36

What is a G-spread

Answer 36

A G-spread is the difference between a bond’s yield and a benchmark yield or yield curve where the benchmark is a government bond yield.

Question 37

What is an I-spread

Answer 37

An I-spread is the difference between a bond’s yield and a benchmark yield or yield curve where the benchmark is a interest swap rate. I-spread is more risky