CH 7_IR and Bonds valuation Flashcards
What type of loan is a bond
interest only loan- borrower pays interest every period, but NONE of the principial is repaid until the end of the loan
Coupons
the interest payments that are paid out regularly
Face value or Par value
the value paid out at the end of the loan
what is the par value usually
1000
what is a bond that sells for pay value called
par bond
What is the coupon rate
the annual coupon/face value
$1000 bond with interest pay of $50
what is the coupon
what is the par value
what is the coupon rate
50
1000
50/1000= 5%
Time to maturityq
of year until the face value is paid
what changes- bond coupon or interest rates over time?
interest rates are what changes over time
when interest rates rise, what ahppens to the pv of bond remaining cf
falls down and the bond is worth less
what happens to bond value when interest rates fall
bond is worth more!
how can you determine the value of a bond on a particular date?
- know the # of periods remaining until maturity
- face value
- coupon
- market interest rate for bonds with similar features
What is yield to maturity
itnerest rate required in the market on a bond
Is yield and yield to maturity the same thing?
what is the graphical relationship between price and yield to maturity? (price and market interest rate)
YES!
price goes up, ytm goes down
price goes down, ytm goes up
what is the logic behind calcuating the present value of a bond
it is basically an annuity and then a lump sum at the end
use the pv of annuity formulas to calculate the present value and then add the lump sum
when the bonds coupon rate is = going interest rates in the market, bond will sell for?
its face value
when the bonds coupon rate is < going interest rates in the market, bond will sell for?
a discount
when the bonds coupon rate is > going interest rates in the market, bond will sell for?
a premium
what deos it mean if a bond is selling for a discount
BASICALLY, the bond is worth less than other bonds issued on the market today
therefore it is sold at a lower price so investors are getting the same benefit that others get on similar bonds
investors who invest in bonds w lower coupon rates than interest rate in market are losing out on money they would have gotten if they bought a different investmetn, therefore this levels the plaing field
What does it mean when a bond sells at a premium?
investors pay extra to buy the bond because they will recieve more money over the duration of th ebond
formula to calculate the pv of a bond?
logic
formula
bond value= pv of coupons + pv of face amt
bond value- c * (1- 1/(1+r)^t )/r + F/(1+r)^t
what is interest rate risk
risk that arises for bond owners from changing interest rates (market yields)
what two factors affect the sensitivity of a bond on interest rate changes
- time to maturity (longer = more risks)
- coupon rate (lower= more risk)
longer bonds= more risk
!!! duh because there is more time for interest rates to fluctuate
How to find the yield to maturity (r)
**CHECK THIS!!!
use a financial calculator
N= # OF PERIODS
PV= -CURRENT PRICE OF BOND
FV= +1000 USUALLY
PMT= +COUPON RATE * FV
2 types of security a corproatiion can issue
equity secrurity
debt security
equity security
ownership interest in the firm
paying dividends to shareholders iS not a cost of doing business and is therefore NOT TAX DEDUCTIBLE
residual claim: you have only rights to whats left over after laibilties paid
bankruptcy beenfit= cant cause bankruptyc by issues equity
debt securityi
debt must be repaid
creditors dont have voting power
paying interest on debt is A COST OF DOING BUSINESS, AND IS TAX DEDUCTIBLE
UNPAID DEBT=LIABILITY, creidots can take legal action (Can cause liqudiation or reorg)
possibility of financial failure
why do corporations often create debt securities that is relaly equity?
cuz of tax benefits of debt and possibility of having no bankruptcy from equity
long term debt vs shrt term debt
1 yr +
vs
1 yr or less
synonyms ofo debt secrutities
notes, debenture, bond
2 types of long term debt
public issue and privately placed
the bond indenture
written aggreement b/w corp and creditor
has:
- basic terms of bonds
- amounts of the bonds issued
- description of property used as security
- repayment agreement
- call provision
- detail of protective covenant
terms of a bond
pricipal value
security on bond
- collateral: whats pledged to protect creditors
- mortgage securitues: secure loaonds on mortgage of propertty
- debenture: unsecured debt with og maturity >10 years
- Notes: unsecured debt with og maturity <10 years
debenture
unsecrued bond (no specfific pledge is made)
note meaning
if maturity of unsecured bond (the eebenture) is less than 10 years when it is orginally issued
seniority
sometimes some bonds are senior and some are junior
senior bonds are paid off frist if bankruptcy
SINKING FUNDS ARE AN EXAMPLE
repayment
bonds can be repaid at maturity or they may be repaid in part or in entirety priior to maturity
ex of early repayment: :sinking fund
what is a sinking fund
A sinking fund is an account managed by the bond trustee for the purpose of repaying the bonds. The
company makes annual payments to the trustee, who then uses the funds to retire a portion of the debt. The
trustee does this by either buying up some of the bonds in the market or calling in a fraction of the
outstanding bonds. We discuss this second option in the next section.
There are many different kinds of sinking fund arrangements. The fund may start immediately or be delayed
for ten years after the bond is issued. The provision may require the company to redeem all or only a
portion of the outstanding issue before maturity. From an investor’s viewpoint, a sinking fund reduces the
risk that the company will be unable to repay the principal at maturity, so it’s credit positive.
Some bonds simply have a defined amortization schedule of blended principal and interest payments directly
to the investor. The disadvantage of this “amortizing bond” structure is that it significantly complicates
secondary trading and, therefore, comes with a liquidity premium
call provision
some bonds lalow companies to repurchase or call part/all of the bond
call price - stated value= call premium
(Call premium gets smaller over time)
not as important in early years bc bonds arent called early, they get caleld in later years
protective covenant
part of a loan agreement that limits certain actions a company might otherwise take during the term of the loan
REDUCE AGENCY COSTS to BOND HOLDERS (limit things ocmpany can do!)
negative covenant: limits actionso f company
positive covenant: specifies actions/conditions company must abide by!!
bond rating
-what do they concern?
!credit risk! not interest rate risk!!!!
- so the price of a highly rated bond can still be quite volatile
AAA= best
A= worst of the best
BBB= average
B= not sure
CCC= ew
D= terrible, bankruptcy type shit
AA ratings awarded often, AAA very rarely
i
investment grade bonds are usually rated at least?
BBB
junk bond
high yield high risk, usually below BBB
UNUSAL BONDS INCLUDE
STRIPPED BONDS
FLAOTING RATE BONDS
ETC
what creates unusual bonds
financial engineering
Successful financial engineering reduces and controls risk
and minimizes taxes
what does financial engineering do
creates exotic, hybrid securitiess that have features of equity but are treated as debt
Financial engineers can alter this division of claims by selling bonds with warrants attached giving
bondholders options to buy stock in the firm
stripped bond- zero coupon bond
bond paying NO coupons, therefore these bonds are sold at much lower than stated value!!
(coupon rate =0%).
- The entire yield-to-maturity comes from the
difference between the purchase price and the par value. - Cannot sell for more than par value.
- Sometimes called zeroes, or deep discount bonds.
- Bondholder must pay taxes (ouch!) on accrued
interest every year, even though no interest is
received.
stripped bond extra
For tax purposes, the owner must pay taxes on interest accrued every year, even though no interest is
actually received. This tax feature makes taxable stripped bonds less attractive to taxable investors because
the tax bill must be funded from other sources. However, they are still a very attractive investment for taxexempt investors with long-term dollar-denominated liabilities, such as pension funds, because the future
dollar value is known with relative certainty. Stripped coupons can be attractive to individual investors for
tax-sheltered registered retirement savings plans (RRSPs) because they don’t have to worry about paying
taxes each year that are not funded by cashflows (taxes are paid instead when the money is withdrawn from
the RRSP). It turns out that stripped bonds can also be attractive in a taxable account because taxes are
only assessed on the interest rate rather than on the coupon rate. In our low interest environment, most
bonds have coupons bigger than their interest rate, so taxable investors in coupon bonds end up getting
overtaxed. On stripped bonds they pay a fair tax, not an unfairly low one
floating rate bond
- Coupon rate floats depending on some index value.
- There is less price risk with floating rate bonds
− The coupon floats, so it is less likely to differ
substantially from the yield-to-maturity. - Coupons may have a “collar” - the rate cannot go
above a specified “ceiling” or below a specified
“floor”
The conventional bonds we have talked about in this chapter have fixed-dollar obligations because the
coupon rate is set as a fixed percentage of the par value. Similarly, the principal is set equal to the par value.
Under these circumstances, the coupon payment and principal are fixed.
With floating-rate bonds (floaters), the coupon payments are adjustable. The adjustments are tied to the
Treasury bill rate or another short-term interest rate. For example, the Royal Bank has outstanding $250
million of floating-rate notes maturing in 2083. The coupon rate is set at 0.40% more than the bankers’
acceptance rate.
Floating-rate bonds were introduced to control the risk of price fluctuations as interest rates change. A
bond with a coupon equal to the market yield is priced at par. In practice, the value of a floating-rate bond
depends on exactly how the coupon payment adjustments are defined. In most cases, the coupon adjusts
with a lag to some base rate, and so the price can deviate from par within some range. For example,
suppose a coupon-rate adjustment is made on June 1. The adjustment might be based on the simple average
of Treasury bill yields during the previous three months. In addition, the majority of floaters have the
following features:
7
8
1. The holder has the right to redeem their note at par on the coupon payment date after some specified
amount of time. This is called a put provision, and it is discussed later.
- The coupon rate has a floor and a ceiling, meaning the coupon is subject to a minimum and a maximum
other bond types
CAT BONDS:
Other Bond Types
* Catastrophe bonds (World Cup)
* Income bonds
* Convertible bonds (can turn them into shares – one
bond can become 40 shares…but there’s no turning
back!)
* Put bond (retractable bond)
* There are many other types of provisions that can
be added to a bond and many bonds have several
provisions - it is important to recognize how these
provisions affect required returns
Most cat bonds, however, cover natural disasters. For example, in November 2014, Kilimanjaro Re
Limited issued catastrophe bonds valued at $500 million for Everest Reinsurance and it covered major
losses from earthquakes in the U.S. and Canada.
As these examples illustrate, bond features are really limited only by the imaginations of the parties
involved. Unfortunately, there are far too many variations for us to cover in detail here. We therefore close
out this discussion by mentioning only a few of the more common types.
Income bonds are similar to conventional bonds, except that coupon payments depend on company
income. Specifically, coupons are paid to bondholders only if the firm’s income is sufficient. In Canada,
income bonds are usually issued by firms in the process of reorganizing to try to overcome financial
distress. The firm can skip the interest payment on an income bond without being in default. Purchasers of
income bonds receive favourable tax treatment on interest received. Real return bonds have coupons and
principal indexed to inflation to provide a stated real return. In 1993, the federal government issued a
stripped real return bond packaging inflation protection in the form of a zero-coupon bond.
A convertible bond can be swapped for a fixed number of shares of stock at any time before maturity at the
holder’s option. Convertibles are debt-equity hybrids that allow the holder to profit if the issuer’s stock
price rises.
Asset-backed bonds are backed by a diverse pool of illiquid assets such as accounts receivable collections,
credit card debt, or mortgages. If an issuing company defaults on its bond debt repayments, bondholders
become legally entitled to cash flows generated from these illiquid pools of assets. Asset backing or
securitization reduces risk provided that the assets are of high quality. In the credit crisis of 2007–2008,
bonds backed by sub-prime mortgages to risky borrowers lost most of their value.
A retractable bond or put bond allows the holder to force the issuer to buy the bond back at a stated price.
As long as the issuer remains solvent, the put feature sets a floor price for the bond. It is, therefore, just the
reverse of the call provision and is a relatively new development. We discuss convertible bonds, call
provisions, and put provisions in more detail in Chapter 25.
A given bond may have many unusual features. An example from bank regulatory capital is CoCo bonds.
CoCo is the nickname for “contingent convertible” bonds, which are also putable, callable, and
subordinated. The contingent convertible clause is similar to the normal conversion feature, except the
contingent feature must be met. For example, a contingent feature may require that the company stock trade
at 110% of the conversion price for 20 out of the most recent 30 days. Valuing a bond of this sort can be
quite complex, and the yield to maturity calculation is often meaningless. After the 2008 financial crisis and
accompanying regulatory changes, banks issued CoCo bonds to strengthen their capital base and absorb
2. The coupon rate has a floor and a ceiling, meaning the coupon is subject to a minimum and a maximum.
losses in times of financial distress. The important feature of CoCo is that it is convertible to equity at the
discretion of the banking regulator (such as OSFI in Canada). Moody’s reported a total of $288 billion in
CoCo bonds issued by banks around the globe from 2009 to 2014, mostly by European and Asian banks.
In July 2014, Royal Bank of Canada issued $1.0 billion of a type of CoCo called non-viable contingent
capital (NVCC) subordinated debt, a first among Canadian banks. In July 2020, Royal Bank again was first
to the Canadian market with the issue of a new structure called a Limited Recourse Capital Note (LRCN).
All of these structures help banks to solve the puzzle of creating loss-absorbing, extendible-maturity
securities that are also tax-deductible and purchasable by the bond market. In this way CoCo, NVCC, and
LRCN supplement equity capital.
trading volume of bonds vs trading volume of stocks (which is higher?)
trading volume: amount of money chanigng hands
BONDS!!
Extremely large number of bond issues, but
generally low daily volume in single issue
Where does trading of most bonds take place?
what does this cause
over the counter (no particular place where buying an dselling occurs) BC ELECTRONIC
very little transparency
Why is bond market bigger than stock market?
more bonds are issued than stocks! rather debt than equity
how much do you actually pay when you buy a bond?
- quoted price/clean price?
- dirty price/full price?
clean price: the quoted price
-> this is net of accrued interest!! (Deduction)
dirty price: clean price + accrued interest is added
How to calculate the accrued interest on a bond (that goes into the dirty price)?
fraction of the coupon period that has passed x multiply it by the next coupon
2/6 x $30
2 months of the semi annual payments has passed x 30 which is the next coupon
how to calculate the clean price?
dirty price - accrued interest = clean price
bond fund
a MTF that invests in bonds and other debt securities
bonds and restructuring
As mentioned in Professor Altman’s “In Their Own Words” box earlier in this chapter, debt plays an
important role in corporate restructuring activities, such as leveraged buyouts (LBOs). In an LBO, a small
group of investors, usually a private equity firm, purchases all the equity shares of a public company. The
purchase is usually financed with significant amount of debt—sometimes up to 90%. For example, in March
2015, Toronto-based private equity firm Onex acquired Swiss packaging firm SIG Combibloc Group for
€3.75 billion. The transaction was financed with €3 billion in debt, including leveraged loans, high-yield
bonds, and a revolving credit facility.
Real rates
interest rates that have been ajusted for inflation
nominal rate
interest rates that have not been adjusted for inflation
WHAT DOES INFLATION DO?
makes your dollars worth less!!!
When you have a given PV and FV and you calculate the r, what type sof itnerest rate is that?
NOMINAL RATE!!
The nominal rate on an investment is the percentage change in the number of dollars you have
The real rate of an investment is the percentage change in how much you can buy with your dollars, in other
words, the percentage change in your buying power.
Fisher Effect
- investors care about real rates bc at the EOD they care about what their money can buy
- R= NOMINAL, r= real, h=inflation
1 + R = (1+r) x (1+h)
math it out
R ~= r + h
bc last component is very small
You can isolate for the real rate and nominal rate
HOW does inflation impact present values?
discount NOMINAL cf at NOMINAL rate
or REAL CF at REAL rate
you will get the correct answer
be careful of what cf is real or nominal and what rate is real or nominal
what does term structure of interest rates mean?
relationship between short and long term interest rates
what does the term structure of interst ates tell us?
what nominal interest rates are on
DEFAULT FREE
PURE DISCOUNT bonds
ANY MATURITY
TERM STRUCTURE OF INTEREST RATES:
These rates are, in essence, “pure” interest rates because
they involve no risk of default and a single, lump-sum future payment. In other words, the term structure
tells us the pure time value of money for different lengths of time.
Long term rates are higher than short term rates
term structure is upward sloping
THIIS IS NORMAL
short term rates are higher than long term rates
downward sloping term structure
THIS IS INVERTED!!
when can the term structure can also be humped
when interst rates increase at first but then begin to decline
what determines the shape of the term structure
1) expected future inflation (inflation premium)
2) real rate of interest (compendation investors demand for giving up the use of their money)
3) interest rate risk (interest rate risk premium)
real rate of interest: the underlying component that determines the nominal interest rate and the term structure!!! it doesnt really determine shape of term structure but the overall level of interest rates mostly!!
real rate of interest: the underlying component that determines the nominal interest rate and the term structure!!! it doesnt really determine shape of term structure but the overall level of interest rates mostly!!!
inflation premium
when inflation happens it erods the value of money, therefore the investors demand compensation for this loss by getting HIGHER NOMINAL RATES
what is the interest rate risk premium
As we discussed earlier
in the chapter, longer-term bonds have much greater risk of loss resulting from changes in interest rates
than do shorter-term bonds. Investors recognize this risk, and they demand extra compensation in the form
of higher rates for bearing it. This extra compensation is called the interest rate risk premium. The longer
the term to maturity, the greater the interest rate risk, so the interest rate risk premium increases with
maturity. However, as we discussed earlier, interest rate risk increases at a decreasing rate, so the interest
rate risk premium does as well.
Putting the pieces together, we see that the term structure reflects the combined effect of the real rate of
interest, the inflation premium, and the interest rate risk premium. Figure 7.5 shows how these can
interact to produce an upward-sloping term structure (in the top part of Figure 7.5) or a downwardsloping term structure (in the bottom part).
upward sloping term structire componsnition
upward sloping: interest rate risk premium
middle: inflation premium
flat line: real rate
the line on top (slope)= nominal interest rate
x acis: time to maturity
y axis: interest rate
downward sloping term structre
downward sloping: interest rate risk premium
middle downard: inflation premium
flat line: real rate
the line on top (slope)= nominal interest rate
x acis: time to maturity
y axis: interest rate
what causes the shape of the yield curve?
relfection of the term structure of interest rates!!
default risk premium
the extra comp investors make in case the bond issuer defaults
JUNK BONDS ARE BS CAUSE
ds. Thanks to a clever bit of marketing, such bonds are
now commonly called “high-yield bonds,” which has a much nicer ring to it; but now you recognize that
these are really high-promised-yield bond
JUNK BONDS: BB, B, CCC, CC, C, D
LIQUIDITY PREMIUM
if you wanted to sell quickly, you
would probably not get as good a price as you could otherwise. Investors prefer liquid assets to illiquid
ones, so they demand a liquidity premium on top of all the other premiums we have discussed. As a result,
all else being the same, less liquid bonds will have higher yields than more liquid bonds
bond yields represent the combination of 6 things
- real rate of interest
- expected future inflation (inflation premium)
- interest rate risk (interest premium)
- default risk (premiuum)
- tax status
- lack of liquitdity (Liquidity premium)
how does tax status affect the bond yield
Taxability also affects the bond yields as bondholders have to pay
income tax on the interest income they receive from privately issued bonds.
how to calculate YTM with Semiannual Coupons
THE MARKET INTEREST RATE = YTM
SEMIANNUAL COUPONS= U GET PAID 2X YEAR
N= # OF PERIODS (Year *2)
PV= - current price
PMT= +how much each coupon will pay you
FV= +par value
I/Y= will give you the semi annual interest rate
I/Y * 2 WILL GIVE YOU THE YEARLY INTEREST RATE
Bonds of similar risk (and maturity) will be priced to
yield about the same return, regardless of the
coupon rate.
If you know the price of one bond, you can estimate
its YTM and use that to find the price of the second
bond
High Grade
− DBRS’s AAA - capacity to pay is exceptionally
strong.
− DBRS’s AA - capacity to pay is very strong
Medium Grade
− DBRS’s A - capacity to pay is strong, but more
susceptible to changes in circumstances.
− DBRS’s BBB - capacity to pay is adequate, adverse
conditions will have more impact on the firm’s ability
to pay
Low Grade
− DBRS’s BB, B, CCC, CC
− Considered speculative with respect to capacity to
pay
Very Low Grade
− DBRS’s C - bonds are in immediate danger of
default.
− DBRS’s D - in default, with principal and/or
interest in arrearS
what is the worst investment grade bond
BBB
− Term structure of interest rates shows the
relationship between interest rates and maturity
would a govt of canada BB bond or corporate bod have greater int rate risk
the government security will have lower coupons because of its lower default risk, so
it will have greater interest rate risk
the term structure is based on pure discount bonds. The yield curve is based on coupon-bearing issues
Canada bid and ask quotes are sometimes given in terms of yields, so there would be a
bid yield and an ask yield. Which do you think would be larger? Explain
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Prices and yields move in opposite directions. Since the bid price must be lower, the bid yield must be
higher.
YIELD TO MATURITY= YIELD= REQUIRED RETURN= market int rate
COUPON RATE= what youre getting paid in %
PULL TO PAR EFFECT!!!
THIS IS WHY IN TH ELONG RUN ALL BONDS (DISC OR PREMIUM) ALWAYS GO TO PAR
All else held equal, the premium over par value for a premium bond declines as maturity approaches, and the
discount from par value for a discount bond declines as maturity approaches. This is called “pull to par.” In
both cases, the largest percentage price changes occur at the shortest maturity lengths
All else the same, the lower the coupon rate on a bond, the greater is its price sensitivity to changes in interest
rates
the longer the maturity the more sensitivity
The “EST Spread” column shows the difference between the YTM of the bond quoted and the YTM of the
Government of Canada bond with a similar maturity. The column lists the spread in basis points. One basis
point is one-hundredth of one percent, so 100 basis points equals one percent. The spread for this bond is 468
basis points, or 4.68%. This makes the equivalent Treasury yield:
Equivalent Government bond yield = 6% – 4.68% = 1.32%
