Transcript Document

Bond Prices and Yields
11.1 Bond Characteristics
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Face or par value
Coupon rate
◦ Zero coupon bond
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Compounding and payments
◦ Accrued Interest
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Indenture
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T Note maturities range up to 10 years
T bond maturities range from 10 – 30 years
Bid and ask price
◦ Quoted in points and as a percent of par
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Accrued interest
◦ Quoted price does not include interest accrued
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Accrued interest
◦ Interest that accrues between coupon payment
dates
Accrued interest=(annual coupon payment)/2 *days
since last coupon payment/days separating coupon
payments, if semiannually paid

Example:
◦ Coupon rate 8%, 40 days have passed since the last
coupon payment, if semiannually paid
The accrued interest on the bond
=8%*1000*0.5*40/182=8.79
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Most bonds are traded over the counter
Registered (record)
Bearer bonds (without record)
Call provisions (price?)
Convertible provision (conversion value)
Put provision (putable bonds) (price?)
Floating rate bonds (yield spread fixed)
Preferred Stock (cumulate, not tax
deductible, offsetting tax adv , 30% of
dividend taxed)
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Coupon, maturity, price, yield to maturity,
rating
Call provisions (price?)
◦ Allowing the issuer to repurchase the bond at a
specified call price before the maturity date
◦ Refunding: retire high-coupon debt and issue new
bonds at a lower coupon rate
◦ Call option valuable to the firm, higher coupon and
promised yields to maturity than non-callable
bonds
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Put provision (puttable bonds) (price?)
◦ Give the option to the bondholder to extend the
bond’s life, when the coupon rate exceeds current
market yield
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Floating rate bonds (yield spread fixed)
◦ Interest payments tied to some measure of current
market rate. Yield spread fixed if financial health
kept.
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Convertible provision (conversion value)
◦ Give bondholders an option to exchange each
bond for a specified number of shares of
common stock
◦ Conversion ratio, Market conversion value
Preferred Stock (cumulate, not tax
deductible, offsetting tax adv)
International bonds
◦ Foreign bonds: issued by a borrower from a
country other than the one in which the bond is
sold
◦ Eurobonds: bonds issued in the currency of one
country but sold in other national markets.
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International Governments and
Corporations
◦ Foreign bonds
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Foreign Issuer , Denominated in local currency
Yankee bonds (in USA)
Samurai bonds (in JAPAN)
Bulldog bonds (in UK)
◦ Eurobonds
 Foreign issuer, denominated in foreign currency
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Inverse Floaters (suffer doubly and benefit
doubly)
◦ The coupon rate falls when market rate rises
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Asset-backed bonds
◦ Income from a specified group of assets is used to
service the debt
 Indexed
Bonds
◦ Payments are tied to a general price index
or the price of a particular commodity
◦ Example: Treasury inflation protected
securities (TIPS), par value tied to general
level of prices, coupon payments and final
repayment of par value increase in direct
proportion to the Consumer Price Index.
◦ risk-free real rate
11.2 BOND PRICING
 Value
a security, discount its
expected cash flows by the
appropriate discount rate
 Bond value= present value of
coupons + present value of par
value
ParValue
T
C
t
PB  

T
t
(1 r )
t 1 (1 r )
T
PB =
Ct =
T =
r =
Price of the bond
interest or coupon payments
number of periods to maturity
semi-annual discount rate or the semi-annual
yield to maturity
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Price= coupon *annuity factor (r, T)
+ Par value * PV factor (r, T)
1
1
annuity factor (r, T)= 1 
r  1  r T
1
PV factor (r, T)=
1  r 
T




20
P
 40 ´ 
B
P
B
t 1
1
1

´
1000
t
20
(1 .03)
(1.03)
 1,148 .77
Coupon = 4%*1,000 = 40 (Semiannual)
Discount Rate = 3% (Semiannual)
Maturity = 10 years or 20 periods
Par Value = 1,000
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Prices and Yields (required rates of return)
have an inverse relationship
When yields get very high the value of the
bond will be very low
When yields approach zero, the value of the
bond approaches the sum of the cash flows
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Coupon rate=8%, semiannual, face
value=1000
Maturity : 1-yr , 10-yr, 20-yr, 30-yr
Market interest rate, 4%--12%
TIME
TO
MATU
RITY
4%
6%
8%
10%
12%
1
￥1,038.83
￥-1,019.13
￥-1,000.00
￥-981.41
￥-963.33
10
￥1,327.03
￥-1,148.77
￥-1,000.00
￥-875.38
￥-770.60
20
￥1,547.11
￥-1,231.15
￥-1,000.00
￥-828.41
￥-699.07
30
￥1,695.22
￥-1,276.76
￥-1,000.00
￥-810.71
￥-676.77
MARKET INTEREST RATE
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Issued at par value
Secondary market, price move in accordance
with market forces, fluctuate inversely with
the market interest rate
Interest rate fluctuations, main source of risk
in fixed-income market
Maturity, key factor of sensitivity
Longer maturity, greater sensitivity
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Invoice price= flat price + accrued interest
11.3 BOND YIELDS
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Measure of rate of return that accounts for
both current income and the price increase
over the life
Total return: current income and price change
Average rate of return (bought now and held
until maturity)
YTM is the discount rate that makes the
present value of a bond’s payments equal to
its price
Solve the bond formula for r
ParValue
T
C
t
PB  

T
t
(1 r )
t 1 (1 r )
T
35 1000
950  

T
t
(1 r )
t 1 (1 r )
20
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10 yr Maturity
Coupon Rate = 7%
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Price = $950
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Solve for r = semiannual rate r = 3.8635%
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8% coupon, 30-year bond selling at
$1,276.76:
60
$40
$1, 000
$1, 276.76  

t
60
(1  r )
t 1 (1  r )
r = 3%, semiannual rate
Bond Equivalent Yield (semiannual yield doubled, YTM)
7.72% = 3.86% x 2;
6%=3%*2
Effective Annual Yield (accounts for compound interest)
(1.0386)2 - 1 = 7.88%; (1.03)2 - 1 = 6.09%
Current Yield (annual coupon payment divided by bond
price)
Annual Interest / Market Price
$70 / $950 = 7.37 %; $80 / $1276.76 = 6.27 %
Coupon rate
7% =70/1000; 8% =80/1000
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YTM
◦ internal rate of return
◦ Compound rate of return over the life (assumption,
all bond coupons can be reinvested at the yield)
◦ Proxy for average return
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Premium bonds (selling above par)
◦ Coupon rate > current yield > YTM
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Discount bonds (selling below par)
◦ Coupon rate < current yield < YTM
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if the bond is callable
Example , Callable at $1100
The call provision allows the issuer to
repurchase the bond at call price
Yield to Call
◦ Call price replaces par
◦ Time until call replaces time until maturity
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8% coupon, 30-year bond selling at
$1150, callable in 10 years at call
price of 1100
yield to call
yield to maturity
coupon payment
40
40
number of semiannual periods
20
60
final payment
1100
1000
price
1150
1150
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Reinvestment Assumptions
◦ All coupon are reinvested at an interest rate equal
to YTM
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With a reinvestment rate equal to YTM, the
realized compound yield equal to YTM
Conventional YTM not equal realized
compound return, if reinvestment rates can
change over time
Example: 2 year, selling at par (1000),
coupon rate 10%, annual pay
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If interest rate earned on the first
coupon is less than 10%., the final value
of the investment will be less than 1210,
realized compound return will be less
than 10%
Example:
◦ if reinvest interest rate 8%
1000 1  r   1208
2
r  9.91%
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Horizon analysis
◦ Forecasting the realized compound yield over
various holding periods or investment horizons
◦ Forecast of total return depends on forecasts of
both the selling price of the bond and the rate to
reinvest coupon income
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Horizon analysis (Example)
◦ 30-year, 7.5% annual payment coupon bond, sell for
980, YTM is 7.67%, plan to hold for 20 years.
◦ Forecast that YTM will be 8% when it is sold,
reinvestment rate on the coupons will be 6%
◦ At the end of your investment horizon, the bond will
have 10 years remaining, the forecast sales price
(when YTM is 8%) will be 966.45.
◦ 20 coupon payments will grow with compound
interest (6%)to 2758.92
◦ 980 investment will grow in 20 years to
966.45+2758.92=3725.37
980 1  r   3725.37
20
r  6.90%
1 
1  1000
75 
 1 

 966.45
10 
10
8%  1.08  1.08
1 
1 
20
75 
 1 

1.06
 2758.92
20 
6%  1.06 
$980(1  r ) 20  966.45  2758.92  3725.37
r  6.9%
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When interest rates change, bond investors
are subject to two sources of offsetting risk
◦ Rate rise, bond prices fall, reduce the valued of the
portfolio
◦ Reinvested coupon income will compound more
rapidly at those higher rates. The reinvestment rate
risk will offset the impact of price risk
11.4 BOND PRICES OVER TIME
HPR = [ I + ( P1 - P0 )]
/
where
I = interest payment
P1 = price in one period
P0 = purchase price
P0
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Requires actual calculation of reinvestment
income
Solve for the Internal Rate of Return using the
following:
◦ Future Value: sales price + future value of coupons
◦ Investment: purchase price
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Par bond
◦ Coupon rate equals market interest rate (fair
compensation, no further capital gain)
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Discount Bond
◦ Coupon rate is lower than market rate (need to earn
price appreciation, built-in capital gain)
◦ Bond price will increase to par over its maturity
◦ Yield to maturity exceeds coupon rate
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Discount Bond Example
◦ Market rate when issuing, 7% , annual coupon rate
7%. when the market rate is 8%
◦ 3 years left, Bond price= 70* annuity factor (8%, 3)
+ 1000 * PV factor (8%,3)=974.23
◦ 2 years left, Bond price= 70* annuity factor (8%, 2)
+ 1000 * PV factor (8%, 2)=982.17
◦ HPR over this year
=(982.17-974.23+70)/974.23=8%
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Premium Bond
◦ Coupon rate exceeds market rate (investors need to
bid up the price above their par value, capital losses
offset the large coupon payment, fair rate)
◦ Coupon rate exceeds yield to maturity
◦ Bond price will decline to par over its maturity
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YTM , measure of the average rate of return if
the bond is held to maturity
If YTM is unchanged over the period, the HPR
equals YTM
If YTM fluctuate, so will HPR.
Unanticipated changes in market rates will
result in unanticipated changes in bond
returns and HPR can be better or worse than
YTM which it initially sells.
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YTM depends on coupon, current price, par
value. Observable today
HPR is a rate of return over a particular
investment period and depends on the
market price of the bond at the end of the
holding period
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No coupons and provides all returns in form
of price appreciation
Provide only one cash flow on maturity date
US. Treasury bills
STRIPS (Treasury strips) :break down the cash
flows of a Treasury coupon bond to be paid
by the bond into a series of independent
securities, each security is a claim to one of
the payments of the original bond
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Prices of zeros over time
◦ On maturity dates, sell par
◦ Before maturity, sell at discounts from par,
approach par value
11.5 DEFAULT RISK AND BOND
PRICING
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Rating companies
◦ Moody’s Investor Service
◦ Standard & Poor’s
◦ Fitch
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Rating Categories
◦ Investment grade
◦ Speculative grade
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Coverage ratios
EBIT/INTEREST, ratio of earnings to all fixed cash
obligations
Leverage ratios
D/E
Liquidity ratios
current asset/current liabilities
Profitability ratios
ROA, ROE
Cash flow to debt
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Z-score
◦ Edward Altman
◦ Used discriminant analysis to predict bankruptcy,
get a score based on financial financial ratio
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Indenture, contract between the issuer and
the bondholder (Protective covenants)
◦ Set of restrictions that protect the rights of the
bondholders
◦ Provisions relating to collateral, sinking funds,
dividend policy, further borrowing
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Sinking funds- Help ensure the commitment
of the par value payment at the end of the
bond’s life, the firm agrees to establish a
sinking fund to spread the payment burden
over several years
◦ The firm may repurchase a fraction of the
outstanding bonds
◦ May purchase a fraction of the outstanding at a
special call price
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Subordination of future debt
◦ Restrict the amount of additional borrowing.
Additional debt might be required to be
subordinated in priority to existing debt
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Dividend restrictions
Collateral
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Promised yield and expected yield
◦ The promised or stated yield will be realized only
if the firm meets the obligations of the bond
issue, maximum possible YTM
◦ When a bond more subject to default risk, price
will fall, its promised YTM will rise, default
premium will rise.
Default premium is the difference between
the promised yield on a corporate bond and
the yield of an otherwise-identical
government bond that is riskless in terms
of default.
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Risk structure of interest rates
◦ Greater default risk, higher default premium
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Default premiums
◦ Yields compared to ratings
◦ Yield spreads over business cycles
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Major mechanism to reallocate credit risk in the
fixed-income markets
First establish a legally distinct entity to buy
and later resell a portfolio of bonds or other
loans (Structured Investment Vehicle, SIV, often
used to create the CDO
 Raise funds by issuing short-term
commercial paper, using the proceeds to
buy corporate bonds or other forms of debt
 Loans are pooled together and then split
into a series of classes (tranche)
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Each tranche is given a different level of
seniority in terms of its claims on the
underlying loan pool, and each can be sold as
a stand-alone security
Proceeds of the loans in the pool are
distributed to pay interest to each tranche in
order of seniority.
Priority structure implies the different
exposure to credit risk.
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Mortgage-backed CDOs were an Investment
disaster in 2007
CDOs formed by pooling sub-prime
mortgage loans made to individuals whose
credit standing did not allow them to qualify
for conventional mortgages. When home
prices stalled in 2007, and interest rates on
these typically adjustable-rate loans reset to
market levels, mortgage delinquencies and
home foreclosures soared, investors lost
billions of dollars