Class Business
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Upcoming Homework
Bond Page of the WSJ and other
Financial Press Jan 23, 2003
Bond Page of the WSJ contd. Jan 23, 2003
Alternative Measures of Yield
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Yield to Call
– Call price replaces par
– Call date replaces maturity
Holding Period Yield (actual return)
– Considers actual reinvestment of
coupons
– Considers any change in price if the bond
is held less than its maturity
Realized Compound Yield
– Reinvestment rate of coupons
Default Risk
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Agency Assessment
– Coverage ratios
– Leverage ratios
– Liquidity ratios
– Profitability ratios
– Cash flow to debt
Company’s Protection Against
– Sinking funds
– Subordination of future debt
– Dividend restrictions
– Collateral
Risk Premiums – Corporate Yields over T-bill Yields
Term Structure of Interest Rates
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Relationship between yields to maturity and maturity
Yield curve - a graph of the yields on bonds relative to
the number of years to maturity
– Usually Treasury Bonds
– Have to be similar risk or other factors would be
influencing yields
Expectations Hypothesis
Key Assumption: Bonds of different maturities are perfect substitutes
Implication: Expected Return on bonds of different maturities are equal
For n-period bond:
ynt =
yt + yt+1 + yt+2 + ... + yt+(n–1)
n
In words: Interest rate on long bond = average short rates expected to occur over life of long bond
Numerical example:
One-year interest rate over the next five years 5%, 6%, 7%, 8% and 9%:
Interest rate on two-year bond:
(5% + 6%)/2 = 5.5%
Interest rate for five-year bond:
(5% + 6% + 7% + 8% + 9%)/5 = 7%
Interest rate for one to five year bonds:
5%, 5.5%, 6%, 6.5% and 7%.
Liquidity Premium Theory
Key Assumption: Bonds of different maturities are substitutes, but are
not perfect substitutes
Implication: Modifies Expectations Theory with features of Segmented
Markets Theory
Investors prefer short rather than long bonds  must be paid positive
liquidity (term) premium, lnt, to hold long-term bonds
Results in following modification of Expectations Theory
yt + yet+1 + yet+2 + ... + yet+(n–1)
ynt =
+ lnt
n
Relationship Between the Liquidity Premium and
Expectations Theories
Innovations in the Bond Market
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Reverse floaters
Asset-backed bonds
Pay-in-kind bonds
Catastrophe bonds
Indexed bonds
– TIPS (Treasury Inflation Protected
Securities)
Managing Fixed Income Securities:
Basic Strategies
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Active strategy
– Trade on interest rate predictions
– Trade on market inefficiencies
Passive strategy
– Control risk
– Balance risk and return
Bond Pricing Relationships
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Inverse relationship between price and yield
An increase in a bond’s yield to maturity results in
a smaller price decline than the gain associated
with a comparable decrease in yield
Long-term bonds tend to be more price sensitive
than short-term bonds
As maturity increases, price sensitivity increases at
a decreasing rate
Price sensitivity is inversely related to a bond’s
coupon rate
Duration
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A measure of the effective maturity of a bond
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The weighted average of the times (periods) until
each payment is received, with the weights
proportional to the present value of the payment
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Duration is equal to maturity for zero coupon
bonds
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Duration of a perpetuity is (1+r)/r
Duration Formula
T
CFt
DUR   t *
t
1  i 
t 1
T
CFt

t
t 1 1  i 
t  period when cash flow occurs
CFt  cash flow in period ' t'
T  maturity
i  interest rate (YTM)
Duration Formula
Another Perspective
CFt
*t
t
T

1 i
DUR  t 1
T
CFt
t 1 1  i t
where
P  t 1
T
CFt
,
t
1  i 
CFt
t
T 1  i 
*t
 t 1
P
CFt
t

1 i
wt 
P


T
t 1
wt * t
Workout Problem-Duration
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Calculate the duration of an asset that makes nominal payments
of $120 one year from now, $140 two years from now, and $160
three years from now. Assume the YTM is 10%. Calculate the
duration of another asset that makes nominal payments of $160
one year from now, $140 two years from now, and $120 three
years from now, also with an YTM of 10%.
–
Spreadsheet
Duration Properties
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The longer the term to maturity of a bond, everything else
being equal, the greater its duration.
When interest rates rise, everything else being equal, the
duration of a coupon bond falls. (convexity)
The higher the coupon rate on the bond, everything else
being equal, the shorter the bond’s duration.
Duration is additive: The duration of a portfolio of securities
is the weighted average of the durations of the individual
securities, with the weights reflecting the proportion of the
portfolio invested in each.