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Chapter 10
Portfolio Management
Portfolio Management
BONDS :
Bonds are
long-term fixed obligation debt
instruments representing a contractual
obligation on the part of the issuer to pay
definition,
fixed income securities because they
impose fixed financial obligations on the
Bonds are long term obligations with maturities
Portfolio Management
Bond Characteristics
The coupon, maturity, par value and the type of
ownership are important
intrinsic features of a
The
coupon refers to the periodic interest that
the issuer pays to the holder of the bonds. This
is known as
interest income, coupon income or
The
term-to-maturity specifies the date or
(expires).
Term bond has a single maturity
date, while
serial bond has a series of maturity
Portfolio Management
Bond Characteristics
The
par value represents the original value of
the obligation assigned to a security when it is
Bonds differ in their terms of ownership. With a
bearer bond, the holder, or bearer, is the
ownership. Interest from a bearer bond is
obtained by clipping coupons attached to the
bonds and sending them to the issuer for
payment. In contrast, the issuers of registered
bonds maintain records of owners and pay the
Portfolio Management
Specific Characteristics
The
call provision gives the right to call in the bonds
and retire it by paying off the obligation.
The
sinking fund provides for orderly and systematic
periodic retirement of the bond during its life.
The
collateral refers to the security behind the bond,
which may range from none (for a debenture) to the
pledge of real property (for a mortgage bond).
The
conversion feature gives a corporate bondholder
the option to turn the bonds into the corporation and
receive a stated number of shares of stock.
Portfolio Management
Specific Characteristics
Zero coupon bonds pay no interest during the bond’s life but
are instead sold at a discount and redeemed for face value at
Bonds are
rated, primarily by Standard & Poor’s corporation
and by Moody’s, as to their relative probability. Ratings range
from AAA (the highest) to D (those bonds in default), with the
first four grades (AAA from BBB) considered investment grade.
Junk bonds are high-risk, high yield bonds that carry ratings
of BB (S&P) or Ba (Moody’s) or lower, with correspondingly
The major source of bond risk is
interest rate of risk, whereby
a change in interest rates causes an inverse change in bond
prices. Other sources of bond risk are
inflation, default,
reinvestment rate, maturity, call and liquidity risks.
Portfolio Management
Specific Characteristics
Zero coupon bonds pay no interest during the bond’s life but
are instead sold at a discount and redeemed for face value at
Bonds are
rated, primarily by Standard & Poor’s corporation
and by Moody’s, as to their relative probability. Ratings range
from AAA (the highest) to D (those bonds in default), with the
first four grades (AAA from BBB) considered investment grade.
Junk bonds are high-risk, high yield bonds that carry ratings
of BB (S&P) or Ba (Moody’s) or lower, with correspondingly
The major source of bond risk is
interest rate of risk, whereby
a change in interest rates causes an inverse change in bond
prices. Other sources of bond risk are
inflation, default,
reinvestment rate, maturity, call and liquidity risks.
Basis points – One percentage point is equal to 100 basis
Portfolio Management
Bond Valuation
Bond price is essentially a function of coupon,
maturity, and prevailing market interest rates.
The intrinsic value of a bond should equal to the
The
present value model computes a specific
value for the bond using a single interest rate
discount factor (RRR), and the
yield model
computes the promised rate of return based on
Portfolio Management
Bond Valuation
Present Value Model
Pm = the current market price of the bondN= the number of years to matrurityCi = the annual coupon payment for bond I
i= the prevailing YTM for this bond issuePp = the par value of the bond
Portfolio Management
Bond Valuation
Example: 8 percent coupon bond that matures in 20
years with a par value of Tk 1000.
The calculation implies that an investor who holds
this bond to maturity will receive Tk 40 every six
months for 20 years (40 periods) and Tk 1000 at the
maturity of the bond in 20 years.
If we assume a prevailing YTM for this bond of 10
percent (MRRR), the value for the bond using the
above equation would be:
= Tk 40 * 17.1591 +1000 * .1420= Tk 686.36 +142.00 = Tk. 828.36
Portfolio Management
Bond Valuation
YTM is defined as the promised
compounded rate of return an investor will
receive from a bond purchased at the
current market price and held to maturity.
Similar to IRR in FM, the YTM is the
interest rate that equates the PV of the
expected cash flows to be received on the
bond to its market price.
Portfolio Management
Bond Valuation
An 8% bond with 20 years remaining to
maturity and a current price of Tk 900 has
an approximation yield of 8.95 percent:
App. YTM = [80 + (100/20)] / [(1000+900)/2] = 8.95%
Portfolio Management
Bond Valuation using Spot Rates
The assumption that all cash flows are
reinvested at computed YTM often is very
unrealistic because it requires flat, constant
yield curve. The yield curve typically is
upward sloping for several reasons.
Thus investor at any point in time require a
different rate of return for flows at different
times. Spot rates are the rates used to
discount a flow at a point in time.
it = the spot rate for Treasury securities at time t.
Portfolio Management
Bond Valuation using Spot Rates
The rates on a series of zero coupon
government bonds created by stripping
coupon government bonds are used as spot
The key to bond yield and prices is interest
rates. Three aspects of interest rates are the
level of interest rates over time,
term structure of interest rates, and
yield spreads.
Portfolio Management
What determines interest rates?
The level of market interest rates for short term,
risk free securities is a function of the real rate of
interest and inflationary expectation. Inflationary
expectations are the primary variable in
understanding changes in market rates for short-
term, default-free securities.
Other interest rates vary from the short-term
riskless rate as a result of maturity differentials
and risk premiums.
The term-structure of interest rates denotes the
relationship between market yields and time to
maturity. A yield curve graphically depicts this
relationship, with upward-sloping curves being the
Portfolio Management
Creating Theoretical Spot-Rate Curve
The process of creating a theoretical spot-
rate curve from coupon securities is called
bootstapping wherein it is assumed that
the value of the treasury coupon security
should be equal to the value of package of
zero coupon securities that duplicates the
coupon bond’s cash flow.
Bond price volatility depends on coupon
and maturity. Bonds with longer maturities
and/or lower coupons respond most
vigorously to a given change in market
Portfolio Management
What determines the price volatility for
The specific factors
that affect the amount of price
change for a yield change in defferent bonds are listed
and discussed here. This can also be referred to as the
interest rate sensitivity of a bond.
A given change in interest rates can cause vastly
different percentage price changes for alternative
bonds, which implies different interest rate sensitivity.
A bond price change is measured as the percentage
change in the price of the bond, computed as follows:
Portfolio Management
Bond price volatility also is measured in
terms of percentage changes in bond prices.
It is influenced by more than yield behavior
Malkiel’s model demonstrates that the market
price of a bond is a function of four factors:
(
1) its par value,
(2) its coupon,
(3) the number of years to its maturity,
and
(4) the prevailing market interest rate.
Portfolio Management
Malkiel’s mathematical proofs showed the following relationships
between yield (interest rate) changes and bond price behavior:
Bond prices move
inversely to bond yields (interest rate)
For a given change in yields (interest rates), longer-maturity
bonds post larger price changes; thus, bond price volatility is
directly related to term to maturity.
Price volatility (percentage of price changes) increases at a
diminishing rate as term to maturity increases.
Price movements resulting from equal absolute increases or
decreases in yield are
not symmetrical. A decrease in yield raises
bond prices by more than an increase in yield of the same
Higher coupon issues show smaller percentage price fluctuation
for a given change in yield; thus bond price volatility is
inversely
Portfolio Management
Trading Strategies
If one expects a major
decline in interest rates, one knows that
bond prices will increase, so one wants a portfolio of bonds with
the
maximum interest rate sensitivity so that one will enjoy
maximum price changes (capital gains) from the change in
This strategy will imply that one should attempt to build a
portfolio of
long-maturity bonds with low coupon (ideally a
long-term zero coupon bond). A portfolio of such bonds
should experience the maximum price appreciation for a
given decline in market interest rates.
In contrast, If one expects an
increase in market interest rates,
one knows that bond prices will decline, and one wants a portfolio
with the
minimum interest rate sensitivity to minimize the capital
One would want to change one portfolio to short-maturity bonds
Portfolio Management
Duration Measures
Because the price volatility of a bond varies inversely with
coupon and directly with its term to maturity, a succinct
measure having considered both coupon and maturity will
suffice to develop strategy.
A measure of interest-rate sensitivity of a bond is referred
to as
duration.
hMacaulay duration is a measure of the
time flow of cash from
hDuration of a bond that provides cash flow
c i at time
t i is
where
B is its price &
y is its yield (continuously compounded)
Portfolio Management
When the yield
y is expressed with compounding
m times per year
is referred to as the “modified duration”
Duration Matching
This involves hedging against interest rate risk by matching the durations of assets and liabilities
It provides protection against small parallel shifts in the zero (spor-rate) curve
Portfolio Management
Convexity
Source: http://dufinance.ac.bd/application/teacher/uploaded_notes/b3NtYW4=.MjAwOC0xMS0xMl8yMToxMTowOA==1.pdf
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