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 Ii= 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