bonds
DESCRIPTION
TRANSCRIPT
Types of Bonds
• Coupon bonds and zero coupon bonds
•Convertible and non-convertible bonds
•Infrastructure bonds
•RBI relief bonds
•Tax savings bonds
•Government bonds and corporate bonds
•Municipal bonds
Bond Characteristics
A bond is described in terms of:
• Par value
• Coupon rate
• Liquidity
• Maturity date
• Callability
• Re-investment Risk
The Fundamentals of Bond Valuation
The present-value model
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Where:Pm=the current market price of the bondn = the number of years to maturityCi = the annual coupon payment for bond ii = the prevailing yield to maturity for this bond issuePp=the par value of the bond
The Present Value ModelThe value of the bond equals the present
value of its expected cash flows
where:
Pm = the current market price of the bond
n = the number of years to maturity
Ci = the annual coupon payment for Bond I
i = the prevailing yield to maturity for this bond issue
Pp = the par value of the bond
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The Yield ModelThe expected yield on the bond may be
computed from the market price
where:
i = the discount rate that will discount the cash flows to equal the current market price of the bond
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Computing Bond Yields
Yield Measure PurposeNominal Yield Measures the coupon rate
Current yield Measures current income rate
Promised yield to maturity Measures expected rate of return for bond held to maturity
Promised yield to call Measures expected rate of return for bond held to first call date
Realized (horizon) yield Measures expected rate of return for a bond likely to be sold prior to maturity. It considers specified reinvestment assumptions and an estimated sales price. It can also measure the actual rate of return on a bond during some past period of time.
Nominal Yield
Measures the coupon rate that a bond investor receives as a percent of the bond’s par value
Current Yield
Similar to dividend yield for stocksImportant to income oriented investors
CY = Ci/Pm where: CY = the current yield on a bond
Ci = the annual coupon payment of bond i
Pm = the current market price of the bond
Promised Yield to Maturity
• Widely used bond yield figure
• Assumes– Investor holds bond to maturity– All the bond’s cash flow is reinvested at the
computed yield to maturity
Computing the Promised Yield to Maturity
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Solve for i that will equate the current price to all cash flows from the bond to maturity, similar to IRR
Computing Promised Yield to Call
where:
Pm = market price of the bond
Ci = annual coupon payment
nc = number of years to first call
Pc = call price of the bond
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Realized (Horizon) YieldPresent-Value Method
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Calculating Future Bond Prices
where:
Pf = estimated future price of the bond
Ci = annual coupon payment
n = number of years to maturity
hp = holding period of the bond in years
i = expected semiannual rate at the end of the holding period
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REALISED YIELD TO MATURITY
FUTURE VALUE OF BENEFITS
(1+r*)5 = 2032 / 850 = 2.391 r* = 0.19 OR 19 PERCENT
0 1 2 3 4 5 INVESTMENT 850 ANNUAL INTEREST 150 150 150 150 150 RE-INVESTMENT
PERIOD (IN YEARS) 4 3 2 1 0 COMPOUND FACTOR
(AT 16 PERCENT) 1.81 1.56 1.35 1.16 1.00 FUTURE VALUE OF
INTERMEDIATE CASH FLOWS 271.5 234.0 202.5 174.0 150.0 MATURITY VALUE 1000
TOTAL FUTURE VALUE = 271.5 + 234.0 + 202.5 + 174.0 + 150.0 + 1000= 2032
Yield Adjustments for Tax-Exempt Bonds
Where:FTEY = fully taxable yield equivalenti = the promised yield on the tax exempt
bondT = the amount and type of tax exemption
(i.e., the investor’s marginal tax rate)
T-1
iFTEY
Bond Valuation Using Spot Rates
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where:
Pm = the market price of the bond
Ct = the cash flow at time tn = the number of years
it = the spot rate for Treasury securities at maturity t
What Determines Interest Rates
• Inverse relationship with bond prices
• Forecasting interest rates
• Fundamental determinants of interest rates
i = RFR + I + RP where:
– RFR = real risk-free rate of interest– I = expected rate of inflation– RP = risk premium
What Determines Interest Rates
• Effect of economic factors– real growth rate– tightness or ease of capital market– expected inflation– or supply and demand of loanable funds
• Impact of bond characteristics– credit quality– term to maturity– indenture provisions– foreign bond risk including exchange rate risk and
country risk
Spot Rates and Forward Rates
• Creating the Theoretical Spot Rate Curve
• Calculating Forward Rates from the Spot Rate Curve
ILLUSTRATIVE DATA FOR GOVERNEMNT SECURITIES
Face Value Interest Rate Maturity (years) Current Price Yield to maturity
100,000 0 1 88,968 12.40
100,000 12.75 2 99,367 13.13
100,000 13.50 3 100,352 13.35
100,000 13.50 4 99,706 13.60
100,000 13.75 5 99,484 13.90
FORWARD RATES
88968
100000
• ONE - YEAR TB RATE100000
88968 = r1 = 0.124(1 + r1)
• 2 - YEAR GOVT. SECURITY12750 112750
99367 = + + r2 = 0.1289 (1.124) (1.124) (1 + r2)
• 3 - YEAR GOVT. SECURITY13500 13500 113500
100352 = + + (1.124) (1.124) (1 .1289) (1.124) (1.1289) (1 + r3)
r3 = 0.1512
Term Structure of Interest Rates
• It is a static function that relates the term to maturity to the yield to maturity for a sample of bonds at a given point in time.
• Term Structure Theories– Expectations hypothesis– Liquidity preference hypothesis– Segmented market hypothesis or preferred
habitat theory or institutional theory or hedging pressure theory
Expectations Hypothesis
• Any long-term interest rate simply represents the geometric mean of current and future one-year interest rates expected to prevail over the maturity of the issue
Liquidity Preference Theory
• Long-term securities should provide higher returns than short-term obligations because investors are willing to sacrifice some yields to invest in short-maturity obligations to avoid the higher price volatility of long-maturity bonds
Segmented-Market Hypothesis
• Different institutional investors have different maturity needs that lead them to confine their security selections to specific maturity segments
Trading Implications of the Term Structure
• Information on maturities can help you formulate yield expectations by simply observing the shape of the yield curve
Yield Spreads
• Segments: government bonds, agency bonds, and corporate bonds
• Sectors: prime-grade municipal bonds versus good-grade municipal bonds, AA utilities versus BBB utilities
• Coupons or seasoning within a segment or sector
• Maturities within a given market segment or sector
Yield Spreads
Magnitudes and direction of yield spreads can change over time
What Determines the Price Volatility for Bonds
Bond price change is measured as the percentage change in the price of the bond
1BPB
EPB
Where:
EPB = the ending price of the bond
BPB = the beginning price of the bond
What Determines the Price Volatility for Bonds
Four Factors
1. Par value
2. Coupon
3. Years to maturity
4. Prevailing market interest rate
What Determines the Price Volatility for Bonds
Five observed behaviors1. Bond prices move inversely to bond yields (interest rates)2. For a given change in yields, longer maturity bonds post
larger price changes, thus bond price volatility is directly related to maturity
3. Price volatility increases at a diminishing rate as term to maturity increases
4. Higher coupon issues show smaller percentage price fluctuation for a given change in yield, thus bond price volatility is inversely related to coupon
What Determines the Price Volatility for Bonds
• The maturity effect
• The coupon effect
• The yield level effect
• Some trading strategies
The Duration Measure• Since price volatility of a bond varies
inversely with its coupon and directly with its term to maturity, it is necessary to determine the best combination of these two variables to achieve your objective
• A composite measure considering both coupon and maturity would be beneficial
• Duration is defined as a bond’s price sensitivity to interest rate changes
• Higher the duration, greater is the sensitivity• Number of years to recover the trust cost of a
bond
The Duration Measure• For instance, if the interest rate
increases from 6% to 7%, the price of a bond with 5 years duration will move down by 5%, and that of 10 years duration by 10%....... so on.
• Variables that affect the duration are:– Coupon Rate– YTM– Interest Rate changes
The Duration Measure
Developed by Frederick R. Macaulay, 1938
Where:
t = time period in which the coupon or principal payment occurs
Ct = interest or principal payment that occurs in period t
i = yield to maturity on the bond
price
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Characteristics of Macaulay Duration
• Duration of a bond with coupons is always less than its term to maturity because duration gives weight to these interim payments– A zero-coupon bond’s duration equals its
maturity
• There is an inverse relationship between duration and coupon
• There is a positive relationship between term to maturity and duration, but duration increases at a decreasing rate with maturity
• There is an inverse relationship between YTM and duration
Modified Duration and Bond Price Volatility
An adjusted measure of duration can be used to approximate the price volatility of an option-free (straight) bond
m
YTM1
durationMacaulay duration modified
Where:
m = number of payments a year
YTM = nominal YTM
Modified Duration and Bond Price Volatility
• Bond price movements will vary proportionally with modified duration for small changes in yields
• An estimate of the percentage change in bond prices equals the change in yield time modified duration
iDP
P
mod100
Where:
P = change in price for the bond
P = beginning price for the bond
Dmod = the modified duration of the bond
i = yield change in basis points divided by 100