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CHAPTER 6
VALUATION AND MANAGEMENT OF BONDS
Chapter 6Valuation & Management of Bonds 2
CONTENTS
Introduction Features of the bond
– Face Value– Coupon Rate– Periodicity of coupon payments– Maturity – Redemption Value
Types of Bonds– Fixed and Floating Rate Bonds– Indexed Bonds– Callable & Puttable Bonds– Zero Coupon and Deep Discount Bonds – Convertible Bonds
Cash Flow of the bond
Chapter 6Valuation & Management of Bonds 3
CONTENTS
Pricing of bond/Yield on the bond– Current Yield– Yield to Maturity– Realised Yield– Yield To Call
Deep Discount/Zero Coupon Bonds & STRIPS TERM STRUCTURE OF INTEREST RATES
– Finding Term Structure– Term Structure & YTMs– Expectations of interest rates and implied forward
rates
Chapter 6Valuation & Management of Bonds 4
CONTENTS
Theories of Term Structure– Expectation Hypothesis– Liquidity Preference Hypothesis– Market Segmentation/Preferred Habitat
DURATION OF THE BOND– Sensitivity of bond prices– Properties of duration
Bond Rating Bond Management Strategies
– Buy & hold strategy– Bond laddering– Maturity matching vs. Duration matching
Active bond management strategies– Riding the yield curve
Chapter 6Valuation & Management of Bonds 5
BONDS
Bonds have emerged as one of the prominent financial instruments of capital markets world over
Bonds are the instruments of borrowings.
They promise a fixed return until their maturity and the payback of principal upon maturity.
Chapter 6Valuation & Management of Bonds 6
FEATURES OF THE BOND
The terms and conditions for the issue of bonds are pre decided at the time of the issue as a part of bond indenture
Main features of bond indenture are: – face value, – coupon rate, – periodicity of coupon payments, – maturity period and – redemption value
Chapter 6Valuation & Management of Bonds 7
TYPES OF BONDS
Fixed rate and floating rate bondsIndexed bondsCallable /puttable bonds
– Bonds that can be called by the issuer prior to the maturity are known as callable Bonds, while whose redeemable at the option of subscribers are known as puttable bonds
Redemption in lump sum /phased redemption
Chapter 6Valuation & Management of Bonds 8
TYPES OF BONDS
Zero Coupon/Deep Discount Bonds– Bonds that do not pay any interest but are
issued at discount to the face value and redeemed at face value are called Deep Discount Bonds
Convertible Bonds– Convertible bonds are those, which convert
a part of the bond into equity shares. It combines the features of bonds and equity in a composite instrument
Chapter 6Valuation & Management of Bonds 9
CASH FLOW OF THE BOND
Cash flows of bonds are made up of two components: the periodic coupon payments and principal repayment
Time (months fromnow)
0 6 12 18 24 30 36
Coupon received 0 5 5 5 5 5 5
Principal paid (-) and redeemed (+)
-100 105
Total cash flow -100 5 5 5 5 5 110
Chapter 6Valuation & Management of Bonds 10
PRICING OF BOND
The value of bond is arrived by discounting the future cash flows from the bonds at an appropriate discount rate
Discount rate must appropriately be adjusted for the – riskiness of the cash flows, – prevalent market conditions and – timing of cash flows to truly reflect the
expectations
Chapter 6Valuation & Management of Bonds 11
VALUE OF THE BOND & DISCOUNT RATE
Value of the Bond and Discount Rate
60
80
100
120
140
5% 6% 7% 8% 9% 10% 11% 12% 13% 14% 15%Discount Rate (%)
Value
(Rs.)
Chapter 6Valuation & Management of Bonds 12
VALUE OF THE BOND & DISCOUNT RATE
Discount rate is a function of risk. Higher the risk, higher the discount rate and consequently lower the price of bond
When discount rate, r > coupon rate, iPrice < Face Value
When discount rate, r < coupon rate, iPrice > Face Value
When discount rate, r = coupon rate, iPrice = Face Value
Chapter 6Valuation & Management of Bonds 13
VALUE OF THE BOND AND RISK FREE RATE
Value of the bond does not rise above a certain maximum
Bond Value and Risk Free Rate
Price
Risk Free Rate
Discount Rate
Chapter 6Valuation & Management of Bonds 14
VALUE OF THE BOND WITH TIME
The difference between the price and the redemption value narrows as maturity nears and price converges to its redemption value at maturity irrespective of the discount rate.
Bond Price and Time
PricePremium Bond
Par Value= Redemption Value
Discount BondMaturity
Time
Chapter 6Valuation & Management of Bonds 15
YIELD ON THE BOND
There are four types of yields: – current yield; – yield to maturity; – realised yield and – yield to call (relevant only for callable
bonds)
Current yield is the annual coupon payment divided by the current price.
x100P Price, Current
Value Face x Coupon Amount, Interest=(%) YieldCurrent
0
Chapter 6Valuation & Management of Bonds 16
YIELD TO MATURITY (YTM)
Yield to maturity (YTM) is the rate of return the investor would earn if he holds the bond till the date of maturity.
YTM satisfies the following
A 5 year bond with coupon of 12% payable annually and selling at Rs. 90 would have YTM of r such that
ntn
1 tt
0
YTM)+(1R
+YTM)+(1C
=
P Price,=bond the of Value
∑
665432
0
r)+(1100
+r)+(1
12+
r)+(112
+r)+(1
12+
r)+(112
+r)+(1
12+
r)+(112
=
00.90=P Price,
Chapter 6Valuation & Management of Bonds 17
YTM AND VALUE OF BOND
YTM considers the time value of money while calculating returns for the investor.
There is an inverse relationship between the price and the YTM of the bond.
Chapter 6Valuation & Management of Bonds 18
REALISED YIELD
Realised yield is the rate of return investor earns on bonds if he sells the bonds before its maturity. It has two components: annual coupons received till the date of sale and the capital appreciation realised on sale.
nn
y0 TV=)r(1+ x P
Chapter 6Valuation & Management of Bonds 19
YIELD TO CALL
Yield to call is the return the investors earn on the callable bonds till the time the bonds are called. It comprises of two components: annual coupons till the date of call and the call price.
For a 5-year 12% annual coupon bond trading at Rs. 90, callable after four years at Rs. 105 the YTC is computed as below:
4
4
1 t
ntn
1 tt
0
YTC)+(1105
+YTC)+(1
12=
YTC)+(1R
+YTC)+(1C
=
90=P Price,=bond the of Value
∑
∑
Chapter 6Valuation & Management of Bonds 20
DEEP DISCOUNT/ZERO COUPON BONDS AND STRIPS
Zero coupon bonds do not pay any interest and instead provide all the returns in the form of capital gains.
They are issued at price substantially lower than the par value and are redeemed at par.
Chapter 6Valuation & Management of Bonds 21
ZERO COUPON BONDS
The value of zero coupon bonds is arrived by discounting the par value (redemption price) at an appropriate discount rate
Coupon bearing bonds too can be made to look like zero coupon bonds if we treat all the coupon payments as separate instruments
Tr)+(1Value Face
=Bond Coupon Zero of Value
Chapter 6Valuation & Management of Bonds 22
STRIPS
The process of segregating the coupon payments and redemption value and issuing them as separate securities is called stripping.
Each of the strips becomes a separate instrument that can be traded independently of the composite instrument.
These are known as STRIPS (Separate Trading of Registered Interest and Principal of Securities).
Chapter 6Valuation & Management of Bonds 23
ADVANTAGES OF STRIPS
The advantages of stripping include – increased liquidity due to increased
participation by small investors as coupon stripping results in instruments of smaller denominations,
– larger number of securities available for trading providing depth to the market and
– fair pricing due to increased depth and participation
Chapter 6Valuation & Management of Bonds 24
TERM STRUCTURE OF INTEREST RATES
The timing of cash flows and the discount rates to be used are inter-dependent as the expectations of investors vary with the investment horizon. For example:Term of investment Yield
1 year 8%2 years 9%3 years 10%
Chapter 6Valuation & Management of Bonds 25
TERM STRUCTURE OF INTEREST RATES
The relationship between the yield (interest rate) and the term of investment is called the term structure of interest rates.
TERM STRUCTURE OF INTEREST RATES
9
10
8
5
6
7
8
9
10
11
1 2 3Term of Investment (Years)
Yie
ld (%
)
Chapter 6Valuation & Management of Bonds 26
YTM AND TERM STRUCTURE
Ideally the value of the bond must be arrived at with the discount rate appropriate with the timing of the cash flow as given by term structure of interest rates, rather that single discount rate for all the cash flows irrespective of when they accrue.
Value of the bond using single rate:
Value of the bond using discount rate as per the term structure:
73.049,1.Rs=31.751+16.90+17.99+09.109=)10.0+(1
1000+
)10.0+(1120
+)10.0+(1
120+
)10.0+(1120
=P Price, 3320
58.053,1.Rs=31.751+16.90+00.101+11.111=)10.0+(1
1000+
)10.0+(1120
+)09.0+(1
120+
)08.0+(1120
=P Price, 3320
Chapter 6Valuation & Management of Bonds 27
FINDING TERM STRUCTURE
Though the YTMs are observable the term structure of interest rates needs to be derived on some rationale basis.
Term structure of interest rates is hidden in the YTMs of bonds with progressive maturities.
YTMs of bonds with different maturities do not reflect the term structure unless all of them have only single cash flow attached with them.
Chapter 6Valuation & Management of Bonds 28
FINDING TERM STRUCTURE
The most suitable method to arrive at term structure on interest rates is to get the yields on bonds with increasing maturities but that have single cash flow, as is the case with zero-coupon bonds.
)r+(1
FV=P n
n0
Bond Maturity Price (Rs.)
Yield
Zero Coupon Bond 1 Year 925.00 8.11%
Zero Coupon Bond 2 Year 845.00 8.79%
Zero Coupon Bond 3 Year 770.00 9.10%
All bonds are redeemable at par with Rs. 1,000
Yields have been worked out using following:
Chapter 6Valuation & Management of Bonds 29
IMPLIED FORWARD RATES
Term structure of interest rates not only provides expectations of returns with horizon of investment but also imply forward rates of interest. – For example 8% yield for 1 year investment and
9% for two year investment implies yield expectation of 10% for one year investment one year from now.
– Under conditions of perfect market and well-informed investors the direct investment strategy (investing for two years) and roll over strategy (investing for one year and then rolling over for another year)must result in identical returns.
Chapter 6Valuation & Management of Bonds 30
THEORIES OF TERM STRUCTURE
Expectations Hypothesis– The shape of yield curve is dependent upon the
expectations of investors about the future interest rates.
Liquidity Preference Hypothesis– Liquidity preference theory suggest that the
term structure of the interest rates is governed by preferences of investors for liquidity
Preferred Habitat/Market Segmentation Theory– Preferred Habitat theory recognises that the
investor have preferred investment horizons. Short-term investors invest in securities with short maturities and long-term investors prefer securities with long-term maturities
Chapter 6Valuation & Management of Bonds 31
DURATION OF THE BOND
Values of bonds change with the change in interest rates.
With change in interest rates all bonds do not change in value by the same amount. It depends upon the Duration of the bond.
Price sensitivity of the bond is measured by the term called Duration
Chapter 6Valuation & Management of Bonds 32
COMPUTING DURATION
Duration is the time weighted average of the present values of the cash flows of the bond as proportions of its price.
044
33
22
11
0
n
1 t
P..........+r)+(1CF x 4
+r)+(1
CF x 3+
r)+(1CF x 2
+r)+(1
CF x 1=
P
CF of PV x t=Bond the of Duration
∑
Chapter 6Valuation & Management of Bonds 33
COMPUTING DURATION
Time Cash flow PV (10%) Proportion Time x Proportion
1 80.00 72.73 8.14% 0.0812 80.00 66.12 7.40% 0.1483 80.00 60.11 6.73% 0.2024 80.00 54.64 6.12% 0.2455 80.00 49.67 5.56% 0.2786 80.00 45.16 5.06% 0.3037 80.00 41.05 4.60% 0.3228 1080.00 503.83 56.40% 4.512
Price 893.30 100.00%Duration of the Bond (Yrs) 6.091
Chapter 6Valuation & Management of Bonds 34
SENSITIVITY OF BOND PRICES
Due to convexity of bond price with interest rate the change in price of bonds is linear only approximately.
5.54 -=1.1
6.091-=0.1/1)+(1
6.091-=
YTM/m)+(1Duration-=bond the of Volatility
Chapter 6Valuation & Management of Bonds 35
PROPERTIES OF DURATION
Duration of low YTM bonds is higher and hence they are more sensitive as compared to high YTM bonds.
Duration of low coupon bonds is higher Duration of bonds with longer term to
maturity is higher Duration is always shorter than the term to
maturity and increases as maturity extends Duration of a portfolio of bonds is weighted
average of durations of bonds consisting it.– Duration of Bond Portfolio=Dp= wiD1+w2D2+w3D3…
Chapter 6Valuation & Management of Bonds 36
BOND RATING
Bond rating is an alphanumeric score given to debt issue of a firm by an independent specialised external agency.
It broadly signifies the level of risk associated with such an issue of debt.
Purpose of rating is to facilitate investors to make informed judgment for investing
Chapter 6Valuation & Management of Bonds 37
BOND MANAGEMENT STRATEGIES
Buy-and-Hold Strategy– The simplest of the strategy of
managing the investment in bonds is buy-and-hold.
– Buy-and-hold strategy has the advantage of least transaction cost.
Bond Laddering– Bond laddering strategy is similar to
buy-and-hold with the modification that the portfolio of bonds is chosen with staggered and progressive maturities.
Chapter 6Valuation & Management of Bonds 38
MATURITY VS. DURATION MATCHING – IMMUNISATION
The investors in bond primarily face two kinds of risks 1. Price Risk: Bonds prices change
constantly, albeit not as much as stock prices, with the changing economic conditions that affect the YTM.
2. Reinvestment Risk: Reinvestment risk arises due to inability of the investors to reinvest the interim coupon payments at the desired rate.
Chapter 6Valuation & Management of Bonds 39
MATURITY VS. DURATION MATCHING – IMMUNISATION
By matching maturity with the planned investment horizon the price risk is eliminated but the re-investment risk remains.
By making holding period equal to the duration of the bond the portfolio can be immunized from change in value due to change in interest rates.
Chapter 6Valuation & Management of Bonds 40
MATURITY VS. DURATION MATCHING – IMMUNISATION
Matching investment horizon with duration rather than maturity of the bond keeps terminal wealth constant.
TERMINAL VALUE
600
1,000
1,400
1,800
0 1 2 3 4 5
Time (Years)
Term
inal
Val
ue
at 10% at 5% at 20%
Duration Matching
Maturity Matching
Chapter 6Valuation & Management of Bonds 41
RIDING THE YIELD CURVE
The strategy is used with rising yield curve to get higher returns by selling the bond rather than holding it till maturity.
Assume • a zero coupon bond with two years remaining
for maturity. • The rising yield curve with yields of 7% for
one-year term and 8% for two-year term.
Buy and hold till maturity:– The current price of the bond would be Rs. 857.34
(1,000/1.082). – If planned horizon of investment is two years the
investor would lock-in the return of 8%.
Chapter 6Valuation & Management of Bonds 42
RIDING THE YIELD CURVE
Buy and sell after one year:– if investor sells the bond after one year the bond
would trade at a price higher than expected. – With 8% yield the price should be Rs. 925.92
(1,000/1.08). – But since after one year the time left for maturity
is one year only the new price of the bond should be Rs. 934.58 (1,000/1.07) consistent with the yield curve.
– The investor would realise a return of 9% if the bond is sold one year after investment.