Risk and return bond return...3

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
VALUATION & MANAGEMENT OF BONDS CHAPTER 6

3
CONTENTS

 Pricing of bond/Yield on the bond
 Deep Discount/Zero Coupon Bonds & STRIPS
 Term Structure of Interest Rates
 Theories of Term Structure
 Duration of the Bond
 Bond Rating
 Bond Management Strategies


4
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.


5
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.


6
TYPES OF BONDS
 Fixed rate and floating rate bonds
 Indexed bonds
 Callable /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

7
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

8 CASH FLOW OF THE BOND

 Cash flows of bonds are made up of two
components: the periodic coupon
payments and principal repayment
Time (months from
0 6 12 18 24 30 36
now)

Coupon received 0 5 5 5 5 5 5

Principal paid (-) and
-100 105
redeemed (+)

Total cash flow
-100 5 5 5 5 5 110


9
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


10
VALUE OF THE BOND &
DISCOUNT RATE

Value of the Bond and Discount Rate
140

120
Value (Rs.)

100

80

60
5% 6% 7% 8% 9% 10% 11% 12% 13% 14% 15%
Discount Rate (%)


11
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, i
Price < Face Value
When discount rate, r < coupon rate, i
Price > Face Value
When discount rate, r = coupon rate, i
Price = Face Value


12
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


13
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

Price
Premium Bond

Par Value= Redemption Value

Discount Bond
Maturity
Time


14
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.
Interest Amount, Coupon x Face Value
Current Yield (%) = x100
Current Price, P0

15 YIELD TO MATURITY (YTM)

 Yield to maturity (YTM) is the rate of return the
investor earns if he holds the bond till maturity.
 YTM satisfies the following
Value of the bond = Price, P0
n Ct Rt
= ∑ +
1 (1 + YTM)t (1 + YTM)n

 A 5-year bond with 12% coupon payable annually
selling at Rs. 90 would have YTM of r such that
Price, P0 = 90.00
12 12 12 12 12 12 100
= + 2 + 3 + 4 + 5 + 6 +
(1 + r) (1 + r) (1 + r) (1 + r) (1 + r) (1 + r) (1 + r)6


16 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.


17
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.

n
P0 x (1+ ry ) = TVn


18
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:
Value of the bond = Price, P0 = 90
n Ct Rt
= ∑
t +
1 (1 + YTC) (1 + YTC)n
4 12 105
= ∑
t +
1 (1 + YTC) (1 + YTC)4

DEEP DISCOUNT/ZERO
19 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.
Pr ice Be haviour of Ze r o Coupon Bond
30-Ye ar Ze r o Coupon Bond
Discount Rate 10%
1,000
Bond Price (Rs.)

900
800
700
600
500
400
300
200
100
-
Tim e (yr s .)


20
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

Face Value
Value of Zero Coupon Bond =
(1 + r)T


21
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).


22
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.

23
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%

24
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

11 10

10 9

9 8
Yield (%)

8

7
6

5
1 2 3
Term of Investment (Years)


25
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.
 Value of the bond using single rate:
120 120 120 1000
Price, P0 = + + +
(1+ 0.10) (1+ 0.10)2 (1+ 0.10)3 (1+ 0.10)3
= 109.09 + 99.17 + 90.16 + 751.31 = Rs.1049.73
,

 Value of the bond using discount rate as per the term
structure: 120 120 120 1000
Price, P0 = + 2
+ 3
+
(1+ 0.08)(1+ 0.09) (1+ 0.10) (1+ 0.10)3
= 111.11+ 101.00 + 90.16 + 751.31 = Rs.1053.58
,


26
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.

27
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.
Bond Maturity Price Yield
(Rs.)
Zero Coupon Bond 1 Year 925.00 8.11%



All bonds are redeemable at par with Rs. 1,000
FV
Yields have been worked out using following: P0 =
(1 + rn )n


28
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.


29
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.

30
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.


31
COMPUTING DURATION

 Duration is the time weighted average of
the present values of the cash flows of
the bond as proportions of its price.
n
∑t x PV of CFt
1
Duration of the Bond =
P0
1 x CF1 2 x CF2 3 x CF3 4 x CF4
= + + + + .......... P0
(1 + r)1 (1 + r)2 (1 + r)3 (1 + r)4


32
COMPUTING DURATION

Time Cash flow PV (10%) Proportion Time x Proportion

1 80.00 72.73 8.14%
0.081
2 80.00 66.12 7.40%
0.148
3 80.00 60.11 6.73%
0.202
4 80.00 54.64 6.12%
0.245
5 80.00 49.67 5.56%
0.278
6 80.00 45.16 5.06%
0.303
7 80.00 41.05 4.60%

33
SENSITIVITY OF BOND
PRICES
 Due to convexity of bond price with
interest rate the change in price of bonds
is linear only approximately.
Duration
Volatility of the bond = -
(1+ YTM/m)
6.091 6.091
=- =- = - 5.54
(1+ 0.1/1) 1.1


34 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…

35
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


36
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.


MATURITY VS. DURATION
37 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.


38 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.


39 MATCHING –
IMMUNISATION
 Matching investment horizon with duration rather than
maturity of the bond keeps terminal wealth constant.

1,800
Terminal Value
TERMINAL VALUE

1,400

M aturity
M atching

1,000
Duration
M atching

600

0 1 2 3 4 5

at 10% at 5% at 20% Time (Years)


40
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.
 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%.


41
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.


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