Risk and return bond return...3

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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

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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

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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.

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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.

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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

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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

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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 now)

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

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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

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VALUE OF THE BOND & DISCOUNT RATE

Value of the Bond and Discount Rate

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

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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

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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

Risk Free Rate

Discount Rate

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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

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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

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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

A 5-year bond with 12% coupon payable annually selling at Rs. 90 would have YTM of r such that

YTM)+(1R

+YTM)+(1C

P Price,=bond the of Value

665432

r)+(1100

+r)+(1

r)+(112

+r)+(1

r)+(112

+r)+(1

r)+(112

00.90=P Price,

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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.

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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.

y0 TV=)r(1+ x P

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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:

YTC)+(1105

+YTC)+(1

YTC)+(1R

+YTC)+(1C

90=P Price,=bond the of Value

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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.

Price Behaviour of Zero Coupon Bond30-Year Zero Coupon Bond

Discount Rate 10%

Time (yrs.)

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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

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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).

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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.

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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%

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The relationship between the yield (interest rate) and the term of investment is called the term structure of interest rates.

Term of Investment (Years)

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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:

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

)10.0+(1120

=P Price,3320

58.053,1.Rs=31.751+16.90+00.101+11.111=

)10.0+(1

)09.0+(1

)08.0+(1120

=P Price,3320

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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.

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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.

FV=P n

Bond Maturity Price (Rs.) Yield

Zero Coupon Bond 1 Year 925.00 8.11%

All bonds are redeemable at par with Rs. 1,000

Yields have been worked out using following:

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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.

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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.

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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.

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COMPUTING DURATION

Duration is the time weighted average of the present values of the cash flows of the bond as proportions of its price.

P..........+r)+(1

CF x 4+

r)+(1CF x 3

+r)+(1

CF x 2+

r)+(1CF x 1

CF of PV x t=Bond the of Duration

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COMPUTING DURATION

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

1 80.0072.73 8.14% 0.081

2 80.0066.12 7.40% 0.148

3 80.0060.11 6.73% 0.202

4 80.0054.64 6.12% 0.245

5 80.0049.67 5.56% 0.278

6 80.0045.16 5.06% 0.303

7 80.0041.05 4.60% 0.322

8 1080.00 503.83 56.40% 4.512

Price 893.30 100.00%

Duration of the Bond (Yrs)6.091

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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)+(16.091

YTM/m)+(1Duration

-=bond the of Volatility

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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… VALUATION & MANAGEMENT OF BONDS

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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

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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.

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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.

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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.

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IMMUNISATION Matching investment horizon with duration rather than

maturity of the bond keeps terminal wealth constant.

TERMINAL VALUE

0 1 2 3 4 5

Time (Years)

inal V

at 10% at 5% at 20%

Duration

Matching

Maturity

Matching

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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%.

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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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Risk and return bond return...3

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