SECURITY ANALYSIS &

PORTFOLIO MANAGEMENT

“BONDS"

Bond

Long term debt instruments representing the issuer’s contractual obligation. A certificate of debt that is issued by a government or corporate in order to raise money with a promise to pay a specified sum of money at a fixed time in the future and carrying interest at a fixed rate. Generally, a bond is a promise to repay the principal along with interest (coupons) on a specified date (maturity).

Reasons for issuing debt instruments

To reduce cost of capital To gain the benefit of leverage To effect tax saving To widen the sources of finance To preserve control

Bond Features Maturity

Interest payments

Call feature

Bond Valuation Model

Assumptions

• The bond is held till maturity rather than selling it at a price different from the face value before its maturity expires.

• All the cash flows, received from coupon payments are reinvested at the same YTM, promised.

• The coupon payments are made regularly and the principal in full in scheduled times

Contd.

Po = [C /(1+k)t] + M/(1+k)n

t=1

n

Where

P = value in Rupees

N = number of years

C = annual coupon payment

K=periodic required return

M= maturity value

t=time period when the payment is received

= C * PVIFA k,n + M * PVIF k,n

Measures of Bond Returns Current Yield

Yield to maturity

Yield to call

Realised YTM

Current Yield

The current Yield relates to the annual coupon interest to the market price.

Current Yield =Annual Interest

Price

Illustration: Calculate the current yield on the Rs 1000 par value bond whose coupon rate is 10 percent. The current market price of the bond is Rs 1052.1

Yield to maturity

The promised compounded rate of return on a bond purchased at the current market price and held till maturity.

Or

The yield to maturity is the periodic interest rate that equates the present value of the expected future cash flows (both coupons and maturity value) to be received on the bond to the initial investment in the bond, which is its current price.

Yield to MaturityIn practice an investor considering the purchase

of a bond not quoted promised rate of return. Instead the investor must use the bond price, maturity date and coupon payment to infer the return offered by the bond over its life.

The YTM is defined as the interest rate that makes the present value of a bond payments equal to its price. This interest rate is often viewed as a measure of the average rate of return that will be earned on a bond if it is bought now and held until maturity.

It is also viewed as effective rate of return expected by an investor of a bond if the bond is held to maturity.

Approximate YTM

YTM C + (M-P) / n

0.4 M + 0.6 P

WhereYTM = yield to maturityC = annual interest paymentM = maturity value of the bondP = present price of the bondn= years to maturity

Illustration

Calculate the YTM of a bond having a face value of $100 and

market price of $80 for a period of 8 years. The bond pays a

coupon rate of 9%.

Yield to call

The promised return on a bond from the present to the date that the bond is likely to be called.

Po = [C /(1+k)t] + M*/(1+k)n

t=1

n*

Where M* = call price (in rupees)n*= number of years until assumed call date.

Assumptions (YTM): 1. All coupon and interest payment are made on

schedule.2. The bond held to maturity.3. The coupon payments are fully and

immediately reinvested at precisely the same interest rate as the promised YTM.

Yield to Call:Some bond carry a call feature that entitle the

issuer to call/buyback the bond prior to the stated maturity. For such bonds it is a practice to calculate the YTC as well as YTM.

Approximation formula of YTM. Valuation of Zero coupon bonds. Decision Criteria:Higher the YTM better the bond, from the view

point of the investors. Major drawbacks of YTM:

It is assumed that the cash flows are reinvested at the rate equal to YTM. This may not be true always.

Realised YTM

Present Market Price (1+r*)t = Future value

Where r* = realized YTM

Consider a bond of Rs 1000/- carrying an interest rate of 15 pa and maturing after five years and the reinvestment rate applicable for the future cash flow is 16 %.

Calculate realised yield to maturity.The present market price of the bond is Rs

850

Illustration

A bond having a par value of $10,000 pays interest at a rate of

8 percent. If the reinvestment rate works out to be 10 percent

what is the realised YTM.

Bond Price Theorem(1) The market price of a bond will be equal to the

par value of the bond, if YTM is equal to coupon rate.

(2) If YTM increases above the coupon rate, the market value drops below the face value.

(3) Inverse of theorem 2.(4) For a given difference between YTM & coupon

rate the longer the term to maturity the greater will be the change in the price with change in YTM.

Risk of Bonds Default risk: Arises when company default in

paying interest or principal. Interest rate risk: The change in interest rate

in the general level of economy. Inflation risk: Call risk: Issuer redeemed the bond before

maturity. Liquidity risk: Barring some popular GoI Bonds

the others are not actively traded in the secondary Market.

Duration

Duration measures the weighted average maturity of a bonds cash flows on a present value basis. That is, the present values of the cash flows are used as the weights in calculating the weighted average maturity

Duration can be defined as number of years needed to fully recover purchase price of a bond, given the present value of its cash flows.

Duration: The holding period for which interest rate risk

disappears is known as the duration of the bond.

e.g. A company issues Rs.1000 bond with a coupon of 11% payable annually with a maturity of 6 years . Calculate the duration.

Note If nothing will be mentioned regarding YTM or required rate of return; Coupon rate will be taken as the proxy of YTM or RRR for discounting.

Duration=4698.19/1000=4.698=4.7Years (approx).

Period (1)

Cash flow (2)

PVIF @11% (3)

PF of CF (4)

PVCF * T 5= 4*1

1 110 0.901 99.11 99.112 110 0.812 89.32 178.643 110 0.731 80.41 241.234 110 0.659 72.49 289.965 110 0.593 65.23 326.156 1110 0.535 593.85 3563.10

Total 4698.19

Expected YTM Vs. Stated YTM The stated YTM is the maximum Possible YTM

without considering the default risk. In expected YTM we consider the default risk.

Expected YTM

Stated YTM

Face Value Rs.1000 Rs.1000Coupon 9% Semi

annual9% Semi annual

Years left for maturity

10 10

Current Price 750 750Redemption 700 1000YTM 11.6% 13.7%

Properties of Duration For periodic coupon bonds the duration is less

than the term to maturity. The longer the term to maturity of a coupon

paying bond, the greater the difference between its’ duration and term to maturity.

For Zero coupon bonds the duration is equal to its’ term to maturity.

For perpetual bonds (1+YTM)/YTM.

Example The market price of a Rs 1000 par value

bond carrying a coupon rate of 14% and maturing after five years is Rs 1050.What is the YTM on this bond. What would be realised yield to maturity if the reinvestment rate is 12%.

Example A Rs 100 par value bond bears a coupon

rate of 14% and matures after five years. Interest is payable semi- annually. Compute the value of the bond if the required rate of return is 16%.

PVIFA 16%, 5years=3.274 PVIFA 8%,10years=6.710PVIF 8%,10years=0.463PVIF 16%,5 years= 0.476

Term Structure Interest Rate The difference in yields observed for bonds

which are similar in all respect except in term to maturity is called term structure of interest rate.

The graphical representation between interest rate and term to maturity is called yield curve.

Rising yield curve Declining yield curve Flat yield curve. Humped Yield curve

Face Value Interest Rate

Maturity (yrs)

Current Price

YTM

100000 0 1 88968 12.40100000 12.75 2 99367 13.13100000 13.50 3 100352 13.35100000 13.50 4 99706 13.60100000 13.75 5 99484 13.90

Forward Interest Rate Another perspective on the term

structure of interest rate is provided by the forward rate i.e. interest rate applicable to bonds in future.

From one year treasury billOne year spot rate can be found out as

below88968=100000/1+r1 so r1=0.124

Now consider the two year Govt Security It has two parts Interest of Rs 12750 at

the end of year 1 and Rs 112750 receivable at the end of year2.

Present value of the first part is 12750/(1+r1)=11343.40

For Present value of the second part we have to discount twice with r1and r2

So the equation will be 99367=12750/1.124+112750/1.124(1+r

2)Solving the equation we get r2=0.1289To get the forward rate for year3 we can set

up the equation for value of three year bond.

. Bond Portfolio Management Strategy

Buy-&-hold Strategy Identify the bond with desired characteristics

and hold it till maturity. These investors do not actively traded with

the objective of enhancing return. When a bond is hold till maturity price risk is

eliminated. To eliminate the price risk the investor has to

choose carefully the quality bond. Therefore this strategy will suits the

investors with the objective of minimization of risk with moderate income.

Bond laddering strategy:

Invest in bonds with several maturity dates instead of a single time horizon.

Company

Rating Par Value

Current Semi-annual YTM

Maturity

A A 10,00,000

8% 2013

B BBB 10,00,000

8.5% 2014

C AA 10,00,000

9% 2015

D AAA 10,00,000

9.5% 2016

E AAA 10,00,000

9.75% 2017

When interest rates decline, the investor losses on short term securities since the entire redemption amount has to be reinvested at lower rate where as he gains from the long term investment since they remain locked at higher rate.

When interest rates increase: vice versa. Thus an evenly distributed portfolio across as

maturity ladder offsetting the reinvestment risk.

Laddering also ensure better diversification. The downside: More transaction cost &

administrative cost comparing to buy-&-hold strategy.

Indexing Strategy A bond portfolio is formed with the objective

of replicating the performance of a selected index.

If the investors risk tolerance is low then select an index which includes more Govt. bonds than corporate.

Semi-active management Objective is to build wealth through

investment so as to provide money for retirement, higher education of children etc.

a. Dedication: Create and maintain bond portfolio that has a cash inflow structure closely matches the cash outflow structure of future liabilities.

(i) Pure cash Matching: The cash inflows (coupon & principal) exactly match the required payments for a stream of liabilities.

The easiest way to implement this is to purchase zero coupon bonds whose maturity coincide with the time when money would be needed.

Year Liabilities

Maturity value

Current Purchase price

Current annual YTM

1 5,00,000

5,00,000

4,62,963

8.00%

2 10,00,000

10,00,000

8,49,455

8.50%

3 15,00,00

15,00,00

11,58,278

9.00%

4 20,00,000

20,00,000

13,91,140

9.50%

5 25,00,000

25,00,000

15,52,303

10.00%

Year Liabilities

Bonds Maturity

Cash matching bond portfolio

Coupon rate

1 10,00,000

A 1 8.00%

2 10,00,000

B 2 8.50%

3 15,00,00

C 3 5,00,000 9.00%

4 20,00,000

D 4 7,00,000 9.50%

5 25,00,000

E 5 11,00,000 10.00%

6 30,00,000

F 6 15,00,000 10.50%

7 35,00,000

G 7 22,00,000 10.75%

8 40,00,000

H 8 25,00,000 11.00%

9 45,00,000

I 9 30,00,000 11.25%

10 50,00,000

J 10 32,00,000 11.50%

Y Liabilities

Cash bal at begin

Int. on Cash bal

Coupon received

Redemption

Total cash avl

Surplus

1 10,00,000

0 0 15,96,000

0 15,96,000

5,96,000

2 10,00,000

5,96,000

29,800 15,96,000

0 22,21,800

12,21,800

3 15,00,00 12,21,800

61,090 15,96,000

5,00,000

33,78,890

18,78,890

4 20,00,000

18,78,890

93,945 15,51,000

7,00,000

42,23,835

22,23,835

5 25,00,000

22,23,835

1,11,192

14,84,500

11,00,000

49,19,526

24,19,526

6 30,00,000

24,19,526

1,20,976

13,74,500

15,00,000

54,15,003

24,15,003

7 35,00,000

24,15,003

1,20,750

12,17,000

22,00,000

59,52,753

24,52,753

8 40,00,000

24,52,753

1,22,638

9,80,500

25,00,000

60,55,890

20,55,890

9 45,00,000

20,55,890

1,02,795

7,05,500

30,00,000

58,64,185

13,64,185

10

50,00,000

13,64,185

68,209 3,68,000

32,00,000

50,00,394

394

Immunization In maturity matching price risk is eliminated but not the

reinvestment risk. Using the concept of duration we can immunization the

portfolio from changing interest rate. The zero coupon bond is the simple solution to

immunization but the difficult part is to find out zero coupon bond whose maturity exactly matches with the duration time.

e.g.: Pension plan of ICICI Pru. States that a client Mr. X will receive Rs.10,000 for 15 years. The first payment is likely to be received by him at the end of 6th year.

Mr. Y who is managing the fund, wants to immunize this liability by investing in 10 years & 15 years zero coupon bonds whose maturity value is Rs.1000 per bond. If the current interest rate is 8% p.a. you are required to calculate

(i) How much money should he invest in each zero coupon bond?

(ii) How many bonds in each type he should purchase?

Year Cash Flows

PVIF @ 8% PV of CF N*PVCF

123456 10,000 0.630 6300 378007 10,000 0.583 5830 408108 10,000 0.54 5400 432409 10,000 0.50 5000 4500010 10,000 0.463 4630 46300

11 10,000 0.429 4290 4719012 10,000 0.397 3970 476413 10,000 0.368 3680 4784014 10,000 0.340 3400 4760015 10,000 0.315 3150 4725016 10,000 0.292 2920 4672017 10,000 0.270 2700 4590018 10,000 0.250 2500 4500019 10,000 0.232 2320 4408020 10,000 0.215 2150 43000Total 58,240 6,75,300

Duration= 6,75,300/58,240 = 11.60 years. Present value of deferred payments = Rs.58,240 If “W” is the weight of 10 years coupon bond in

the portfolio10W +15(1-W) = 11.60W = 68%So investment in 10years bond is 68% i.e. 0.68

*Rs.58,240 = Rs.39,603So investment in 15years bond is 32% i.e. 0.32

*Rs.58,240 = Rs.18,637.(ii) Number of bonds:Redemption value of 10 years bond =

39,603*(1.08)10 = Rs.85,500 i.e. 86 bonds.Redemption value of 15 years bond =

18,637*(1.08)15 = Rs.59,119 i.e. 59 bonds

D = PV(CFt)*tt=1

n

Market price

Where

t = the time period at which the cash flow is expected to be received

n = number of years to maturity

Market price = the present value of all the cash inflows

Illustration: calculate the duration of a bond using coupon -10 percent, maturity -5 yrs, ytm-10%, par value -Rs1000

Format for solvingI II III IV=II*III V=IV/MP VI=I*V

t CF PVF

1 100 0.909

2 100 0.826

3 100 0.751

4 100 0.683

5 1100 0.621

Complete the empty columns and calculate the duration.

Characteristics of duration

When a bond has coupon the duration is less than the term to maturity

A bond with a larger coupon will have a shorter duration

A bond with no coupon payments will have a duration equal to the term to maturity

There is a positive relationship between term to maturity and duration

Higher the market yield lower is the duration

Importance of Duration in Bond Analysis

The duration concept is used in certain bond management strategies, particularly immunisation.

Immunisation

The strategy of immunising (protecting) a portfolio against interest rate risk is called immunisation. The strategy of immunising a portfolio against interest rate risk by canceling out its two components, price risk and reinvestment risk.

With an Immunised portfolio

If interest rates go upReinvestment rates

while

The prices of the bonds

If Interest rates go down

Reinvestment rateswhile

The prices of the bonds

Interest rate riskInterest rate risk is broadly composed of two types of risk.

Price risk: Price risk arises due to inverse relationship between bond prices and yields.

Reinvestment risk: It results from uncertainty about the rate at which future coupon and principal can be reinvested.

Illustration: Immunisation

Bond A: Purchased for $1000, five year maturity, 7.9% coupon, 7.9% yield to maturity.

Bond B: Purchased for $ 1000, six year maturity, 7.9% coupon, 7.9% yield to maturity, duration 5 years

Calculate the ending wealth for Bond A if the market yields constant return at 7.9%, ending wealth for bond B when market yield declines to 6% in year 3 and ending wealth for Bond B if the market yield decline to 6 % in year 3 for period of 5 years

Bond Pricing TheoremsTheorem I

Bond prices (or the present value of the bond) move inversely to the YTM (i.e. the discount rate used). In other words, if a bond’s market price increases, then its yield decreases; and conversely, if a bond’s market price decreases then its yield increases.

Illustration: A rupees 1000 par value bond has a life period of 5 yrs. The coupon on the bond is Rs 80. If the required rate of return in 8 percent calculate the present value of the bond. If the required rate of return declines to 7 percent calculate the bond price. If the YTM increases to 10 percent calculate the bond price.

Theorem II

If a bond’s yield does not change over its life then the size of its discount or premium will decrease as its life gets shorter.

Illustration: A rupees 1000 par value bond has a life period of 5 yrs. The coupon on the bond is Rs 60. If the required rate of return in 9 percent calculate the present value of the bond. Calculate the premium or discount for each of the years till maturity.

Theorem III

A decrease in a bond’s yield will raise the bond’s price by the amount that is greater in size than the corresponding fall in bond’s price that would occur if there were an equal sized increase in the bond’s yield.

Illustration: A Rs 1000 par value bond is currently selling at Rs 1000. The coupon rate is 7 percent. Check the validity of the theorem.

Theorem IV

The percentage change in a bond’s price owing to a change in its yield will be smaller if its coupon rate is higher.

Illustration:

Bond D – (Coupon Rate- 9%, life -5 yrs, yield –7%)

Bond C –(Coupon Rate- 7%, life -5 yrs, yield –7%)

Calculate the bond prices of both these bonds if the par value if the par value is 1000 . Check the validity of the theorem by increasing the yield to 8 percent.