Bond Valuation and Assessing Risk.

Presented by

• Darshana Ghodinde. ROLL NO 04

• Mark Godinho ROLL NO 06

• Sumit Choudhary ROLL NO 01

• Smrita Kachru ROLL NO 05

What is Bond?

• A Bond represents a contract under which a borrower promises to pay interest & principal on specific dates to the holders of the bond.

Terminology

• Par Value

• Maturity Period

• Coupon Rate

Present value of an Ordinary Annuity

PV = A 1 - 1

(1+r)n

r

A = annuity

n =numbers of years

r = rate of return

• Suppose that an investor expects to receive Rs 100 at the end of each year for the next 5year. Interest rate 10%

A =100, n=5, r=10%

PV=$100 1 - 1

(1+0.1)5

0.1

=$100 1- 0.609 0.1

=$100*3.790

=$379.0

Valuation of Bond

PV of bond = C + M

(1+r)^t (1+r)^n

C=is the annual coupon payment

M=is the value at maturity ,or par valuer = interest rate, or required yieldn = number of years to maturityPV=is the present value of bonds

Consider a bond has a par value of$1000,pays $100 end of each year in coupon payment ,& has 3 years remaining until maturity, annualized yield is 12% determined the bond price.

Valuation of a 3 year bond

Today year1 year 2 year 3

$100 $100 $100+$1000$89.29

79.72

782.96

$951.97

PV of bond =$100/ (.12)^1 + $100/(.12)^2 + $100/(.12)^3

=$89.29 + $79.72 + $782.96

=$951.97

Valuing Bonds with a Present Value Table

P= C*(PVIFr,n) + M* ( PVIFr,n) PV of bond = $100(PVIF,r=12%,n=1)+

$100(PVIF,r=12%,n=2)+

$1,100(PVIF,r=12%,n=3)

=$100(.8929) + $100(.7972) + $1,100(.7118)

=$89.29 + $79.72 + $782.98

=$951.99

Valuation of bonds with Semiannual Payments

PV of bound with = C/2 + M

semiannual payments [1+r/2]^t [1+r/2]^n

C/2=interest payment is semiannually

n=no. of years multiplied by two, to get half yearly period

r=discount rate is been divided by two to get half yearly period

M=maturity value

The valuation of the bound with semiannual payments, consider a bond has a par value of$1000,10 % coupon rate paid semiannually ,& has 3 years maturity, annualized yield is 12% compute the present value .

PV of bond =

$ 50 1 - 1 + $1000

(1+0.06)6 (1.06)6

0.06

=$950.82

Use of Annuity tables for valuation

PV of the bond = PV of coupon payment

+

PV of principal payment

PV of coupon payment =C (PVIFA,r=12%,n=3)

=$100(2.4018)

=$240.18

The present value of the principal must be determined

PV of principal=$1000(PVIF,r=12%,n=3%)

=$1000(0.7118)

=$711.8

Present value of bond = $240.18+ $711.8

=$951.98

Relationship between required return Coupon rate & the bound price

• Consider the zero coupon bond with 3 years remaining to maturity, $1000 par value ,rate return on the bond is 13%

PV of bond = $0/(1+0.13)^1 + $0/(1+0.13)^2 +1000/(1+0.13)^3

=$0+$0+$693.05

=$693.05

Coupon rate < Required yield – Bond price< Par (Discount bond)

• Consider another bond with similar par value & maturity that offers 13% coupon rate

PV of bond = $130/(1+0.13)^1 + $130/(1+0.13)^2 +1130/(1+0.13)^3

=$115.04+$101.81+$783.15

=$1000

Coupon rate = Required yield – Bond price= Par

• Consider another bond with similar par value & maturity that offers 15% coupon rate

PV of bond = $150/(1+0.13)^1 + $150/(1+0.13)^2 +1150/(1+0.13)^3

=$132.74+$117.47+$797.01

=$1047.22

Coupon rate >Required yield – Bond price> Par (Premium bond)

PV = F(Duration, YTM)

Relationship between discount rate & the present value of $10,000 payment to received in 10 years

Relationship between Time of Payment & Present Value of Payment

value Par

coupon Annualrate Coupon

price Bond

coupon Annual yieldCurrent

Example • The current yield for a 15 years 7%

coupon bond with a par value of Rs 1000, selling for Rs 769.40

Current yield = Rs 70 = 9.10%

Rs769.40

• A bond’s interest rate risk is inversely related to the coupon

• High volatility• Low coupon and• High maturity

• Low volatility• High coupon and• Low maturity

• How do we measure bond’s volatility?

• All else being the same, there is an inverse relationship between YTM and duration

27

• THE RELATIONSHIP BETWEEN CONVEXITY AND DURATION

YTM

P

C

0

The following types of risks are associated with bonds: 

1. Interest rate risk

2. Reinvestment rate risk

3. Yield curve risk

4. Call and prepayment risk

5. Credit risk

6. Liquidity risk

7. Exchange rate risk

8. Risk associated with inflation and erosion of purchasing power

9. Risk due to political & regulatory events and government actions

1. Interest rate risk

• There is an inverse relationship between change in interest rates and bond prices.

MaturityDate

Coupon Rate(%)

Last tradedprice (Rs)

Years toMaturity

Yield toMaturity (%)

22-Nov-07 6.8 74 5.9 22.7

15-May-06 6.8 84.5 4.4 15.7

26-Jul-03 6.5 90.1 1.5 12

1-Sep-02 11.2 102.6 0.6 9.7

13-Dec-10 8.8 103.9 8.9 6.7

22-Apr-05 9.9 107.6 3.3 5.9

24-May-13 9 108.4 11.4 4.6

30-May-13 9.8 112.7 11.4 3.3

30-May-21 10.3 114.2 19.4 3

Let's take the practical. As can be seen from the table above, bond having the highest yield to maturity (YTM) of 22.7% and longer duration (in this case 6 years) will be relatively more volatile compared to `a bond having short maturity and low YTM (6.5% instrument having YTM of 12%).

Example in order to understand the relationship between maturity, bond price and yield

2. Reinvestment risk

• When interest rates are declining, investors have to reinvest their interest income and any return of principal, whether scheduled or unscheduled, at lower prevailing rates.

• Hence, in short it is the risk that future proceeds will have to be reinvested at a lower potential interest rate.

3. Yield curve risk

• When market interest rates, or yields, increase, the price of a bond will decrease and vice versa.

4. Call and prepayment risk

• An issuer calls a bond, often intends to issue new bonds at a lower interest rate.

• The higher a bond’s interest rate relative to current interest rates, the higher the prepayment risk. 

5. Credit risk

• Three types of credit risk:

a)Default risk: The issuer will fails to meet its obligations .

b)Credit spread risk: It is the excess return earned by a bond investor above the return on a benchmark, default free security .

c)Downgrade risk: It is the risk that a bond is reclassified as a riskier security by a credit rating agency.

6. Liquidity risk

• It is the risk that represents the likelihood that an investor will be unable to sell the security quickly and at a fair price.

Maturity Date Coupon Rate(%)

Last tradedqty (nos.)

Last tradedprice (Rs)

Currentyield (%)

Years toMaturity

Yield toMaturity (%)

11-Jun-10 11.5 2,500 115.5 10 8.4 3.5

11-Sep-26 10.2 1,500 115 8.9 24.7 2.7

24-Jun-06 13.9 1,200 121.4 11.4 4.5 2.8

19-May-15 10.8 100 108 10 13.4 6.5

5-Aug-11 11.5 54 117.1 9.8 9.6 2.7

19-Jun-08 12.1 50 116.4 10.4 6.4 3.6

23-May-03 11 45 99.8 11 1.4 11.1

21-May-05 10.5 28 110.4 9.5 3.4 5

A 10.2% bond has the YTM of just 2.7%, but it is one of the most actively traded instruments with a longer maturity period. Thus it offers good liquidity to investors who can buy/sell the instrument easily. On the other hand instrument with a coupon rate of 10.8% with a maturity period of 13 years, although offers high YTM of 6.5%, has a relatively low liquidity.

For example

7. Exchange rate risk

• The investor bears the risk of receiving an uncertain amount when bond payments are converted into the home currency.

8. Risk associated with inflation and erosion of purchasing power

• Higher inflation rates result in a reduction of the purchasing power of bond payments.

• If inflation rises while you hold your bond, the value of your bond may decrease. Upon maturity, your purchasing power will have decreased if inflation has continued to rise.  

9. Risk due to political & regulatory events and government actions

• These are generally related to the occurrence of a particular event and its impact on bond price.

• These can be listed as disasters, corporate restructuring, regulatory issues and political risk.

• This risk applies more to corporate bonds than municipal bonds.

GOVERNMENT BOND vs. CORPORATE BOND

• RISK

• RETURNS

• TAXES ON INTEREST

• GUARANTY

• LONG TERM PRESPECTIVE

• MARKETABILITY

• CREDIT RISK

THANK YOU