UNIT IV_IPM

7/30/2019 UNIT IV_IPM

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UNIT IVUNIT IV

Bond ValuationBond Valuation

BondBond

ParValue

CouponRate

MaturityDate


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Types of BondsTypes of Bonds Government Bonds

Corporate Bonds

Straight Bonds

Zero Coupon Bonds

Floating Rate Bonds

Bonds with Embedded Options

Convertible Bonds

Callable Bonds

Puttable Bonds

Commodity Linked Bonds

Risks in BondsRisks in Bonds

Interest Rate Risk

Inflation Risk

Default Risk

Call Risk

Liquidity Risk

Reinvestment Risk

Foreign Exchange Risk


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PricePrice Yield RelationshipYield Relationship

PRICE

YIELD

Bond ValuationBond Valuation

P = [C / (1 + r)t ] + M / (1 + r)n

P = C x PVIFA r, n + M x PVIF r, n

P = Value (In Rupee)

n = Number of Years

C = Annual Coupon Payment (In Rupee)

r = Periodic Required Return

M = Maturity Value

t = Time Period when the payment is received.


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1.1. Current Yield

CURRENT YIELD = ANNUAL INTEREST / PRICE

It reflects only the coupon Interest Rate.

It doesnt consider Capital Gain or Loss.

It also ignores Time Value of Money.

An Incomplete and Simplistic Measure of Yield

2.2. Yield to Maturity (YTM)

Rate of Return offered by the BOND over its Life

YTM refers to the Discounting Rate which makes the present

value of the cash flows receivable from owning the bond to the

price of the bond.

Formula:

Approximation: YTM = C + ( M P ) / n

0.4 M + 0.6 P

Trial and Error:

YTM = R1 + [R2 R1] PV at R1 P

PV at R1 PV at R2


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3.3. Yield to Call (YTC)

Applicable to Callable Bonds

Similar to YTM except the Duration

M = Call Price

n = Number of Years until the assured call date

4.4. Realized Yield to Maturity

Year INV INTRe- INVPeriod

CompoundFactor

FV ACF

0 (850) - - - - -

1 - 150 4 1.81 271.5 0

2 - 150 3 1.56 234.0 0

3 - 150 2 1.35 202.5 0

4 - 150 1 1.16 174.0 0

5 - 150 0 1.00 150.01032 +

MATURITYPRICE


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5. Holding Period Return

Holding Period Return is the income

Current Return (Interest)

Capital Return (Change in Price)

earned over a given holding period as a percentage of its price at

the beginning

YI ELD CURVE

OR

TERM STRUCTURE OF

I NTEREST RATES


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Yield Curve / Term Structure of InterestRates

The term structure of interest rates, popularly called the

yield curve, shows how yield to maturity (YTM) is related

to maturity for bonds that are similar in all aspects,

excepting maturity.

Another perspective on the term structure of interest

rates is provided by the forward interest rates.

Types of Yield Curve

UPWARDSLOPING

DOWNWARDSLOPING

HUMPEDFLAT


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Calculate Forward Rates

FACEVALUE INTEREST RATEMATURITY(YEARS)

CURRENTPRICE

100,000 0 1 91,000

100,000 10.5 2 99,000

100,000 11.0 3 99,500

100,000 11.5 4 99,900


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Explaining Term Structure

Expectations Theory

Liquidity PreferenceTheory

Preferred HabitatTheory

Market SegmentationTheory

Expectations Theory

Shape of yield curve can be explained by

interest rate expectations of those who

participate in the market.

Long term rate is equal to the geometric

mean of current and future one-year rates

expected by the market participants


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Liquidity Preference Theory

According to this theory, there is UNCERTAINTY about the one-year

period return from a bond whose maturity is greater than one period.

This uncertainty regarding one-period return increases with the

maturity of the bond.

J. R. Hicks argued that investors (being risk averse) require an

inducement to hold long term bonds.

Thus, forward rates should incorporate interest rate expectations as

well as a risk premium.

Preferred Habitat Theory

According to Modigliani and Sutch, who originally

formulated the preferred habitat theory, risk aversion

implies that investors will prefer to match the maturity of

investment to their investor objective.

Long horizons investors Longer maturities Bonds(To Avoid Reinvestment Risk)

Short horizons investors Shorter maturities Bonds

(To Avoid Price Risk)


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Preferred Habitat Theory (2)

According to this theory,

If there is a mismatch between demand and supply of

funds in a certain maturity range,

Some lenders and borrowers may have to be induced

to shift out of their preferred maturity ranges.

Of course, they will have to be compensated for this in

form of a suitable risk premium which depends uponthe degree of risk aversion.

Market Segmentation Theory

Extreme form of the preferred habitat theory

It states

Investors as well as borrowers are unwilling to shift

from their preferred maturity range, come what may!!

Hence according to this theory,

Shape of yield curve is determined entirely by the

supply and demand forces within each maturity

range!!


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Determinants of Interest Rates

Short-term RiskFree Rate

Inflation Rate

Real GrowthRate

TimePreference

MaturityPremium

FutureExpectations

LiquidityPreference

PreferredHabitat

DefaultPremium

BusinessRisk

FinancialRisk

Collateral

SpecialFeatures

Call / PutFeature

ConversionFeature

Others

(Ex. Floating,0-Coupon)

BOND PRI CI NG

THEOREMS

5 BOND PRICING THEOREMS

for a typical bond making

periodic coupon payments and

a terminal principal payment


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BOND PRI CI NGTHEOREMS


THEOREM 1

If a bonds market price increases

then its yield must decrease

conversely if a bonds market price decreases

then its yield must increase

BOND PRI CI NG

THEOREMS


THEOREM 2

If a bonds yield doesnt change over its l ife,

then the size of the discount or premium

will decrease as its life shortens


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THEOREM 3

If a bonds yield does not change over its life

then the size of its discount or premium will

decrease at an increasing rate as its l ifeshortens

BOND PRI CI NG

THEOREMS


THEOREM 4

A decrease in a bonds yield will raise the bonds

price by an amount that is greater in size than the

corresponding fall in the bonds price that wouldoccur if there were an equal-sized increase in the

bonds yield

the price-yield relationship is convex


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THEOREM 5

the percentage change in a bonds price owing to a

change in its yield will be smaller if the coupon

rate is higher

BOND THEOREMS I N BRI EF

Bond price move inversely to changes in interest rates.

Longer maturity makes a bond price more sensitive tointerest rates.

Price sensitivity increases with maturity at a decreasingrate.

Lower coupon rates increase price sensitivity.

A price increase caused by a yield decrease exceeds aprice decrease caused by a similar yield increase.

UNIT IV_IPM

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