IMPACT ON FIXED INCOME

SECURITIES

INTEREST RATE RISK

Bonds, bond prices and interest rates

Bond prices and yieldsBond market equilibriumBond risks

Bonds: 3 types

Zero coupon bondse.g. Tbills

Fixed payment loanse.g. mortgages, car loans

Coupon bondse.g. Tnotes, Tbonds

Zero coupon bonds

Discount bondspurchased price less than face value-- F > P

face value at maturityno interest payments

Example

91 day Tbill, P = Rs.9850, F = Rs.10,000YTM solves

36591)1(

000,10$9850$

i

36591)1(

000,10$9850$

i

9850

100001 365

91 i

91365

9850

100001

i

%25.619850

10000 91365

i

yield on a discount basis (127)

how Tbill yields are actually quotedapproximates the YTM

idb = F - P

Fx

360d

example

91 day Tbill, P = Rs.9850, F = Rs.10,000discount yield =

%93.591

360

000,10$

150$

idb < YTMwhy?

F in denominator 360 day year

Fixed-payment loan loan is repaid with equal (monthly) payments each payment is combination of principal and

interest

example 2: fixed pmt. loan

Rs.20,000 car loan, 5 yearsmonthly pmt. = Rs.500so Rs.15,000 is price todaycash flow is 60 pmts. of Rs.500what is i?

i is annual rate (effective annual interest rate)

but payments are monthly, & compound monthly

(1+im)12 = iim= i1/12-1im is the periodic ratenote: APR = im x 12

602 1

500...

1

500

1

50020000

mmm iii

im=1.44%i=(1+. 0144)12 – 1 =18.71%

%28.17120144. APR

how to solve for i? trial-and-error table financial calculator spreadsheet

Coupon Bond

Bond Yields

Yield to maturity (YTM) chapter 4

Current yieldHolding period return

Yield to Maturity (YTM)

a measure of interest rateinterest rate where

P =PV of cash flows

Current yield

approximation of YTM for coupon bonds

ic =annual coupon payment

bond price

better approximation when maturity is longer P is close to F

example

2 year Tnotes, F = Rs.10,000P = Rs.9750, coupon rate = 6%current yield

ic =600

9750= 6.15%

Current yield = 6.15%True YTM = 7.37%Lousy approximation

only 2 years to maturity selling 2.5% below F

Holding period return

sell bond before maturityreturn depends on

holding period interest payments resale price

example

2 year Tnotes, F = Rs.10,000P = Rs.9750, coupon rate = 6%sell right after 1 year for Rs.9900

Rs.300 at 6 mos. Rs.300 at 1 yr. Rs.9900 at 1 yr.

221

3009900

21

3009750

ii

i/2 = 3.83%i = 7.66%

why i/2?interest compounds annually not

semiannually

The Bond Market

Bond supplyBond demandBond market equilibrium

Bond supply

bond issuers/ borrowerslook at Qs as a function of price, yield

lower bond prices higher bond yields more expensive to borrow lower Qs of bonds

so bond supply slopes up with price

Bond price

Q of bonds

S

Changes in bond price/yield Move along the bond supply curve

What shifts bond supply?

Shifts in bond supply

Change in government borrowing Increase in gov’t borrowing

Increase in bond supply Bond supply shifts right

P

Qs

S

S’

a change in business conditions affects incentives to expand production

exp.profits

supply ofbonds(shift rt.)

exp. economic expansion shifts bond supply rt.

exp. economic expansion shifts bond supply rt.

a change in expected inflation rising inflation decreases real cost of borrowing

exp.inflation

supply ofbonds(shift rt.)

Bond Demand

bond buyers/ lenders/ saverslook at Qd as a function of bond price/yield

Bond yield

Qd ofbonds

priceof bond

Qd of bonds

so bond demand slopes down with respect to price

Bond price

Quantity of bonds

D

Changes in bond price/yield Move along the bond demand curve

What shifts bond demand?

Wealth Higher wealth increases asset demand

Bond demand increases Bond demand shifts right

P

Qd

DD

a change in expected inflation rising inflation decreases real return

inflationexpected to

demand forbonds(shift left)

a change in exp. interest rates rising interest rates decrease value of existing

bonds

int. ratesexpected to

demand forbonds(shift left)

a change in the risk of bonds relative to other assets

relativerisk of bonds

demand forbonds(shift left)

a change in liquidity of bonds relative to other assets

relative liquidityof bonds

demand forbonds(shift rt.)

Bond market equilibrium

changes when bond demand shifts,and/or bond supply shifts

shifts cause bond prices AND interest rates to change

Example 1: the Fisher effectexpected inflation 3%

exp. inflation rises to 4% bond demand

-- real return declines-- Bd decreases

bond supply-- real cost of borrowing declines-- Bs increases

bond price fallsinterest rate rises

Fisher effect

expected inflation rises,nominal interest rates rise

Example 2: economic slowdown

bond demand decline in income, wealth Bd decreases P falls, i rises

bond supply decline in exp. profits Bs decreases P rises, i falls

• shift Bs > shift in Bd

• interest rate falls• shift Bs > shift in Bd

• interest rate falls

Why shift Bs > shift Bd?

changes in wealth are smallresponse to change in exp. profits is large

large cyclical swings in investment

• interest rate is pro-cyclical• interest rate is pro-cyclical

Why are bonds risky?

3 sources of risk Default Inflation Interest rate

Default risk

Risk that the issuer fails to make promised payments on time

Zero for U.S. gov’t debtOther issuers: corporate, municipal, foreign

have some default riskGreater default risk means a greater yield

Inflation risk

Most bonds promise fixed dollar payments Inflation erodes the real value of these payments

Future inflation is unknownLarger for longer term bonds

Interest rate risk

Changing interest rates change the value (price) of a bond in the opposite direction.

All bonds have interest rate risk But it is larger for the long term bonds