Copyright © 2014 Pearson Canada Inc. Chapter 4 UNDERSTANDING INTEREST RATES Mishkin/Serletis The...

Copyright © 2014 Pearson Canada Inc.

Chapter 4

UNDERSTANDING INTEREST RATES

Mishkin/SerletisThe Economics of Money, Banking, and Financial Markets Fifth Canadian Edition

Copyright © 2014 Pearson Canada Inc. 4-2

Learning Objectives

1. Detail the present value concept and the meaning of the term interest rate

2. Discern among the ways of measuring the interest rate

3. Illustrate how bond prices and interest rates are negatively related

4. Explain the difference between nominal and real interest rates

5. Assess the difference between interest rates and rates of return


Measuring Interest Rates

• Present Value:– a dollar paid to you one year from now is less valuable than a

dollar paid to you today– why?

• a dollar deposited today can earn interest and become

$1 x (1+i)n


Discounting the Future

Let i = 0.10

In one year $100 x (1+0.10)= $110

In two years $110 x (1+0.10)=$121

In three years $121 x (1+0.10)= $133

In general $100 dollars in n years:

$100 x (1+i)n


Simple Present Value

PV = today’s present value

CF = future cash flow or payments

i = interest rate

niCFPV

)1(


Time Line

$100 $100

Year 0 1

PV 100

2

$100 $100

n

100/(1+i) 100/(1+i)2 100/(1+i)n


Four Types of Credit Market Instruments

1. Simple Loan – principal is repaid at the maturity date with interest

2. Fixed Payment Loan– principal is repaid by making the same payment (principal +

interest) every period for a set period of time


Four Types of Credit Market Instruments

3. Coupon Bond– a coupon bond pays the owner of the bond a fixed interest

payment (coupon payment) every year until the maturity date, when a specified final amount (face value or par value) is repaid

4. Discount Bond– a discount bond (also called a zero-coupon bond) is bought

at a price below its face value (at a discount), and the face value is repaid at the maturity date


Yield to Maturity

• YTM– the interest rate that equates the present value of cash flow

payments received from a debt instrument with its value today


Simple Loan

PV = amount borrowed = $100CF = cash flow in one year = $110n = number

100$110$)1(

110$100$)1()1(

110$100$

1

1

i

xii


Fixed Payment Loan

LV = loan valueFP = fixed yearly paymentN = number of years until maturity

niFP

iFP

iFPLV

)1(...

)1(1 2


Coupon Bond

P = price of coupon bondC = yearly coupon paymentF = face value of the bondn = years to maturity

nn iF

iC

iC

iC

iCP

)1()1(...

)1()1(1 32


Yields to Maturity on a 10%-Coupon-Rate Bond Maturing in Ten Years (Face Value = $1,000)


Three Facts About Coupon Bonds

1. When the coupon bond is priced at its face value, the yield to maturity equals the coupon rate

2. The price of a coupon bond and the yield to maturity are negatively related

3. The yield to maturity is greater than the coupon rate when the bond price is below its face value


Consol or Perpetuity

Pc = price of the consol

C = yearly interest paymentic = yield to maturity of the consol

• A bond with no maturity date that does not repay principal but pays fixed coupon payments forever

cPC

ci


Discount Bond

F = face value of the discount bond

P = current price of the discount bond

PPFi


Yield on a Discount Basis

• Yield on a discount basis:

idb = yield on a discount basis

F= face value

P= purchase price

maturity todays365

PPFidb


The Distinction Between Interest Rates and Returns

g gain capital of rate

i yieldcurrent

paymentcoupon 1 tat time bond theof price

tat time bond of price 1 t t to timefrom bond theholding fromreturn

1

c

1

1

t

tt

t

t

tt

t

t

t

PPP

PC

PPP

PCRET

CPPRET


The Distinction Between Interest Rates and Returns (cont’d)

• The return equals the yield to maturity only if the holding period equals the time to maturity

• A rise in interest rates is associated with a fall in bond prices, resulting in a capital loss if time to maturity is longer than the holding period

• The more distant a bond’s maturity, the greater the size of the percentage price change associated with an interest-rate change


The Distinction Between Interest Rates and Returns (cont’d)

• The more distant a bond’s maturity, the lower the rate of return the occurs as a result of an increase in the interest rate

• Even if a bond has a substantial initial interest rate, its return can be negative if interest rates rise


One-Year Returns on Different-Maturity 10%-Coupon-Rate Bonds When Interest Rates Rise from 10% to 20%


Interest-Rate Risk

• Prices and returns for long-term bonds are more volatile than those for shorter-term bonds

• There is no interest-rate risk for any bond whose time to maturity matches the holding period


Real and Nominal Interest Rates

• Nominal interest rate makes no allowance for inflation• Real interest rate is adjusted for changes in price level

so it more accurately reflects the cost of borrowing• Ex ante real interest rate is adjusted for expected

changes in the price level• Ex post real interest rate is adjusted for actual changes

in the price level


Fisher Equation

i = nominal interest rater = real interest rateπe = expected inflation rate

eri


Fisher Equation (cont’d)

• When the real interest rate is low, there are greater incentives to borrow

• Low interest rates reduces the incentives to lend

• The real interest rate is a better indicator of the incentives to borrow or lend


Real and Nominal Interest Rates

Copyright © 2014 Pearson Canada Inc. Chapter 4 UNDERSTANDING INTEREST RATES Mishkin/Serletis The...

Documents

Transcript of Copyright © 2014 Pearson Canada Inc. Chapter 4 UNDERSTANDING INTEREST RATES Mishkin/Serletis The...