Chap 2 interest rates

 Term Structure of Interest Rates Pure Expectation Theory  Segmented Markets Theory  Liquidity Premium Theory... Term Structure of Interest RatesYield curve: a plot of the yield on b

Financial Markets

and Institutions

Chapter 2

Interest Rates

 Term Structure of Interest Rates

 Pure Expectation Theory

 Segmented Markets Theory

 Liquidity Premium Theory

Readings

① Chapter 3,4,5 Financial Markets and Institutions; Federic

S Mishkin, Stanley G Eakins; Pearson (2012)

② Chapter 2,3, Financial Markets and Institutions; Jeff

Madura; South-Western Cengage Learning (2010)

③ Giáo trình Tài chính – tiền tệ; TS Nguyễn Hòa Nhân,

PGS.TS.Lâm Chí Dũng, TS.Hồ Hữu Tiến, ThS.Võ VănVang, ThS Trịnh Thị Trinh, ThS Đặng Tùng Lâm Nhà

2.1 Interest rates Measurement

variables in the economy It is imperative that you understand exactly what is meant by the phrase interest rates.

is the most accurate measure of interest rates.

2.1 Interest rates Measurement

2.1.1 Present Value Introduction

 Different debt instruments have very different streams of

cash payments to the holder known as cash flows (CF).

 All else being equal, debt instruments are evaluated against

one another based on the amount of each cash flow and the

timing of each cash flow.

 This evaluation, where the analysis of the amount and

timing of a debt instrument’s cash flows lead to its yield to

2.1 Interest rates Measurement

2.1.1 Present Value Introduction

 Present discounted value is based on the common-sensenotion that a dollar of cash flow paid to you one year fromnow is worth less than a dollar paid to you today

 Because you could invest the dollar in a savings accountthat earns interest and have more than a dollar in one year

 The term present value (PV) can be extended to mean the

PV of a single cash flow or the sum of a sequence or group

of cash flows

2.1 Interest rates Measurement

2.1.1 Present Value Concept

simple loan of $100 for one year, you would require her to repay the principal of $100 in one year’s time along with an additional payment for interest; say, $10.

2.1 Interest rates Measurement

2.1.1 Present Value Concept

 Loan Principal: the amount of funds the lender provides to

the borrower (100$)

 Maturity Date: the date the loan must be repaid; the Loan

Term is from initiation to maturity date (1 year)

 Interest Payment: the cash amount that the borrower must

pay the lender for the use of the loan principal (10$)

 Interest Rate: the interest payment divided by the loan

principal; the percentage of principal that must be paid asinterest to the lender Convention is to express on an

annual basis, irrespective of the loan term (?)

2.1 Interest rates Measurement

2.1.1 Present Value Concept

(1 + 𝑖)𝑛

2.1 Interest rates Measurement

2.1.1 Present Value Concept

 If you make this $100 loan, at the end of year 1 you would

have $110, which can be rewritten as:

 100 + 100 × 0,10 = 100 × 1 + 0,10 = 110 đ

 If you then lent out the $110, at the end of the second year

you would have: …

At the end of the third year: …

2.1 Interest rates Measurement

2.1 Interest rates Measurement

2.1.2 Yield to Maturity

1 Simple Loans

PV = amount borrowed; CF = future cash flow

n = number of yearsEx: If Peter borrows $200 from his sister and next year she wants

$210 back from him, what is the yield to maturity on this loan?

2.1 Interest rates Measurement

2.1.2 Yield to Maturity

2 Fixed payment Loans: are loans where the loan principal andinterest are repaid in several payments over the loan term

LV = loan value

FP = fixed yearly cash flow payment

n = number of years until maturity

2.1 Interest rates Measurement

2.1.2 Yield to Maturity

3 Coupon Bonds:

PV = price of coupon bond

C = yearly coupon payment

F = face value of the bond

n = years to maturity date

2.1 Interest rates Measurement

2.1.2 Yield to Maturity

4 Discount Bonds: The yield-to-maturity calculation for adiscount bond is similar to that for the simple loan

More general, for one-year discount bond:

F = face value of the discount bond

P = current price of the discount bond

1 + 𝑖𝑌𝑀

2.2 Types of Interest rates

Real interest rate & Nominal interest rate

expected changes in the price level

FE equation can be rewritten as:

𝑖𝑟 : Real interest rate

i : Nominal interest rate

𝜋𝑒 : Expected inflation rate

1 + 𝑖 = 1 + 𝑖𝑟 1 + 𝜋𝑒

𝑖 ≈ 𝑖𝑟 + 𝜋𝑒

 If i = 5% and 𝜋𝑒 = 0% then 𝑖𝑟 = ?

2.2 Types of Interest rates

Real interest rate & Nominal interest rate

2.2 Types of Interest rates

Real interest rate & Nominal interest rate

2.2 Types of Interest rates

Simple interest rates & Compound interest rates

 Simple interest: is calculated only on the principal amount

of a loan

𝐹 = 𝑃 × (1 + 𝑛 × 𝑖)𝑆𝑖𝑚𝑝𝑙𝑒 𝑖𝑛𝑡𝑒𝑟𝑒𝑠𝑡 = 𝑃 × 𝑛 × 𝑖

P = Principal

i = annual simple interest rate in percentage terms

n = number of periods

2.2 Types of Interest rates

Simple interest rates & Compound interest rates

 Compound interest: calculated on the principal amount andalso on the accumulated interest of previous periods, andcan thus be regarded as “interest on interest.”

𝐹 = 𝑃 × (1 + 𝑖)𝑛𝐶𝑜𝑚𝑝𝑜𝑢𝑛𝑑 𝑖𝑛𝑡𝑒𝑟𝑒𝑠𝑡 = 𝑃 × (1 + 𝑖)𝑛−𝑃

P = Principal

i = annual compound interest rate in percentage term

n = number of periods

2.3 Risk Structure of Interest rates

2.3 Risk Structure of Interest rates

Factors Affecting Risk Structure of Interest Rates

 Default Risk occurs when the issuer of the bond is unable

or unwilling to make interest payments when promised

 Default-free bonds?

 The spread between the interest rates on bonds with defaultrisk and default-free bonds, called the risk premium,indicates how much additional interest people must earn inorder to be willing to hold that risky bond

2.3 Risk Structure of Interest rates

Factors Affecting Risk Structure of Interest Rates

2.3 Risk Structure of Interest rates

Factors Affecting Risk Structure of Interest Rates

Bond Ratings

 A liquid asset is one that can be quickly and cheaplyconverted into cash.

 The more liquid an asset is, the more desirable it is (higherdemand), holding everything else constant

 Treasury bonds are the most liquid of all long-term bondsbecause they are so widely traded that they are easy to sellquickly and the cost of selling them is low

 Corporate Bonds?

2.3 Risk Structure of Interest rates

Liquidity Factor

2.3 Risk Structure of Interest rates

Liquidity Factor

2.3 Risk Structure of Interest rates

Income Tax Consideration

 Interest payments on municipal bonds are exempt fromfederal income taxes

2.3 Risk Structure of Interest rates

Income Tax Consideration

2.4 Term Structure of Interest Rates

Yield curve: a plot of the yield on bonds with differing terms to maturity

 Upward-sloping: long-term rates are above short-termrates

 Flat: short-term rates and long-term rates are the same

 Inverted: long-term rates are below short-term rates

2.4 Term Structure of Interest Rates

US Treasury Yield Curve

2.4 Term Structure of Interest Rates

Facts Theory of the Term Structure of

Interest Rates Must Explain

1 Interest rates on bonds of different maturities move together

over time

2 When short-term interest rates are low, yield curves are more

likely to have an upward slope; when short-term rates arehigh, yield curves are more likely to slope downward and beinverted

3 Yield curves almost always slope upward

2.4 Term Structure of Interest Rates

2.4.1 Expectations Theory

 The interest rate on a long-term bond will equal an average ofthe short-term interest rates that people expect to occur over thelife of the long-term bond

 Key Assumption: Bonds of different maturities are perfectsubstitutes

 Implication: Expected return on bonds of different maturitiesare equal

2.4 Term Structure of Interest Rates

2.4.1 Expectations Theory

Investment strategies for two-period horizon:

 Buy $1 of one-year bond and when matures buy another

one-year bond

 Buy $1 of two-year bond and hold it

2.4 Term Structure of Interest Rates

2.4.1 Expectations Theory

 Expected return from strategy 1:

 Since 𝑖1,𝑡 × 𝑖1,𝑡+1𝑒 is also extremely small, expected return isapproximately: 𝒊𝟏,𝒕 + 𝒊𝟏,𝒕+𝟏𝒆

1 + 𝑖1,𝑡 1 + 𝑖1,𝑡+1𝑒 − 1 = 1 + 𝑖1,𝑡 + 𝑖1,𝑡+1𝑒 + 𝑖1,𝑡 × 𝑖1,𝑡+1𝑒 − 1

 Expected return from strategy 2:

 Since 𝑖2,𝑡2 is also extremely small, expected return isapproximately: 𝟐𝒊𝟐,𝒕

2.4 Term Structure of Interest Rates

2.4.1 Expectations Theory

(1 + 𝑖2,𝑡)2−1 = 1 + 2𝑖2,𝑡 + 𝑖2,𝑡2 − 1

 From implication above expected returns of two strategies are

For bonds with longer maturities

The n-period interest rate equal the average of the one-period interest rates expected to occur over the n-period of the bond

2.4 Term Structure of Interest Rates

2.4.1 Expectations Theory

𝑖𝑛,𝑡 = 𝑖1,𝑡 + 𝑖1,𝑡+1

𝑒 + 𝑖1,𝑡+2𝑒 + ⋯ + 𝑖1,𝑡+𝑛−1𝑒

𝑛

 Explains why the term structure of interest rates changes at

different times

 Explains why interest rates on bonds with different maturities

move together over time (fact 1)

 Explains why yield curves tend to slope up when short-term rates are low and slope down when short-term rates are high (fact 2)

 Cannot explain why yield curves usually slope upward (fact 3)

2.4 Term Structure of Interest Rates

2.4.1 Expectations Theory

2.4 Term Structure of Interest Rates

2.4.1 Segmented Markets Theory

 Key Assumption: Bonds of different maturities are not substitutes

at all

 Implication: Markets are completely segmented; interest rate at each maturity determined separately

 Investors have preferences for bonds of one maturity over another

 If investors generally prefer bonds with shorter maturities thathave less interest-rate risk, then this explains why yield curvesusually slope upward (fact 3)

 Does not explain fact 1 or fact 2

2.4 Term Structure of Interest Rates

2.4.1 Segmented Markets Theory

2.4 Term Structure of Interest Rates

Liquidity Premium Theory

 Key Assumption: Bonds of different maturities are substitutes,but are not perfect substitutes

 Implication: Modifies Pure Expectations Theory with features ofMarket Segmentation Theory

 Investors prefer short rather than long bonds, must be paid positiveliquidity premium to hold long term bonds

 Results in following modification of Pure Expectations Theory:

2.4 Term Structure of Interest Rates

Liquidity Premium Theory

𝑖𝑛,𝑡 = 𝑖1,𝑡 + 𝑖1,𝑡+1

𝑒 + 𝑖1,𝑡+2𝑒 + ⋯ + 𝑖1,𝑡+𝑛−1𝑒

 Explains All 3 Facts

 Explains fact 3—that usual upward sloped yield curve by liquiditypremium for long-term bonds

 Explains fact 1 and fact 2 using same explanations as pureexpectations theory because it has average of future short rates asdeterminant of long rate

2.4 Term Structure of Interest Rates

Liquidity Premium Theory

2.4 Term Structure of Interest Rates

Liquidity Premium Theory

FIGURE 6 Yield Curves and the Market’s Expectations of Future

Short-Term Interest Rates According to the Liquidity Premium (Preferred

Habitat) Theory

FIGURE 6 Yield Curves and the Market’s Expectations of Future

Short-Term Interest Rates According to the Liquidity Premium (Preferred

Habitat) Theory

Interest Rates in Vietnam