Federal (fed) funds:

Federal Funds Market = sensitive to needs of banks

Interest rate
21/01/2025
3.2 Capital Market
Last section: short-term securities  money market
This section  capital market
Capital markets:
 Securities: maturity > 1 year
Include: bonds (debt instruments – promise of a govt to pay you back – sold by the
govt or private companies), stocks and mortgages
Firms (issue securities) & individuals (buy)
 Motivations / money markets
 Money market  short term
 Capital market  long term
Corporations issue: bonds & stock
Decisions: finance growth with: debt or equity
Distribution of capital between debt / equity: capital structure
Corporations  capital markets:
 Not sufficient capital to fund investmkent
 Preserve their capital to protect against needs
Efficiently functioning capital markets:
 Crucial  business sector
Demonstrated:
 2008-2009 financial crisis: “liquidity dry up”
 ↘activity, ↗Unemployment (U), ↘g (lower GDP)
Households = largest purchasers of capital market securities
Individuals & households:
 Funds in Financial Institutions
 Use the funds to purchase: bonds & stocks
3.2 Capital Market Instruments (CMI)
= debt & equity investments:
  Maturities
3.2.1 Types of Bonds
Bonds = securities:
 Debt owed by issuer to the investor
Issuer pays:
 Specified amount at a given date with periodic interest payments
The first bond was issued by the US govt in 1908: bond with detachable physical
coupons, on the bond the coupons are meant to be teared off and redeemed for
interest
 Name of the issuer: USA
 Face value: $20
 Coupon rate: 3%
 Coupon value: 3% x $20 = $0.60
Amount of interest
Example:
 A bond with a face value F = $1000
 Coupon rate: i = 1%
 Value of the coupon: C =

Treasury notes and bonds

US treasury issues notes and bonds: national debt
Difference:
 Notes : 1  10 years
 Bonds: 10  30 years
 Bills: < 1 year
Price: quoted as % of $100 face value (F)
Free of default risk:
 Govt: print money to pay off debt
≠ risk-free

Treasury bonds interest Rates. IR (1974-2016)

1970s & early 1980s:
 IR on 10-years treasury bonds < rate inflation
  Investors: earned less than inflation rate
Then: IR (10-years T-Bonds)
 Inflation rate
 IR on money market securities because of interest-rate risk

1. Rate of return on short-term bill: < 20-year bond

2. Short-term rates: more volatile thang long-term rates
Short-term rates: more influenced by expected rate of inflation
Investors in long-term securities expect: inflation rates  more normal levels, 
long term rates: less volatile
3.2.2 Corporate Bonds (CB)
Issued by corporations: strong credit ratings: need funds for long periods of time
Holder receives:
 Interest payment twice a year
 Face value at maturity date
Convertible bonds: holder can convert bonds  stocks  more desirable
CB:
 Small outstanding amount, not as liquid as other securities (US govt bonds)
Size:
 Corporate bond market < stock market
However:
 New CB issues each year > volume of new stock issues
Firm’s financing decisions depend more on:
 CB market / stock market
Principal buyers:
 Life insurance companies
 Pension funds
 Households
Corporate Bonds (CB): Degree of risk
Degree of risk varies among bonds:
 Risk of default depends on company’s health
Bonds:
  Lower risk & higher rating (AAA)
 Lower interest rates than riskier (BBB)
Spread between AAA & BBB bonds: historically 1%
2008: Investors seeking safety  spread = 3.38%
3.2.3 Stocks (=shares)
Stock: financial instrument = ownership of the company = claim on a part of profits
Investors: one vote per share
Common stock
 Higher returns / other investments
 Most risk
If company goes bankrupt  common shareholders have no money until the
creditors, bondholders are paid.
At the end of 2008: value = $20 trillion > other securities
However, new stock issues < 1% of the total value of shares outstanding.
Shareholders:
 Individuals: ½ value of stocks; the rest: Pension funds, mutual funds,
insurance companies
3.2.4 Mortgages
Loans to households or firms to purchase: housing or land
 Structure = collateral for the loans
Mortgage market = largest debt market
Residential mortgages > commercial and farm mortgages
Primary lenders in residential mortgage market:
 Savings associations
 Mutual serving banks
Commercial and farm mortgages:
 Commercial banks and insurance companies
Part of the classic American dream is: to own their own home
Price: over $300,000:
 Few of us could hope. If: not able to borrow.
= subcategory of the capital markets (long-term funds)
But ≠ from stock & bond markets
1) Borrowers
 In capital markets = govt + businesses
 In mortgage markets = individuals
2) .
 Mortgage loans: varying amounts of maturities depending on the borrowers’
needs
 Problems for developing a secondary market

CM 2 – 04/02/2025
Questions:
1. A financial market in which only short-term debt instruments are traded is
called the MONEY market
2. Equity instruments are traded in the CAPITAL market
3. Because these securities are more liquid and generally have smaller price
fluctuations, corporations and banks use the MONEY MARKET securities to
earn interest on temporary surplus funds
4. Corporations receive funds when their stock is sold in the primary market.
Why do corporations pay attention to what is happening to their stock in the
secondary market? The existence of the secondary market makes their
stock more liquid and the price in the secondary market sets the
price that the corporation would receive if they choose to sell more
stock in the primary market
5. Contrast investors’ use of capital markets with their use of money markets.
Investors use capital markets for long-term investment purposes.
They use money markets, which have lower yields, primarily for
temporary or transaction purposes.
6. Differentiate between primary and secondary markets. The primary
market is for securities being issued for the very first time, and the
issuer receives the funds paid for the security. The secondary
market is for securities that have been issued previously but are
being traded among investors
7. What are the main characteristics of stocks that differentiate them from
bonds? Stocks do not mature, do not pay a fixed amount every
period, and often give holders the right to vote on management
issues
8. Securities in the mortgage markets are collateralized by real estate. What
does it mean? The banks accepts the home as security. If the borrower
is not able to pay off their loan the bank can sell their real estate

4. Internationalization of Financial Markets (FM)

Before 1980s the US FM > FM outside of the US
Recent years: dominance of US markets: disappearing
Growth of foreign FM results from:
 Increase in savings in foreign countries (Japan, China)
 Deregulation of foreign FM

American corporations and banks: raise funds on international CM

American investors:
 Investment opportunities abroad
Foreign corporations & banks:
 Raise funds from Americans
 Foreigners: Investors in US

Foreign bonds:
 Traditional instruments in the international bond market
 Sold in a foreign country and denominated in that country’s currency
If Volkswagen (German) sells a bons in the US denominated in $ = foreign bond
Foreign bonds = important instrument for centuries
US railroads built in the 19 th century were financed by sales of foreign bonds in
Britain

4.1 Eurobonds
 It is a more recent innovation
 Is a bond denominated in a currency other than that of the country in which it
is sold
 E.g.: bond denominated in US $ sold in London
 Over 80% of new issues in international bond market = Eurobonds
 Eurobond market > US corporate bond market
4.2 Eurocurrencies
= foreign currencies deposited in banks outside the country
Eurodollars
 US dollars deposited in foreign banks outside the US
These short-term deposits earn interest  similar to short-term Eurobonds.
American banks borrow Eurodollar deposits from other banks
 Eurodollars = important source of funds fir American banks

European currency: the Euro (€)

It creates some confusion about the terms: Eurobond, Eurocurrencies and
Eurodollars
A bond denominated in Euros (€) is a Eurobond only if:
 it is sold outside the countries that have adopted Euro (€)

Most Eurobonds:
 are not denominated in Euros (€)
 denominated in US dollars
Eurodollars:
 have nothing to do with Euros (€)
 = $ deposited in banks outside the US

4.3 World Stock Markets

US stock market was the largest in the world
But: growth of foreign stock markets
American investors pay attention:
 Dow Jones (Dow Jones Industrial Average) = 30 companies
 Nikkei (Tokyo) = 225 companies, more generalized
 FTSE 100 = Footsie (London)
 Euronext 100 (Europe)

The Dow Jones Industrial Average is a stock market index that tracks the
performance of 30 large publicly traded companies traded across various sectors of
the US economy, serving as a key indicator of the overall health and trends of the
American stock market.

Internationalization of FM  effects on the US

Foreigners (Japanese or Chinese investors):
  Provide funds to: US corporations and the federal government
Without foreign funds; lower growth
Internationalization FM:
 More integrated world economy
 Flows of goods between countries = commonplace

QUESTIONS:
1. Equity of US companies can be purchased by: US CITIZENS AND FOREIGN
CITIZENS
2. One reason for the extraordinary growth of foreign financial markets:
INCREASES IN THE POOL OF SAVINGS IN FOREIGN MARKETS
3. Bonds that are sold in a foreign country and are denominated in the country’s
currency in which they are sold are known as: FOREIGN BONDS
4. Bonds that are sold in a foreign country and are denominated in a currency
other than that of the country in which it is sold are known: EUROBONDS
5. If Microsoft sells a bond in London and it is denominated in dollars, the bons
is a: EUROBOND
6. US dollar deposits in foreign banks outside the US or in foreign branchers of
US banks are called: EURODOLLARS
7. If Toyota (headquarters in Japan) sells a $1000 bond in the US, the bond is a:
FOREIGN BOND
8. If Volkswagen, a German company, sells a euro-denominated bond in London,
the bond is a: EUROBOND
9. Distinguish between a foreign bond and a Eurobond:
A: A FOREIGN BOND IS SOLD INA FOREIGN COUNTRY AND PRICED IN THAT
COUNTRY’S CURRENCY
B: A EUROBOND:

CHAPTER 3: UNDERSTANDING INTEREST RATES

Interest Rates (IR)  affect personal decisions
 Consume / save
 Buy a house
 Purchase bonds / savings account
IR  economic decisions in business:
 Use funds to invest
 Save money in a bank

Before the study of FM, we need to understand exactly:

 What the phrase “interest rates” means:
 Yield to maturity (YTM)
o Is the most accurate measure of IR
o What economists mean with the term IR
 Measure  YTM

Bond’s IR does not equal how good an investment in a bond is because: only the
rate of return can tell me
 Rate of return ≠ IR
 Real IR / nominal IR
Difference between interest rate and rate of return: The gain or the loss
coming from the change in price of the bond if you need cash before the maturity
date of your investment
Learning definitions:

1. Measuring IR
Debt instruments have:
 Different flows of cash payments = cash flows
 Different timing
Understand:
 How compare the value of one debt instrument with another
 How IR is measured
 Concept of present value (PV)

1.1 Present value: PV (or present discounted value: in French

“Valeur actualisée)
  $1 paid one year from now < $1 paid today because:
o Deposit $1 today in a saving account  interest
o More than $1 in one year

1.1 PV (Simple loan)

Lender provides funds to the borrower (=principal)
 Repaid to lender (maturity), with additional payment (interests)
You made your friend a simple loan for $100 for 1 year, he would:
 Repay principal $100 in 1 year + additional payment: interest $10

IR = interest payment divided by the amount of the loan

Measure of this simple IR, i, is:
i = $10/$100 = 0.10 = 10%

$100 loan  end of the year you have: $110, rewritten as: $100 x (1+0.10) =
$110
If lent out the $110  end of the 2nd year you have: $110 x (1+0.10) = $121

Or equivalently:
$100 x (1+0.10) x (1+0.10)
= $100 x (1+0.10)2
= $121
Continuing the loan  end of the 3rd year: $121 x (1+0.10) = $100 x (1+0.10)3 =
$133
At the end of n years, your $100 turn into: $100 x (1 + i)n
Amounts  end of each year: timeline

Backward: from future to present

$133 = $100 x (1+0.10)3 three years from now is worth $100 today so that:
$100 = 133/(1+0.10)3
PV = CF (cash flow) / (1+i)n
 CM 3 – 11/02/2025
Calculation: today’s value of $ received in the future = discounting the future
Generalization:
 PV: present value
 CF: cash flow
 i: Interest rate
 n: number of years
Formula: PV = CF (cash flow) / (1+i)n

$1 of CF in 10 years  this dollar ≠ valuable as $1 today

The concept of PV = useful for:

Determine today’s value (price) of:
 a credit market instrument (CMI) for an IR (i), by adding PV of all future
payments
 compare values of different credit market instruments

Exercise:
What is the PV of $250 to be paid in 2 years if i=15%
 CF in 2 years = $250
 i: annual interest rate = 0.15
 n: number of years = 2
PV = CF/(1+i)n
PV = $250/(1+0.15)2 = $189

Winning $20 million jackpot

 $ million for 20 years
Have you really won $20 million?
In today’s dollars: $20 million is worth less  NO
Jackpot if we assume i = 10%
 1st payment of $1 million: worth $1 million today
 Payment next year = $1milliom/(1+0.10) = $909.090 >$1 million
 The following year payment = $1 million/(1+0.10) 2 = $826.446 in today’s $

Addition = 9.4 million

In present value terms: you don’t win 20 million dollars but less than half  false
advertising

QUESTIONS:
1. The concept of PRESENT VALUE is based on the common-sense notion that
a dollar paid to you in the future is less valuable to you than a dollar today
2. The present value of an expected future payment FALLS as the interest rate
increases
3. An increase in the time to the promised future payment DECREASES the
present value of the payment  because the more time I have to wait the
less valuable it will be today (jackpot example)
4. With an interest rate of 6% the present value of $100 to be received next
year is approximately $94  PV formula
5. What is the present value of %500 to be paid in two years (n=2) if the
interest rate is 5%? $453.51  PV = 500/(1,05)2
6. If a security pays $55 in one year and $133 in three years, its present value is
$150 if the interest rate is: 10%  PV = 150 = $55/(1,1)1 + $133/(1,1)3
7. If you claim that a lottery winner who will receive $1 million per year for
twenty years has won $10 million, you ignore the process of: DISCOUNTING
THE FUTURE

1.2 Four types of Credit Market Instruments (CMI)

4 basic types of CMI:
 In terms of timing of their CF payments

1.2.1 Simple loan

Lender provides funds  borrower
Funds:
 Repaid to lender at maturity date with additional payment = interest
Ex: commercial loans
1.2.2 Fixed-payment loan (or fully amortized loan)
Lender provides funds  borrower
Funds repaid: same payment every period (month)
Payment: part of principal + interest

Example:
 Borrow $1000
 Fixed-payment loan: pay $136 every year for 25 years
Ex: car loans, mortgages

1.2.3 Coupon bond

Pays the owner:
 Fixed interest payment (coupon) every year  maturity date
 When: face value (FV) is repaid

Example:
 Coupon bond with $1000 FV
 Coupon payment = $1000 per year for 10 years
 Maturity date: FV = $1000

Identified by 3 pieces of information:

 Issuer
 Maturity date
 Coupon rate (amount of yearly coupon: % of FV)
Example:
 Yearly coupon = $100
 FV = $1000
 Coupon rate = $100/$1000 = 0.10 = 10%
Examples of coupon bonds in CMI
 US treasury bonds
 Corporate bonds
1.2.3 Discount bond (zero-coupon bond)
  Bought at a price < FV (discount)
 FV: repaid at maturity date
 Discount bond (≠ coupon bond):
 No interest payments
 Just pays off the FV

Example: one-year discount bon with FV = $1000:

Bought for $900
Owner: repaid the FV = $100

Example: discount bonds:

 Us treasury bills
 Us saving bonds
 long term zero-coupon bonds
These 4 instruments: payments at different times
 payments only at maturity:
o simple loans
o discount bonds
 payments periodically:
o fixed-payment loans
o coupon bonds have

 how would you decide which of these instruments provide you with more income?

These 4 instruments seem so different because: payments at different times

To solve this problem:
 Concept of PV
 Procedure of measuring IR on different instruments

1.3 Yield of maturity: YTM (or IRR: Internal Rate of Return)

 ≠ ways of calculating IR:
 most important = YTM
  YTM = the IR that equates:
o The PV of CF payments received with its value today: V 0

V0 = PV = CF / (1 + YTM)n

 Context  investment choices

o YTM = internal rate of return: IRR

1.3 Yield to maturity (definition)

 YTM of a bond:
o = IRR earned by investor who buys the bond today (market price)
 Assuming that:
o Bond: held until maturity
o All payments (coupon + principal): made as predicted

Economists consider:
 YTM = most accurate measure of IR
To understand the YTM:
 Calculation for the 4 credit instruments

Calculation of the YTM is equating:

 Today’s value of the debt instrument
 With PV of all its future CF payments
V0 = PV = CF/(1+YTM)n

1.3.1 Application: YTM on a simple loan

 Borrow $100 and next years repay $100 back

 YTM on this loan?
PV = CF/(1+i)n
PV: amount borrowed = $100
CF: cash flow in one year = $110
n: number of years = 1
1.3.1 Application: YTM on a simple loan
Calculation YTM familiar:
 = interest payment $10 / loan amount $100
 =simple IR on the loan
For simple loans: IR = YTM
 same term i to denote:
 YTM
 Simple IR
1.3.2 Fixed-payment Loan (FPL)
Same CF payment:
 Every period during the life of the loan
Example: fixed-rate mortgage
 Borrower makes the same payment to the bank every month until the
maturity date: when the loan will be completely paid off

Calculate YTM  equate:

 Today’s value of loan with its PV
1.3.3 Fixed payment loan

 Real estate brokers: pocket calculator

 Tell the house buyer: yearly (or monthly) payments
 If purchase of house: financed by mortgage

1.3.4 Coupon Bond (CB)

 YTM for CB:
o Equate today’s value of the bond with its PV
 More than 1 CF payment  PV of the bond:
o Sum of PV of all coupon payments
o + PV of final payment (=FV of the bond)

Today’s value of the bond = its current price (P)

Application: P of a coupon bond?
Coupon bond:
 F= $1000 (FV of bond)
 n= 10 (years of maturity)
 C= (yearly coupon payments = $100 (r=10%)
 Repayment (F= $1000) after 10 years
Today’s value of bond (current price =P)
=sum of the PV of all the CF
P = C $100/(1+i) + C $100/(1+i) + C $100/(1+i) + … C $100/(1+i) + F $1000/(1+i)

Where:
  P: price of coupon bond
 C: yearly coupon payment
 F: face value
 n: number of years
YTM (i) : not known

CM 4 – 11/03/2025

Application: YTM and the Bond Price for a coupon bond

Price of a 10% coupon bond:
 FV = 1000
 i = 12.25% (YTM)
 n = 8 years
 C = 100
The price P of the bond (PV)?
P = 100 / 1 + 0.1225 + 100 / (1+0.1225)2 ….
P = 889.20

YTM for several bond prices

 r = 10%  coupon rate
 n = 10 years
 FV = 1000 (initial FV)

Price of Bond YTM (%)

($)
1200 7.13
1100 8.48
1000 10.00
900 11.75
800 13.81

1. When P = FV  YTM = coupon rate (r)

2. Price and YTM > negatively related:
 a. YTM rises –> P falls
b. YTM falls –> P rises
3. YTM > r, when P > FV
TRUE FOR ANY COUPN BOND

First Fact:
P = FV  YTM coupon rate (r)

 $1000  bank account: IR = 10%

o $100 every year
o $1000  end of 10 years
 Similar to buy $1000 bond: r = 10%
o $100

Second Fact:
The price of a coupon bond and the YTM: negatively related
 ↗ i (YTM)  ↘ratios
 ↗ IR (measured by YTM) means: - price of bond must fall
↗i↘P

Third fact:
YTM > r ↔ P < FV
 Directly from facts 1 and 2
 When YTM = r  P = FV
 When YTM rises above r  P falls  P < FV

Special Case of Coupon Bond: Consol or Perpetuity

 = perpetual bond:
o No maturity date
o No repayment of principal
o Fixed coupon payments of $C forever
 Price = Pc = C/ ic
Perpetuity: perpetual bond
 Cash flows > 20 years:
 Smal present discounted values 
o Value of a long-term coupon bond:
o Close to value of a perpetuity with same coupon rate
  ic: in (5): close to YTM

Ic = C/PC
  Coupon payment divided by the price of the security (C/P), is called: current
yield (“rdt actuariel”)
 = approximation to describe interest rates on long-term bonds

1.3.4 Discount bond (purchased at a discount P < F)

 YTM for discount bond ↔ simple loan
 Discount bond:
o One year US treasury bill
o Pays a face value of $1000 in one year
 If P = $900
 Equation (1) gives:
900 = 1000/1+i  i = 1000-900/900 = 0.111 = 11.1%
More generally, for any one-year discount bond, the YTM (i):
i=F–P/P
Where:
 F = face value of the discount bond
 P = current price of the discount bond

  YTM = increase in price (F – P) divided by initial price (P)

o Normal circumstances: investors:
o Prosituve return from holding these securities

P<F
 However: not always the case, events in Japan indicate:
 Equation indicates for a discount bond:
o YTM: negatively related to the current bond price (same conclusion
that for a coupon bond)


δi F
δP p {
= 2 < 0 : ↑ P ↔↓ i
↓ P ↔↑ i
Japan in the late 1990s and US during the subprime financial crisis of 2008
 Normally assume: i > 0
 i<0P>F
o means: you are willing to pay more for a bond today than you will
receive for it in the future:
o P>F
  Negative
 In nov 1998:
o Interest rates on Japanese six-month treasury bills: negative
o Interest rate: -0.004%
 In sept 2008, interest rate son three-month T-bills: below zero
 Negative interest rates: unusual

Japan (late 90s) and US (2008)

 Weakness of eco + flight to quality: can’t explain
 Answer = large investors
o More convenient to hold treasury bills as a store of value
o Rather than holding cash because bills
 Denominated in larger amounts can be stored electronically
 some investors were willing to hold them, despite their negative rates:
 Recall: i = F – P /P
↗ D of T-bills in secondary market  ↗ P
↗ P  ↘ (F – P)  i = F – P / P very low: i  0 (i slightly below 0)
The convenience of t-bills  their interest rates can go lower than 0

Negative interest rates today (e.g. Key Interest Rates of ECB)

 negative interest rates:
o deposits incur a charge for storage at a bank rather than receiving
interest income
 instead of receiving money on deposits (interest):
o depositors must pay to keep their money with the bank
 this environment is intended:
o to incentivize banks to lend money more freely

How does a negative interest rate work?

 i < 0 often the result of:
o effort to boost economic growth through financial means
 i < 0: deflation
o people and businesses hold too much money instead of spending
 results in:
o sharp decline in demand
o decrease in prices

Real world example of i < 0

 Recent ears: central bank
 Not clear if:
o This policy worked in these countries in the way it was intended

2. The distinction between interest rates (i) and rate or returns (R).
2.1 The rate of return
 For any security, R=
o Payments to the owner (coupon)
o + the change in its value (Pt+1 – Pt)
o Expressed as a fraction of its purchase price
 What is R for a $1000 – FV coupon bond with:
o A coupon rate of 10%
o That is bought for $1000
o Held for one year
o sold for $12000
CM 5 – 18/03/2025
2nd: Initial current yields
3rd: Purchase price of the bond
4th: expected value of

2.1 The rate of return

A rise in interest

3.1.1 Wealth
The economic growth (business cycle expansion)
Increase in wealth  increase in the quantity of bonds demanded at each bond
price (or interest rate)
Corresponds to a shift in the demand curve to the right
Only wealth increases:
 Other variables remain unchanges
  Bond prices remain the same
At point B: initial demand curve for bonds
 Increase in wealth  increase in quantity of bonds demanded at the same
price
 Point B’ in Bd2

Lower expected interest rates in the future:

 Increase the demand for long-term bonds and shift the demand
curve to the right

Changes in expected returns on assets

Can also shift the demand curve fo bonds

If people:
 More optimistic about the stock market
 They expect higher stock prices in the future
 Both expected capital gains and expected return on stocks would rise

With: expected return on bonds constant:

 Increase in expected capital gains and returns on stocks
 Decrease expected return on bonds relative to stocks
 Decrease in demand for bonds
 The demand curve for bonds shifts to the left

A change in expected inflation:

 Alter expected returns on physical assets (real assets) such as cars and
houses
 Which affect the demand for bonds
o Higher prices on cars and house sin the future
o Higher normal capital gains

The resulting rise in the expected returns today on these real asssets will lead to a
fall in the expected return on bonds relative to the expected return on real assets
today and thus a

3.2 Shifts in the Supply of bonds

Factors:
 Expected profitability of investment opportunities
 Expected inflation
 Government budget

3.2.3 Government budget

The activities of the govt can influence the supply of the bonds
The US Treasury issues bonds to finance govt deficits (gap between govt
expenditures and revenues)
When these deficits are large:
 Treasury sells more bonds
 Quantity of bonds supplied at each bond price increases
Higher govt deficits increase the supply of bonds and shifts the supply curve to the
right
Govt surplueses (late 1900s) decrease the supply of bonds and shift the suipply
curve to the left

US date and state local govts:

 also issue bonds to finance their expenditures
 can also affect the supply of bonds
moreover: conduct of monetary policy involves:
 purchase and sale of bonds
 which influences the supply of bonds