Chapter Five
Money Markets
OUTLINE:
1-5 Definition Of Money Market.
2-5 Yields On Money Market Securities.
3-5 Money Markets Securities.
4-5 Money Market Participants.
5-5 International Aspects Of Money Markets.
1-2
1-5: Money Markets
Why Do We Need Money Markets?
 The immediate cash needs of individuals,
corporations, and governments.


E.g. Corporation’s sales do not necessarily
happen with the same pattern as their
expenses such as wages.
Money markets involve debt instruments or
securities with original maturities of one
year or less.
1-3
These Short-term Debt Instruments:

Issued by economic agents that require
short-term funds.
 e.g. inventory, wages, … etc.

Purchased by economic agents that have
excess short-term funds.
 Keep only a minimum excess cash balance to
meet the day-to-day needs. Why?
 To avoid the opportunity cost.
1-4

Opportunity Cost:
The forgone interest cost from the holding of
cash balances when they are received.
Once Issued:
Money market instruments trade in active
secondary markets. Why?
 To provide market participants with shortterm liquidity that they need.

1-5
Money Market Securities Features:
1. Generally sold in large denominations.



In units of 1$ million to 10$ million.
Difficult for individual investors to be
involved in the initial sale of a money
market security for the transaction's costs.
individual
invest
through
financial
institutions such as mutual funds.
1-6
2. Money market instruments have low
default risk.
 Default risk: the risk of latte or nonpayment of
principal and/or interest.
 Money market instruments issued only by
high-quality borrowers with little risk of default.
3. Money market instruments have an
original maturity of one year or less.
 short-term maturity  lower interest rate
risk, but lower rate of return.
1-7
2-5: Money Market Yields
What is a Money Market Yield?
The interest rate earned by investing in
securities with high liquidity and maturities of
one year or less than one year.


Notes:
Some securities interest rates are based on a 360-day
year, while others are based on a 365-day year.
Adjusting interest rates by using:
 Bond Equivalent Yields (ibe).
 Effective Annual Return (EAR)
1-8

Bond Equivalent Yields (ibe):
It is the quoted nominal, or stated, yield earned on
a security.
 It is the rate used to calculate the present value of
an investment.

𝑖𝑏𝑒 =
(𝑃𝑓 − 𝑃0 )
𝑃0
×
365
𝑛
Where:
Pf = face value.
P0 = purchase price of the security.
n = number of days until maturity.
1-9

Effective Annual Return (EAR):
It is a quoted nominal or stated rate earned on an
investment over a one-year period.
 It does not consider the effects of compounding of
interest during a less than one-year investment
horizon.
 If interest is paid or compounded more than once
per year, the true annual rate earned is the EAR
on an investment.

1-10

The bond equivalent yield (ibe) on money market
securities with a maturity of less than one year
can be converted to an effective annual interest
return (EAR) using the following equation:
𝑖𝑏𝑒
𝐸𝐴𝑅 = 1 +
365 𝑛
365
𝑛
−1
1-11
EX(5-1): calculation of EAR
Suppose you can invest in a money market
security that matures in 75 days and offers a 3
percent nominal annual interest rate. What is
the effective annual interest return on this
security?
𝑖𝑏𝑒
𝐸𝐴𝑅 = 1 +
365 𝑛
365
0.03
𝐸𝐴𝑅 = 1 +
365 75
𝐸𝐴𝑅 = 3.036%
𝑛
−1
365
75
−1
1-12

Money Market Securities Use Special Rate
Quoting:
1. Discount yields (id).
2. Single-Payment yields (isp).
1-13
1. Discount yields (id):
The interest rate is quoted on an annual basis
assuming a 360-day year as a percent of face value.
- e.g. treasury bills, commercial paper, and banker’s
acceptances rates.
- The return on these securities results from the
purchase of the security at a discount from its face
value (P0) and the receipt of face value (Pf) at maturity.
(𝑃𝑓 − 𝑃0 )
360
𝑖𝑑 =
×
𝑃𝑓
𝑛
Where:
Pf = the face value of the security
P0 = the purchase price of the security
n = the number of days until maturity
1-14

Convert discount yields (id) into bond equivalent
yields (ibe):
𝑃𝑓
365
𝑖𝑏𝑒 = 𝑖𝑑 ×
×
𝑃0
360

Convert bond equivalent yields into effective
annual returns (EAR)
𝑖𝑏𝑒
𝐸𝐴𝑅 = 1 +
365 𝑛
365
𝑛
−1
1-15
EX(5-2): Comparison of discount yield, bond equivalent
yield, and EAR
Suppose you can purchase a $1 million Treasury bill that
is currently selling on a discount basis at 98.50% of its
face value. The T-bill is 140 days from maturity.
Find Discount yield, Bond equivalent yield, and EAR:
 i d=
$1,000,000 −$985,000
$1,000,000
×
360
140
= 3.857%
$1,000,000 −$985,000
365
 ibe=
×
= 3.970%
$985,000
140
𝑃𝑓
365
Or 𝑖𝑏𝑒 = 𝑖𝑑 ×
×
= 3.970%
𝑃0
360
0.03970 365 140
 EAR= 1 +
− 1 = 4.019%
365 140
1-16
2. Single-Payment yields (isp):
The interest rate is quoted on an annual basis
assuming a 360-day year as a percent of purchase.
- e.g. federal funds, repurchase agreements, and
negotiable certificates of deposit.
- The interest payment only once paid at maturity.
- The return on these securities results from receiving a
terminal payment of interest plus the face value.
𝑖𝑠𝑝
(𝑃𝑓 − 𝑃0 )
360
=
×
𝑃0
𝑛
Where:
Pf = the face value of the security
P0 = the purchase price of the security
n = the number of days until maturity
1-17

Convert a single-payment yield (isp) to a bond
equivalent yield (ibe):
ibe = isp (365/360)

Convert a bond equivalent yield (ibe) to an EAR:
𝑖𝑏𝑒
𝐸𝐴𝑅 = 1 +
365 𝑛
365
𝑛
−1
1-18
EX(5-3): Comparison of single-payment
yield, bond equivalent yield, and EAR
Suppose you can purchase a $1 million negotiable
CD that is currently 105 days from maturity. The CD
has a quoted annual interest rate of 4.16 percent for
a 360-day year.
What is the bond equivalent yield?
ibe = 4.16% (365/360) = 4.218%
What is the EAR on CD?
𝐸𝐴𝑅 = 1 +
0.04218
365 105
365
105
− 1 = 4.282%
1-19
3-5: Money Market Instruments


Money market securities are issued by
corporations and government units to obtain
short-term fund.
Money market securities are:






Treasury bills (T-bills)
Federal funds (fed funds)
Repurchase agreements (repos or RP)
Commercial paper (CP)
Negotiable certificates of deposit (CD)
Banker’s acceptances (BA)
1-20
1- Treasury Bills (T-Bills)
Treasury bills are short-term obligations of the
government issued to cover current government
budget shortfalls (deficits) and to refinance maturing
government debt.

T-bills are sold through an auction process.

T-bills maturities are 4, 13, 26, and 52 weeks.

T-bills are issued in denomination of multiples of
$100.
1-21

Existing T-bills can be bought and sold in an
active secondary market.

T-bills are default risk free “risk-free asset”.
Why?
T-bills are backed by government.

T-bills have little interest rate risk and little
liquidity risk. Why?
For the short-term maturity and the active
secondary market.
1-22
T-Bill Auctions (New Issue):
The formal process by which the government
sells new issues of Treasury bills.
 Bids are submitted by government securities
dealers, financial and nonfinancial corporations,
and individuals.
 Bids can be competitive or non-competitive.
 Successful bidders (competitive and noncompetitive) are awarded securities at the same
price which is the lowest price of the competitive
bids accepted.

1-23
Competitive Bids:
- Bidders specify the amount of par value of bills
desired (minimum of $100) and the discount yield,
rather than the price.
- Bids are ranked from the lowest discount yield
(highest price), to the highest yield (lowest price).
- The cut-off yield or the stop-out rate is the
highest accepted discount yield.
- All bids with yields above the stop-out yields are
rejected.
1-24
Noncompetitive Bidders:
- Non-competitive bids are limited to $5 million.
- Bidders specify only the desired amount of the face
value of the bills.
- Bidders agree to accept whatever interest rate is
decided at the auction.
- Bidders will not know exactly what interest rate they
will receive until the auction closes.
- Bidders are guaranteed that their bid will be accepted.
- Non-competitive bids allow small investors to
participate in the T-bill auction market without incurring
large risks.
1-25
Treasury Bill Yields:
- T-Bills are sold on a discount basis.
- T-Bills are issued at a discount from their face
value.
- T-Bills’ returns come from the difference
between the purchase price and the face value
received at maturities.

𝑖𝑇𝑏𝑖𝑙𝑙 , 𝑑
𝑝𝑓 − 𝑝0
360
=
×
𝑝𝑓
𝑛
1-26
Bid: discount yield
based on the current
selling price.
Asked: discount yield
based on the current
purchase price.
Chg.: the change in
the asked
(discount)yield from
the previous day’s
closing yield.
Asked yield: the
asked discount yield
converted to a bond
equivalent yield.
1-27

T-Bill Price:
The ask price (P0) is:
 P0 = 𝑃𝑓 − 𝑖 𝑇𝑏𝑖𝑙𝑙,𝑑 ×
𝑛
360
× 𝑃𝑓
 P0 = 𝑃𝑓 [ 1 + 𝑖 𝑇𝑏𝑖𝑙𝑙,𝑏𝑒 ×
𝑛
365
]
1-30
2- Federal Funds (fed funds)
Short-term loans between financial institutions
usually for a period of one day (overnight).


Banks with excess funds (surplus of reserves at
Federal Bank) will lend fed funds.
Banks with deficient funds (shortage of reserves
at Federal Bank) will borrow fed funds.
 Federal Funds Rate:
The interest rate for borrowing fed funds.
1-32
1-33

The interbank lending system takes a form
of unsecured loans , how?
The borrowing bank does not have to pledge
collateral for the funds (in millions) it receives.
Fed funds have no secondary market.

Fed Fund Yield:

Fed funds are single-payment loans paying
interest only once at maturity.
(𝑃𝑓 − 𝑃0 )
360
𝑖𝑠𝑝 =
×
𝑃0
𝑛
1-34
3- Repurchase Agreement (repo or RP)
An agreement involving the sale of a
securities by one party to another with a
promise to repurchase the securities at a
specified price and on a specified date in the
future.

RP is a collateralized fed funds loan:
 RP are low credit risk investments and have
lower interest rates than uncollateralized.
1-36
1-37




Repo with one-day maturity are called
overnight repos.
Repo with long maturity are called term
repos.
Repo maturity from 1 to 14 days in short
terms, and from 1 to 3 months in longerterm.
Repo involve denominations of $25 million
if the repo maturity less than one week,
and $10 million for longer-term repos.
1-38

A reverse RP is the lender’s position in the repo
transaction, an agreement involving the
purchase (buying) of securities by one party
from another with the promise to sell them back
at a given date in the future.

Repurchase Agreement Yield:
Fed funds are single-payment loans paying
interest only once at maturity.
𝑖𝑠𝑝
(𝑃𝑓 − 𝑃0 )
360
=
×
𝑃0
𝑛
1-39
4- Commercial Paper (CP)
An unsecured short-term promissory note
issued by a corporation to raise short-term
cash, often to finance working capital
requirements.
CP is one of the largest of the money market
instruments, why?
Companies with strong credit ratings can borrow
money at a lower interest rate by issuing CP than
by directly borrowing from banks.

1-41

CP is sold in denominations of $100,000,
$250,000, $500,000, and $1 million.

CP maturities ranged between 1 and 270 days.

CP can be sold:
Directly by the issuers to the buyer (mutual
fund).
 Indirectly by brokers and dealers in the CP
market. (more expensive to the issuer)

1-42

CP is generally held by investors from the time
of issue until maturity:
 There is no active secondary market for
commercial paper.

Commercial Paper Yields:
Yields are quoted on a discount basis.
𝑝𝑓 − 𝑝0
360
𝑖𝑑 =
×
𝑝𝑓
𝑛
1-43
5- Negotiable Certificates of Deposit (CD)
A bank-issued time deposit that specifies an
interest rate and maturity date and is
negotiable (salable) in the secondary market.


CDs are bearer instruments:
 whoever holds the CD when it matures
receives the principal and interest.
CDs can be traded in secondary markets; the
original buyer is not necessary the owner at
maturity.
1-45




CDs have denominations range from $100,000
to $10 million.
CDs are purchased by mutual funds for the
large denomination.
CDs maturities range from two weeks to one
year.
Negotiable CD Yields:
CDs are single-payment securities.
𝑖𝑠𝑝
(𝑃𝑓 − 𝑃0 )
360
=
×
𝑃0
𝑛
1-46
EX(5–9) Calculation of the Secondary Market
Yield on a Negotiable CD
A bank has issued a six-month, $1 million negotiable CD with a 0.72%
quoted annual interest rate.
What is the bond equivalent yield on the CD?
ibe = isp (365/360) = 0.0072 (365/360)= 0.73% (annual)
at maturity (in 6 months), how much will the CD holder
receive?
FV6months = PV (1 + i be,6months)
FV6months = $1m (1 + 0.0073/2) =$1,003,650 (for $1m deposited today)
What is the EAR on the CD?
𝐸𝐴𝑅 = 1 +
0.0073 2
2
− 1 =0.7313%
1-47
Immediately after the CD is issued, the secondary
market price on the $1 million CD falls to $999,651.
What will happen to the secondary market bond
equivalent yield?
It will increase:
N:1, PV: -999,651, FV:1,003,650, PMT:0, CPT I/Y:0.40%
 ibe = 0.8001% (annual)
OR:
FV6months = PV (1 + i be,6months)
 $1,003,650= $999,651 (1 + i be,6months)
 i be,6months = 0.40%
 ibe = 0.8001% (annual)
1-48
What will happen to the secondary market singlepayment yield?
It will increase:
ibe = isp (365/360)
0.008001= isp (365/360)  isp = 0.7891%
What will happen to the secondary market EAR?
It will increase:
𝐸𝐴𝑅 = 1 +
0.008001 2
2
− 1 = 0.8017%
1-49
6- Banker’s Acceptances
A time draft payable to a seller of goods,
with payment guaranteed by a bank.


BAs used in international trade transactions to
finance trade in goods that have yet to be
shipped from a foreign exporter (seller) to a
domestic importer (buyer).
BAs are bearer instruments; they can be traded
in secondary markets.
1-51



BAs maturities range from 30 to 270 days.
BAs denominations in the secondary market are
from $100,000 to $500,000.
BAs have low default risk with low interest rate.
Why?


Backed by commercial bank guarantees.
Banker’s Acceptances Yields:
BAs are sold on a discounted basis:
(𝑃𝑓 − 𝑃0 )
360
𝑖𝑑 =
×
𝑃𝑓
𝑛
1-52
4-5: Money Market Participants
1-53

The U.S. Treasury:
- T-bills are the most actively traded of the money
market securities.

The Federal Reserve:
- The Federal Reserve is the most important participant
in the money markets.
- Fed Reserve holds T-bills to increase the money
supply.
- Fed Reserve sell T-bills to decrease the money
supply.
- Fed Reserve uses Repo to smooth interest rates and
the money supply.
1-54

Commercial Banks:
- Banks participate as issuers and/or investors of
almost all money market instruments.

Money Market Mutual Funds:
- Mutual funds purchase large amounts of money
market securities and sell shares in these pools based
on the value of their underlying securities, allowing small
investors to invest in money market instruments.

Brokers And Dealers:
- Brokers’ and dealers’ services are important to the
smooth functioning of money markets.
1-55

Corporations:
- They raise large amounts of funds in the money
markets, primarily in the form of commercial paper.
- They invest their excess cash funds in money market
securities.

Other Financial Institutions:
- Because their liability payments are unpredictable, they
must maintain large balances of liquid assets by
investing in highly liquid money market securities.

Individuals:
Individual investors participate in the money markets
through investments in money market mutual funds.
1-56
5-5: International Money Markets

Money markets across the world have been
growing in size and importance.

International financial contracts call for payment in
U.S. dollars, this created Eurodollar deposits.

Eurodollar deposits:
Dollar-denominated deposits held in U.S. bank
branches overseas and in other foreign banks.
1-57

Eurodollar market:
The market in which Eurodollars trade.

London Interbank Offered Rate (LIBOR):
The rate offered for sale on Eurodollar funds.
- The fed funds rate is generally lower than the
LIBOR.
1-58
The end of chapter 5
1-59
1: a $1 million T-bill, current selling price 97.375% of
the face value, 65 days from maturity:

Discount yield:
id =

$1,000,000 −$973,750
$1,000,000
= 14.538%
Bond equivalent yield:
ibe = =

×
360
65
$1,000,000 −$973,750
$973,750
×
365
65
= 15.138%
EAR:
EAR = 1 +
0.15138
365 65
365 65
− 1 = 16.111%
1-60
2: a $5 million commercial paper, current selling
price 98.625% of the face value, 136 days from
maturity:

Discount yield:
id =

$5,000,000 −$4,931,250
$5,000,000
= 3.640%
Bond equivalent yield:
ibe = =

×
360
136
$5,000,000 −$4,931,250
$4,931,250
×
365
136
= 3.742%
EAR:
EAR = 1 +
0.03742
365 136
365 136
− 1 = 3.786%
1-61
3: a negotiable CD, 115 days from maturity, with
a quoted nominal yield of 6.56%:

Bond equivalent yield:
ibe = = 6.56% ×

365
( )
360
= 6.651%
EAR:
EAR = 1 +
0.06651
365 115
365 115
− 1 = 6.804%
1-62
4: fed funds, 3 days from maturity, with a quoted
yield of 0.25%:

Bond equivalent yield:
ibe = = 0.25% ×

365
( )
360
= 0.25347% = 0.2535%
EAR:
EAR = 1 +
0.002535 365 3
365 3
− 1= 0.25381%= 0.2538%
1-63
5: a $10,000 T-Bill , 68 days from maturity, the
current price of the T-Bill is $9,875:

Discount yield on this T-Bill is:
id =
$10,000 −$9,875
$10,000
×
360
68
= 6.617% = 6.62%
1-64
14: Repurchase agreement: buy Treasury securities
from a correspondent bank at price of $24,950,000
with the promise to buy them back at a price of
$25,000,000
A- The yield on this repo if it has a 7-day maturity:
isp=
$25,000,000 −$24,950,000
$24,950,000
×
360
7
= 10.306%
B- The yield on this repo if it has a 21-day maturity:
isp=
$25,000,000 −$24,950,000
$24,950,000
×
360
21
= 3.435%
1-65
18: a six-months, $2 million negotiable CD, with a 0.52%
quoted annual interest rate.
A- The bond equivalent yield, and the EAR on the CD:
ibe = 0.52% (365/360) = 0.527%
EAR = 1 +
0.00527
2
2
− 1 = 0.5279% =0.528%
B- Negotiable CD holder receives at maturity:
FV6months = $2,000,000 (1 + 0.00528
) = $2,005,280
2
C- After CD issued, the secondary market price on the $2
million CD falls to $1,998,750. (Face value 2 million).
$2,005,280
$1,998,750 = [1+(𝐸𝐴𝑅/2)]
 EAR = 0.65340%
0.65340%= 1 +
𝑖𝑏𝑒
2
2
− 1  ibe= 0.65234%
New quoted yield: isp = 0.65234% (360/365) = 0.64340%
1-66