MONEY AND BANKING
ECONOMICS AND BUSINESS ECONOMICS YEAR 2
Week 1
A security gives the owner of it the right to demand the future earnings of assets from the one that
has issued it. A common stock is a security that represent ownership in a corporation. Another
security is a bond, which is a proof of debt with which the owner takes on the obligatoin to make
payments during an established period. The interest rate, price that needs to be paid for the
borrowing of money, is determined at the bond market. In the economy there are different interest
rates for different loans or bonds.
Some type of bonds can be viewed in the graph below. The corporate Baa bonds, which shows the
interest rate of a relatively low-risk bond. A Treasury bill (T-bill) which is a short-term U.S.
government debt obligation backed by the treasury department with a maturity of one year or less.
Normally applies: the longer the maturity date, the higher the interest rate that the T-Bill will pay to
the investor. This is the reason that normally the blue line is underneath the red line.
It is important to study several different sectors in order to understand the economy:
- Financial markets, markets that divert money from persons/institutions/governments that
have too much of it to persons/institutions/governments that have shortages. A well-
functioning financial market is therefore a prerequisite for economic growth. Examples of
financial markets are the bond- and share-markets.
- Financial intermediaries are institutions that borrow money from people (that have savings)
and loan to other players. Banks are the biggest financial intermediaries, so they play a very
big role in the economy.
- Fiscal and monetary policy, the fiscal policy concerns the decisions about the expenses of
the government and the tax measures. A budget deficit arises when the expenses of the
government exceed the return of the taxes. The government needs to remedy this deficit by
, borrowing money which leads to a bigger debt burden. The monetary policy is a set of tools
used by a nation’s central bank to control the overall money supply and promote economic
growth and employ strategies such as revising interest rates and changing bank reserve
requirements. The money supply plays an important role within the conjuncture cycles, the
upgoing and down going movement of the cumulative production (aggregate output)
produced within the economy.
The Credit market refers to the market through which companies and governments issue debt to
investors. There are four main types of Credit market Instruments, which make credit transactions
possible:
- Simple loan, the lender provides the borrower with an amount of funds (principal) that must
be repaid at the maturity date, along with an additional interest payment. The principal of a
CF
loan is the initial size of a loan. To calculate the present value use: PV = . With “i”
( 1+ i )n
being the time value of money.
- Fixed-payment loan, must be repaid by making the same payment (consisting of a part of the
principal and interest) every period for the entire duration of the loan. The loan value (=LV)
FP FP FP
can be calculated by using the fixed payments (=FP). LV = + + …+
1+i ( 1+i )2 ( 1+i )n
- Coupon bond, pays the owner of the bond a fixed payment (coupon payment) every year
until the maturity date, when a specified final amount (face value) is repaid. To calculate the
price of the bond we need the fixed coupon payment (=C=CF), the face value of the bond
(=F), time to maturity n and the Yield to Maturity ( i c).
C C C F
P= + +…+ + n . A special version of the coupon bond is the consol
1+i c ( 1+i c ) 2 n
( 1+ic ) ( 1+ic )
coupon bond or perpetual bond (prep). This is a bond with no maturity that thus does not
repay the principal but that pays fixed coupon payments forever. The price of the consol can
be calculated with the yearly coupon payment (=C) and the yield to maturity of the consol ( i c
C
). P= .
ic
- Discount (zero-coupon) bond, a bond which is bought at a price below the face value
(discount) and where the face value is repaid at maturity. When buying at a discount it
implies that the yield is positive. Some practitioners, discuss discount bonds as coupon bonds
that are traded below par. But we follow the definition of Mishkin: the notion of discount
bond thus is to be treated as a synonym for a zero-coupon bond, that is for a bond that has
F
no coupon payments. For a one-year discount bond: P= .
1+i c
The Yield to Maturity is the interest rate that equates today’s value with today’s present value of all
future cash flows up to the maturity date. Three key facts of the relationship between price and Yield
to Maturity:
When the bond is priced at its face value (“at par), the yield to maturity equals the coupon
rate.
For a loan, the interest rate is equal to the yield to maturity.
Prices and yields to maturity are negatively related. The higher the price of the bond (with
the same face value) the lower the Yield to Maturity.
, The yield to maturity is larger than the coupon rate when the bond price is below the par
value.
The interest rate is the annual rate that is paid on a bond, while yield to maturity is the return an
investor would earn if they held the bond until it reached maturity. But if you have a Zero-Coupon
Bond, the interest rate and yield to maturity are the same (denoted as i). The expected return of
e F−P
such a bond is then: R =i= , with F being the face value of the discount bond and P being the
P
initial purchase price of the discount bond.
Distinction between Interest Rate and (Rate of) Return. The (expected) Rate of return at time t on a
C + Pe t+1 −P t
e e
coupon bond that will be held from time t until time t+1: RET =R = =i c + g , where
Pt
e
C P −Pt
i c = =current yield and ge = t+1 =rate of expected capital gain.
Pt Pt
Relationship between interest rate and rate of return. Bonds have an inverse relationship to interest
rates. When the cost of borrowing money rises (interest rates rise), bond prices usually fall which
means that the rate of expected capital gain decreases which leads to the (expected) rate of return
decreasing.
The interest rate risk is the potential that a change in overall interest rates will reduce the value of a
bond or other fixed-rate investment. That is why long-term bonds are more volatile than those of
short-term bonds. But if you hold the bond until maturity, so holding period equals time to maturity,
then there is no interest-rate risk.
Real interest rate is the nominal interest rate but then adjusted for the expected inflation rate. So
r (sometimes alsoi r )=i−π e (fisher equation: i=r + π e ). The real interest rate reflects the true cost
of borrowing as well as the true return to lending. When the real interest rate is lower, the incentives
to borrow are larger -> higher inflation.
The fisher equation (i=r + π e ) is an approximation although it typically is presented as an equality.
This is an acceptable practice as long as one examines an environment in which both the real interest
rate and the expected inflation rate are small. We get this equation by expressing, in purchasing
power terms, the expected real outcome of investing “1” now for one year in two ways: 1+r and
1+i
. Because we can express it in two ways they are equal to each other, thus:
1+ π e
1+i NIC
1+r = =RIC= .When we elaborate this equation we get: 1+i=1+r + π e +r∗π e .
1+ π
e
PIC
Because r ∧π e are small (normally ± 0.02) r∗π e ≈ 0. So, then we get left with the Fisher equation:
i ≈r + π e.
There are two kinds of real interest rates:
The ex ante real interest rates are predictions based on the expected inflation rate and thus
give an indication of what the real cost (benefit) of borrowing (lending) is expected to be
over -for instance- the next year. This method is used by the calculations above.
ECONOMICS AND BUSINESS ECONOMICS YEAR 2
Week 1
A security gives the owner of it the right to demand the future earnings of assets from the one that
has issued it. A common stock is a security that represent ownership in a corporation. Another
security is a bond, which is a proof of debt with which the owner takes on the obligatoin to make
payments during an established period. The interest rate, price that needs to be paid for the
borrowing of money, is determined at the bond market. In the economy there are different interest
rates for different loans or bonds.
Some type of bonds can be viewed in the graph below. The corporate Baa bonds, which shows the
interest rate of a relatively low-risk bond. A Treasury bill (T-bill) which is a short-term U.S.
government debt obligation backed by the treasury department with a maturity of one year or less.
Normally applies: the longer the maturity date, the higher the interest rate that the T-Bill will pay to
the investor. This is the reason that normally the blue line is underneath the red line.
It is important to study several different sectors in order to understand the economy:
- Financial markets, markets that divert money from persons/institutions/governments that
have too much of it to persons/institutions/governments that have shortages. A well-
functioning financial market is therefore a prerequisite for economic growth. Examples of
financial markets are the bond- and share-markets.
- Financial intermediaries are institutions that borrow money from people (that have savings)
and loan to other players. Banks are the biggest financial intermediaries, so they play a very
big role in the economy.
- Fiscal and monetary policy, the fiscal policy concerns the decisions about the expenses of
the government and the tax measures. A budget deficit arises when the expenses of the
government exceed the return of the taxes. The government needs to remedy this deficit by
, borrowing money which leads to a bigger debt burden. The monetary policy is a set of tools
used by a nation’s central bank to control the overall money supply and promote economic
growth and employ strategies such as revising interest rates and changing bank reserve
requirements. The money supply plays an important role within the conjuncture cycles, the
upgoing and down going movement of the cumulative production (aggregate output)
produced within the economy.
The Credit market refers to the market through which companies and governments issue debt to
investors. There are four main types of Credit market Instruments, which make credit transactions
possible:
- Simple loan, the lender provides the borrower with an amount of funds (principal) that must
be repaid at the maturity date, along with an additional interest payment. The principal of a
CF
loan is the initial size of a loan. To calculate the present value use: PV = . With “i”
( 1+ i )n
being the time value of money.
- Fixed-payment loan, must be repaid by making the same payment (consisting of a part of the
principal and interest) every period for the entire duration of the loan. The loan value (=LV)
FP FP FP
can be calculated by using the fixed payments (=FP). LV = + + …+
1+i ( 1+i )2 ( 1+i )n
- Coupon bond, pays the owner of the bond a fixed payment (coupon payment) every year
until the maturity date, when a specified final amount (face value) is repaid. To calculate the
price of the bond we need the fixed coupon payment (=C=CF), the face value of the bond
(=F), time to maturity n and the Yield to Maturity ( i c).
C C C F
P= + +…+ + n . A special version of the coupon bond is the consol
1+i c ( 1+i c ) 2 n
( 1+ic ) ( 1+ic )
coupon bond or perpetual bond (prep). This is a bond with no maturity that thus does not
repay the principal but that pays fixed coupon payments forever. The price of the consol can
be calculated with the yearly coupon payment (=C) and the yield to maturity of the consol ( i c
C
). P= .
ic
- Discount (zero-coupon) bond, a bond which is bought at a price below the face value
(discount) and where the face value is repaid at maturity. When buying at a discount it
implies that the yield is positive. Some practitioners, discuss discount bonds as coupon bonds
that are traded below par. But we follow the definition of Mishkin: the notion of discount
bond thus is to be treated as a synonym for a zero-coupon bond, that is for a bond that has
F
no coupon payments. For a one-year discount bond: P= .
1+i c
The Yield to Maturity is the interest rate that equates today’s value with today’s present value of all
future cash flows up to the maturity date. Three key facts of the relationship between price and Yield
to Maturity:
When the bond is priced at its face value (“at par), the yield to maturity equals the coupon
rate.
For a loan, the interest rate is equal to the yield to maturity.
Prices and yields to maturity are negatively related. The higher the price of the bond (with
the same face value) the lower the Yield to Maturity.
, The yield to maturity is larger than the coupon rate when the bond price is below the par
value.
The interest rate is the annual rate that is paid on a bond, while yield to maturity is the return an
investor would earn if they held the bond until it reached maturity. But if you have a Zero-Coupon
Bond, the interest rate and yield to maturity are the same (denoted as i). The expected return of
e F−P
such a bond is then: R =i= , with F being the face value of the discount bond and P being the
P
initial purchase price of the discount bond.
Distinction between Interest Rate and (Rate of) Return. The (expected) Rate of return at time t on a
C + Pe t+1 −P t
e e
coupon bond that will be held from time t until time t+1: RET =R = =i c + g , where
Pt
e
C P −Pt
i c = =current yield and ge = t+1 =rate of expected capital gain.
Pt Pt
Relationship between interest rate and rate of return. Bonds have an inverse relationship to interest
rates. When the cost of borrowing money rises (interest rates rise), bond prices usually fall which
means that the rate of expected capital gain decreases which leads to the (expected) rate of return
decreasing.
The interest rate risk is the potential that a change in overall interest rates will reduce the value of a
bond or other fixed-rate investment. That is why long-term bonds are more volatile than those of
short-term bonds. But if you hold the bond until maturity, so holding period equals time to maturity,
then there is no interest-rate risk.
Real interest rate is the nominal interest rate but then adjusted for the expected inflation rate. So
r (sometimes alsoi r )=i−π e (fisher equation: i=r + π e ). The real interest rate reflects the true cost
of borrowing as well as the true return to lending. When the real interest rate is lower, the incentives
to borrow are larger -> higher inflation.
The fisher equation (i=r + π e ) is an approximation although it typically is presented as an equality.
This is an acceptable practice as long as one examines an environment in which both the real interest
rate and the expected inflation rate are small. We get this equation by expressing, in purchasing
power terms, the expected real outcome of investing “1” now for one year in two ways: 1+r and
1+i
. Because we can express it in two ways they are equal to each other, thus:
1+ π e
1+i NIC
1+r = =RIC= .When we elaborate this equation we get: 1+i=1+r + π e +r∗π e .
1+ π
e
PIC
Because r ∧π e are small (normally ± 0.02) r∗π e ≈ 0. So, then we get left with the Fisher equation:
i ≈r + π e.
There are two kinds of real interest rates:
The ex ante real interest rates are predictions based on the expected inflation rate and thus
give an indication of what the real cost (benefit) of borrowing (lending) is expected to be
over -for instance- the next year. This method is used by the calculations above.
