Lecture 1
Money and Banking
Dirk Veestraeten
References to figures and tables
The references to the figures and tables that are used in this lecture can be found at the
end of this presentation.
Topics
• Course information
• Understanding interest rates
• Behaviour of interest rates
Course information
Mandatory readings:
• Mishkin, F.S. (2022). The Economics of Money, Banking & Financial Markets. 13th
edition, ISBN: 978-1-292-40948-1, 718 pages (ca. €70);
• Veestraeten (2019). “Macroprudential regulation: Guiding principles and instruments”,
mimeo. Available on Canvas.
Tutorials:
18 groups (check Canvas for quite some rescheduling).
Canvas:
Consult it regularly for announcements, solutions to the tutorial exercises,
important messages related to the exam, etc.
Course information
Exams:
•
representative (midterm and final) exam questions can be found on Canvas.
•
exam materials: everything (book (including the appendices), all materials on Canvas, etc.).
•
mid-term exam of 1.5 hours, only multiple-choice questions, 30% of the final mark of the
course (result will be ignored in the resit exam).
•
final exam of 2 hours that counts for 70% of the final mark and that consists of multiplechoice questions and open questions. Note: the open questions at the final exam cover the
materials of the entire course, whereas the multiple-choice questions at the final exam only
cover the last three lecture week of the course.
•
In order to pass the course in the first exam round, the grade for the final exam should at least
be 5.5 (no rounding) and the weighted average of the marks for the mid-term exam and the
final exam should at least be 5.5 (no rounding).
Course information
•
Resit exam: 2 hours with multiple-choice questions and open questions that both
cover the materials of the entire course. The result for the mid-term exam is ignored.
In order to pass the course in the resit round, the grade for the resit exam should at
least be 5.5 (no rounding). There are no conditions as to participation. Note: the resit
exam is scheduled to take place in the first week of January which may be quite
unattractive for some students (especially probably the exchange students).
•
All exam questions are formulated in English and are to be answered in English.
Language dictionaries are not allowed for at the exams.
•
Note that only so-called UvA-pocket calculators are allowed during the midterm
exam, the final exam and the resit exam. This is a strict rule of the faculty and
the lecturers have no say in this. Students can buy such UvA-pocket calculator at
Sefa (central hall of the E-building).
•
The faculty’s policy of using a guessing correction for the multiple-choice questions
will be applied (see the syllabus for the formula).
Course information
Important note on the lectures and tutorials:
•
Attendance at the lectures and tutorials is not compulsory.
•
However, past experience has illustrated convincingly that a high correlation exist
between attendance and the final mark for the course. That should not come as a
surprise as the exams obviously test knowledge that will be trained/discussed
intensively in the lectures and tutorials.
Course information
Week 1:
Understanding Interest Rates and their Behaviour
Week 2:
Risk and Term Structure of Interest Rates; Stock Market
Week 3:
Economics of Financial Structure; Economics of Banking
Week 4:
Midterm exam
Week 5:
Financial Crises and the Global Financial Crisis
Week 6:
Goals and Structure of Central Banks; Money Supply Process
Week 7:
Tools, Strategy and Tactics of Monetary Policy; Aspects of Micro- and
Macroprudential Regulation
Week 8:
Some representative exam questions; Final Exam
Interest rates on selected bonds (1950-2020)
Present Value (or Present Discounted Value)
PV = today’s present (discounted) value
CF = future cash flow (payment)
i = the interest rate
n = years to maturity
CF
PV =
(1 + 𝑖)n
The Yield to Maturity (YTM) is the interest rate that equates today’s value with
today’s present value of all future cash flows up to the maturity date (i.e., up to
the final date).
Credit Market Instruments
Four Main Types:
1.
Simple loan (e.g., some commercial loans, interbank loans)
2.
Fixed-payment loan (e.g., fixed-rate mortgage)
3.
Coupon bond (e.g., government and corporate bonds)
4.
Discount (zero-coupon) bond (e.g., Treasury bills)
Simple Loan
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.
PV = today’s (present) value of loan
CF
PV =
(1 + i ) n
CF = cash flow
n = number of years
110
E.g. 100 =
=> (1 + i )100 = 110
1
(1 + i )
110 − 100 10
i=
=
= 0.10 = 10%
100
100
Fixed-Payment Loan
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.
LV = loan value
FP
FP
FP
LV =
+
+ ... +
2
(1 + i ) (1 + i )
(1 + i ) n
FP = fixed payment
n = years until maturity
E.g., Fixed-Payment Loan (LV=1000, FP = 126, n = 25)
126
126
126
1000 =
+
+ ... +
 i = 12%
2
25
(1 + i ) (1 + i )
(1 + i )
Coupon bond
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.
F = face value of the bond
C
C
C
F
P=
+
+. . . +
+
2
n
1+i (1+i)
(1+i) (1+i) n
n = number of years until maturity
P = price of the bond
C = fixed coupon payment = cF
c = coupon rate
Coupon Bond: Examples
What is the yield to maturity of this coupon bond?
P = 1,000 ("at par") F = 1,000 c = 10% n = 10
100
100
100
100
1,000
1,000 =
+
+
+. . . +
+
2
3
10
(1+i ) (1+i )
(1+i)
(1+i)
(1+i)10
=> i = 10%
And...
P = 900 ("below par") F = 1,000 c = 10% n = 10
100
100
100
100
1,000
900 =
+
+
+. . . +
+
2
3
10
(1+i ) (1+i )
(1+i)
(1+i)
(1+i)10
=> i = 11.75%
Relationship Between Price and Yield to Maturity
Three Key Facts
1. When the bond is priced at its face value (“at par”), i.e., P = F, the yield to
maturity equals the coupon rate, i.e., i = c
2. Prices and yields to maturity are negatively related
3. The yield to maturity is larger (smaller) than the coupon rate when the bond
price is below (above) the par value, i.e., is below (above) par
Special case of the coupon bond: Consol or Perpetuity
Consol: a bond with no maturity date that thus does not repay the principal (there
is no principal) but that pays fixed coupon payments forever. The formula for the
price of the consol (Pc) is:
Pc = C / ic
Pc = price of the consol
C = yearly coupon payment
ic = yield to maturity of the consol or ic = C / Pc
For coupon bonds, the equation for the yield of a consol gives an easy-to-calculate
approximation of the yield to maturity of the coupon bond. This approximation is
the more accurate, the nearer the price is to par and the longer the maturity of the
coupon bond is.
Discount (Zero-Coupon) Bond
Discount (zero-coupon) bond: bought at a price below the face value (i.e., is bought at a
discount), and the face value is repaid at maturity (similar to the simple loan). Obviously,
the notion of “buying at a discount” implies that the yield is positive.
One-year discount bond:
F
F −P
P=
=> i =
(1 + i )
P
1,100 - 1,000
e.g . 10% =
1,000
Discount (Zero-Coupon) Bond
Important note:
•
Some practitioners, however, discuss discount bonds as coupon bonds that are traded
below par.
•
We follow the definition of Mishkin: the notion of discount bond thus is to be treated
as a synonym for a zero-coupon bond, i.e., for a bond that has no coupon payments.
Distinction Between Interest Rate and (Rate of) Return
(Expected) Rate of return at time t on a coupon bond that will be held
from time t until time t+1:
e
RETt = Rt =
C + Pet+1 – Pt
Pt
where: ic =
ge =
C
Pt
Pet+1 – Pt
Pt
= ic + g e
= current yield
= rate of expected capital gain
Relationship Between Interest Rate and (Rate Of) Return
Maturity and the Volatility of Bond Returns
Key Facts:
1. Only bonds whose return = the yield are the ones with maturity = the holding period
(and obviously vice versa).
2. Typically, if the maturity > the holding period and i ↑, then P↓ implying a capital loss
(this is the general rule, see the tutorial for a counterexample to this general rule).
3. The longer the time to maturity, the greater is the percentage price change of the bond
that is caused by an interest rate change.
4. The longer the time to maturity, the more the rate of return will change with a change
in the interest rate.
5. A bond with a high initial yield can still have a negative rate of return if i ↑.
Maturity and the Volatility of Bond Returns
Conclusions from this analysis:
1. Prices and returns are more sensitive/volatile to changes in interest rates for long(er)term bonds: these bonds have a higher “interest-rate risk”.
2. No interest-rate risk for any bond whose time to maturity equals the holding period.
Distinction between real and nominal interest rates
Real interest rate (r) = nominal interest rate (i) “adjusted” for the expected inflation
rate (e)
r = i – e
Fisher equation:
i = r + e
1. The real interest rate is at times also denoted as ir
2. The real interest rate reflects the true cost of borrowing as well as the true return to
lending.
3. When the real interest rate is lower, the incentives to borrow (lend) are larger
(smaller):
if i = 5% and e = 3% => r = 5% – 3% = 2%
if i = 8% and e = 10% => r = 8% – 10% = –2%
Distinction between real and nominal interest rates
Note: The previous slide defined the ex ante real interest rate. Often, also ex post real
interest rates are discussed.
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.
The ex post real interest rates use the past inflation rate to calculate what the real cost
(benefit) of borrowing (lending) has been over – for instance – the past year.
US Real and Nominal Interest Rates (Three-month
Treasury Bill, 1953-2020)
Behaviour of Interest Rates
•
Factors explaining fluctuations in nominal interest rates
•
Tool: supply and demand analysis
Demand for and Supply of Bonds
•
Demand for bonds: At lower prices (higher interest rates), ceteris
paribus, the quantity demanded of bonds is higher.
=> negative relationship between price and quantity
•
Supply of bonds: At lower prices (higher interest rates), ceteris paribus,
the quantity supplied of bonds is lower.
=> positive relationship between price and quantity
Derivation of the Demand for Bonds
(F – P)
R = i =
P
Zero-Coupon Bond
Point A:
F = face value of the discount bond = 1000
P = 950
P = initial purchase price of the discount bond
e
(1000 – 950)
i=
950
i = interest rate or yield to maturity
Re = expected return
= 0.053 = 5.3%
d
Let us assume that the quantity of bonds demanded B is at:
d
B = 100 billion
Derivation of the Demand of Bonds
Point B:
P = 900
(1000 – 900)
i=
= 0.111 = 11.1%
900
d
B = 200 billion
d
Point C: P = 850, i = 17.6% B = 300 billion
d
Point D: P = 800, i = 25.0% B = 400 billion
d
Point E: P = 750, i = 33.0% B = 500 billion
d
The demand curve is B and connects the points A, B, C, D, E, and it has the usual
downward slope.
Derivation of the Supply of Bonds
s
Point F: P = 750, i = 33.0%, B = 100 billion
s
Point G: P = 800, i = 25.0%, B = 200 billion
s
Point C: P = 850, i = 17.6%, B = 300 billion
s
Point H: P = 900, i = 11.1%, B = 400 billion
s
Point I: P = 950, i = 5.3%, B = 500 billion
s
The supply curve is B and connects the points F, G, C, H, I, and it has the usual
upward slope.
Demand and
Supply Analysis
of the Bond
Market
Market Equilibrium
d
s
1. Occurs when B = B , at
P* = 850, i* = 17.6%
2. When P = 950, i = 5.3%,
s
d
B > B (excess supply): P
 to P*, i to i*
3. When P = 750, i = 33.0,
d
s
B > B (excess demand):
P  to P*, i  to i*
Shift in the Demand for Bonds
Factors that Shift the Demand for Bonds: “Theory of Asset
Demand”
1. Wealth: total resources in the economy / at the level of the individuals
Economy grows: wealth , Bd , Bd shifts to the right
Note: when wealth increases, we can expect that the demand for all asset categories
increases (cf. portfolio diversification).
2. Expected return of bonds relative to the expected return of other assets
•
Expected return of bonds relative to that of other assets decreases: Bd shifts to the
left
•
Expected interest rate (ceteris paribus): ie , Pe , Re , Bd shifts to the left
•
Expected inflation (ceteris paribus): e , r , Bd shifts to the left
Factors that Shift the Demand for Bonds: “Theory of Asset
Demand”
3. Risk when investing in bonds relative to the risk of other assets
Risk of bonds relative to the risk of other assets , Bd , Bd shifts to the left
4. Liquidity of bonds relative to the liquidity of other assets (liquidity = the ease and
speed with which an asset can be turned into cash at low cost and without incurring a
major value loss)
Liquidity of bonds relative to the liquidity of other assets , Bd , Bd shifts to the right
An example of an increase in the liquidity of bonds: the introduction of the Belgian
OLOs (in French / Dutch: Obligations Linéaires / Lineare Obligaties, in English:
linear bonds).
Bonds with one particular coupon rate, face value and one particular maturity date
are called “lines” (e.g., the “line” of March 2029 6% coupon bonds of F = €10,000).
New bonds are issued that have the coupon rate, face value and the maturity date of
a particular “line”. They may be issued at a higher/lower/identical price when
compared with the previous bonds of that “line” such that their yield to maturity
reflects the market conditions at the time of issuance.
Each new bond issuance then increases the outstanding amount of that particular
“line”, i.e., the size of the market of that particular “line” and hence its liquidity
increases.
- 35 -
Shifts in the Supply of Bonds: “Theory of Asset Supply”
Factors that Shift the Supply of Bonds : “Theory of Asset
Supply”
1. Expected Profitability of Investments
Business cycle expansion, investment opportunities , Bs , Bs shifts to the
right.
2. Expected Inflation
 e , r , Bs , Bs shifts to the right: the lower real interest rate thus leads
to a larger supply of bonds for a given nominal interest rate (cf. movement
of Bs to the right) given that the real cost of bond financing decreases.
3. Government Deficit
Deficit (G - T) , Bs , Bs shifts to the right.
Note: Keynes’ liquidity preference framework has been covered in other
courses such that its treatment on p. 150-161 in Chapter 5 is NO exam
material
References to tables and figures
All figures, tables, diagrams, etc. are made by Dirk Veestraeten unless stated otherwise.
1. Slide 8: Figure 1 on p. 52 of Mishkin (2022), “The Economics of Money, Banking, and Financial Markets”, Pearson Education.
2. Slide 15: Table 1 on p. 120 of Mishkin (2022), “The Economics of Money, Banking, and Financial Markets”, Pearson Education.
3. Slide 20: Table 2 on p. 126 of Mishkin (2022), “The Economics of Money, Banking, and Financial Markets”, Pearson Education.
4. Slide 25: Figure 1 on p. 130 of Mishkin (2022), “The Economics of Money, Banking, and Financial Markets”, Pearson Education.
5. Slide 31: Figure 1 on p. 138 of Mishkin (2022), “The Economics of Money, Banking, and Financial Markets”, Pearson Education.
6. Slide 32: Figure 2 on p. 141 of Mishkin (2022), “The Economics of Money, Banking, and Financial Markets”, Pearson Education.
7. Slide 36: Table 2 on p. 142 of Mishkin (2022), “The Economics of Money, Banking, and Financial Markets”, Pearson Education.
8. Slide 37: Figure 3 on p. 145 of Mishkin (2022), “The Economics of Money, Banking, and Financial Markets”, Pearson Education.
9. Slide 39: Table 3 on p. 144 of Mishkin (2022), “The Economics of Money, Banking, and Financial Markets”, Pearson Education.