INVESTMENT MANAGEMENT 2023-
2024
Inhoudsopgave
Lecture 1 – H5, H6, H7.................................................................................................................................... 3
Chapter 5.1 – Measuring returns over different holding periods.........................................................................3
Chapter 5.2 – Interest rates and inflation rates...................................................................................................4
Chapter 5.3 – Risk and risk premiums..................................................................................................................5
Chapter 5.4 – The normal distribution..................................................................................................................6
Chapter 5.5 – Deviations from normality and tail risk.........................................................................................6
Chapter 5.6 – Learning from historical returns....................................................................................................7
Chapter 5.7 – Historic returns on risky portfolios.................................................................................................8
Chapter 5.8 – Normality and long-term investments...........................................................................................8
Chapter 6.1 – Risk and risk aversion.....................................................................................................................9
Chapter 6.2 – Capital allocation across risky and risk-free portfolios................................................................10
chapter 6.3 – The risk-free asset........................................................................................................................10
Chapter 6.4 – Portfolios of one risky asset an a risk-free asset..........................................................................10
Chapter 6.5 – Risk tolerance and asset allocation.............................................................................................11
Chapter 6.6 – Passive strategies: the capital market line..................................................................................11
Chapter 7.1 – Diversification and portfolio risk..................................................................................................11
Chapter 7.2 – Portfolios of two risky assets.......................................................................................................12
Chapter 7.3 – Asset allocation with stocks, bonds, and bills..............................................................................13
Chapter 5 – introduction to risk, return, and the historical record....................................................................13
Chapter 6&7 – Capital allocation to risky assets & optimal risky portfolios......................................................16
Lecture 2 – H8, H9, H10................................................................................................................................ 18
Chapter 8.1 – A single-factor security market....................................................................................................18
Chapter 8.2 – The single-index model................................................................................................................18
Chapter 9.1 – The capital asset pricing model...................................................................................................19
Chapter 10.1 – The CAPM and the investment industry....................................................................................20
Chapter 10.2 – Arbitrage pricing theory.............................................................................................................21
chapter 10.3 – The APT and the CAPM...............................................................................................................21
Chapter 10.4 – A multifactor APT.......................................................................................................................22
Chapter 10.5 – The Fama-French (FF) three-factor model.................................................................................22
Lecture 3 – H16, H24.................................................................................................................................... 23
, Chapter 24.1 – The concentional theory of performance evaluation.................................................................23
Chapter 16.1 – Interest rate risk.........................................................................................................................24
Chapter 16.2 – Convexity....................................................................................................................................25
Lecture 4 – H20, H21.................................................................................................................................... 26
Chapter 20.1 – The option contract....................................................................................................................26
Chapter 20.2 – Values of options at expiration..................................................................................................27
Chapter 20.3 – Option strategies.......................................................................................................................27
chapter 20.4 – The put-call parity relationship..................................................................................................29
chapter 21.1 – Option valuation: introduction...................................................................................................29
Chapter 21.2 – Restrictions on option values.....................................................................................................30
Chapter 21.3 – Binominal option pricing............................................................................................................30
Chapter 21.4 – Black-Scholes option valuation..................................................................................................31
The Greeks..........................................................................................................................................................35
Lecture 5 – H22, H23, H11........................................................................................................................... 37
Chapter 22.1 – The futures contract...................................................................................................................37
Capter 22.3 – Futures markets strategies..........................................................................................................37
Chapter 23.2 – Stock-index futures....................................................................................................................37
Chapter 23.5 – Commodity futures pricing........................................................................................................39
Chapter 11.1 – Random walks and efficient markets.........................................................................................39
Guest lecture............................................................................................................................................... 40
, LECTURE 1 – H5, H6, H7
CHAPTER 5.1 – MEASURING RETURNS OVER DIFFERENT HOLDING
PERIODS
Holding period return = r (T) = (price increase + income)/ P(T)
Where P(T) is the price paid today for a zero-coupon bond with maturity date T.
The zero-coupon bond with longer maturity will have a lower present value and a
lower price, therefore providing a higher total return. Face value is the price you
paid when buying the bond. The present value is how much it’s worth right
now.
The total return on each bond can be calculated with:
Typically, an investment return is expressed as an effective
annual rate (EAR), this is defined as the percentage increase in funds per year.
EAR = (1 + r(T)) ^m – 1, where m is the compound.
The above is more relevant for long term investments. However, investments
over a shorter period <1 year don’t really use compounding. This is being called
annual percentage rates (APR). For example, the monthly interest rate
multiplied by 12 you must pay for debt within your credit card balance.
With n compounding periods per year, we can find the EAR from the APR by first
computing the per-period rate as APR/n and then compounding for n periods:
You can calculate the APR by:
If n gets larger, we effectively approach continuous compounding (CC), and
the relation of EAR to the annual percentage rate (R cc) for the continuously
compounded case, is given by:
Here is e is approximately 2,71828. To find
rcc from the effective annual rate (EAR), you
use the following formula:
Ln(x) is the inverse of exp(x).
, CHAPTER 5.2 – INTEREST RATES AND INFLATION RATES
Interest rates directly determine expected returns in the fixed-income market.
There are four fundamental factors that determine the level of interest rates:
- The supply of funds from savers, primarily households.
- The demand for funds from businesses to be used to finance investments
in plant, equipment, and inventories (real assets or capital formation).
- The government’s net demand for funds as modified by actions of the
Federal Reserve Bank.
- The expected rate of inflation.
There are two types of interest rates: nominal interest rate and real interest
rate. The nominal interest rate is the rate at which the dollar value of your
account grows. The real interest rate is the rate at which the goods you can buy
with your funds grows (inflation). The consumer price index (CPI) measures
the purchasing power by averaging the prices of goods and services in the
consumption basket of an average urban family of four.
Suppose the rate of inflation (i) is running at i=6%/ so a loaf of bread that cost €1
last year might cost €1,06 this year. Last year you could buy 1.000 loaves. After
investing for a year, you can buy €1.100/€1,06=1.038 loaves. The rate at which
your purchasing power has increased is therefore 3,8%.
, this can be rearranged to solve for the real state as:
.
A common approximation to this relation is .
There are three basic factors that determine the real interest: supply, demand,
and government actions. The nominal rate is the real rate plus the expected rate
of inflation.
The supply curve: the higher the real
interest rate, the greater the supply
of household savings.
The demand curve: when the real
interest rate on the funds needed to
finance projects are lower, you want
to invest more in physical capital.
Through changing fiscal and monetary
policies, the government and the central
bank (Federal Reserve) can shift the supply
and demand curves.
Irving Fisher argued that the nominal rate
ought to increase one-for-one with expected
inflation, E(i). The so-called Fisher
hypothesis is:
2024
Inhoudsopgave
Lecture 1 – H5, H6, H7.................................................................................................................................... 3
Chapter 5.1 – Measuring returns over different holding periods.........................................................................3
Chapter 5.2 – Interest rates and inflation rates...................................................................................................4
Chapter 5.3 – Risk and risk premiums..................................................................................................................5
Chapter 5.4 – The normal distribution..................................................................................................................6
Chapter 5.5 – Deviations from normality and tail risk.........................................................................................6
Chapter 5.6 – Learning from historical returns....................................................................................................7
Chapter 5.7 – Historic returns on risky portfolios.................................................................................................8
Chapter 5.8 – Normality and long-term investments...........................................................................................8
Chapter 6.1 – Risk and risk aversion.....................................................................................................................9
Chapter 6.2 – Capital allocation across risky and risk-free portfolios................................................................10
chapter 6.3 – The risk-free asset........................................................................................................................10
Chapter 6.4 – Portfolios of one risky asset an a risk-free asset..........................................................................10
Chapter 6.5 – Risk tolerance and asset allocation.............................................................................................11
Chapter 6.6 – Passive strategies: the capital market line..................................................................................11
Chapter 7.1 – Diversification and portfolio risk..................................................................................................11
Chapter 7.2 – Portfolios of two risky assets.......................................................................................................12
Chapter 7.3 – Asset allocation with stocks, bonds, and bills..............................................................................13
Chapter 5 – introduction to risk, return, and the historical record....................................................................13
Chapter 6&7 – Capital allocation to risky assets & optimal risky portfolios......................................................16
Lecture 2 – H8, H9, H10................................................................................................................................ 18
Chapter 8.1 – A single-factor security market....................................................................................................18
Chapter 8.2 – The single-index model................................................................................................................18
Chapter 9.1 – The capital asset pricing model...................................................................................................19
Chapter 10.1 – The CAPM and the investment industry....................................................................................20
Chapter 10.2 – Arbitrage pricing theory.............................................................................................................21
chapter 10.3 – The APT and the CAPM...............................................................................................................21
Chapter 10.4 – A multifactor APT.......................................................................................................................22
Chapter 10.5 – The Fama-French (FF) three-factor model.................................................................................22
Lecture 3 – H16, H24.................................................................................................................................... 23
, Chapter 24.1 – The concentional theory of performance evaluation.................................................................23
Chapter 16.1 – Interest rate risk.........................................................................................................................24
Chapter 16.2 – Convexity....................................................................................................................................25
Lecture 4 – H20, H21.................................................................................................................................... 26
Chapter 20.1 – The option contract....................................................................................................................26
Chapter 20.2 – Values of options at expiration..................................................................................................27
Chapter 20.3 – Option strategies.......................................................................................................................27
chapter 20.4 – The put-call parity relationship..................................................................................................29
chapter 21.1 – Option valuation: introduction...................................................................................................29
Chapter 21.2 – Restrictions on option values.....................................................................................................30
Chapter 21.3 – Binominal option pricing............................................................................................................30
Chapter 21.4 – Black-Scholes option valuation..................................................................................................31
The Greeks..........................................................................................................................................................35
Lecture 5 – H22, H23, H11........................................................................................................................... 37
Chapter 22.1 – The futures contract...................................................................................................................37
Capter 22.3 – Futures markets strategies..........................................................................................................37
Chapter 23.2 – Stock-index futures....................................................................................................................37
Chapter 23.5 – Commodity futures pricing........................................................................................................39
Chapter 11.1 – Random walks and efficient markets.........................................................................................39
Guest lecture............................................................................................................................................... 40
, LECTURE 1 – H5, H6, H7
CHAPTER 5.1 – MEASURING RETURNS OVER DIFFERENT HOLDING
PERIODS
Holding period return = r (T) = (price increase + income)/ P(T)
Where P(T) is the price paid today for a zero-coupon bond with maturity date T.
The zero-coupon bond with longer maturity will have a lower present value and a
lower price, therefore providing a higher total return. Face value is the price you
paid when buying the bond. The present value is how much it’s worth right
now.
The total return on each bond can be calculated with:
Typically, an investment return is expressed as an effective
annual rate (EAR), this is defined as the percentage increase in funds per year.
EAR = (1 + r(T)) ^m – 1, where m is the compound.
The above is more relevant for long term investments. However, investments
over a shorter period <1 year don’t really use compounding. This is being called
annual percentage rates (APR). For example, the monthly interest rate
multiplied by 12 you must pay for debt within your credit card balance.
With n compounding periods per year, we can find the EAR from the APR by first
computing the per-period rate as APR/n and then compounding for n periods:
You can calculate the APR by:
If n gets larger, we effectively approach continuous compounding (CC), and
the relation of EAR to the annual percentage rate (R cc) for the continuously
compounded case, is given by:
Here is e is approximately 2,71828. To find
rcc from the effective annual rate (EAR), you
use the following formula:
Ln(x) is the inverse of exp(x).
, CHAPTER 5.2 – INTEREST RATES AND INFLATION RATES
Interest rates directly determine expected returns in the fixed-income market.
There are four fundamental factors that determine the level of interest rates:
- The supply of funds from savers, primarily households.
- The demand for funds from businesses to be used to finance investments
in plant, equipment, and inventories (real assets or capital formation).
- The government’s net demand for funds as modified by actions of the
Federal Reserve Bank.
- The expected rate of inflation.
There are two types of interest rates: nominal interest rate and real interest
rate. The nominal interest rate is the rate at which the dollar value of your
account grows. The real interest rate is the rate at which the goods you can buy
with your funds grows (inflation). The consumer price index (CPI) measures
the purchasing power by averaging the prices of goods and services in the
consumption basket of an average urban family of four.
Suppose the rate of inflation (i) is running at i=6%/ so a loaf of bread that cost €1
last year might cost €1,06 this year. Last year you could buy 1.000 loaves. After
investing for a year, you can buy €1.100/€1,06=1.038 loaves. The rate at which
your purchasing power has increased is therefore 3,8%.
, this can be rearranged to solve for the real state as:
.
A common approximation to this relation is .
There are three basic factors that determine the real interest: supply, demand,
and government actions. The nominal rate is the real rate plus the expected rate
of inflation.
The supply curve: the higher the real
interest rate, the greater the supply
of household savings.
The demand curve: when the real
interest rate on the funds needed to
finance projects are lower, you want
to invest more in physical capital.
Through changing fiscal and monetary
policies, the government and the central
bank (Federal Reserve) can shift the supply
and demand curves.
Irving Fisher argued that the nominal rate
ought to increase one-for-one with expected
inflation, E(i). The so-called Fisher
hypothesis is:
