INHOUDSOPGAVE
Portfolio Management ....................................................................................................................................3
Course introduction............................................................................................................................................. 3
Overview ........................................................................................................................................................ 3
Decision making under uncertainty .................................................................................................................... 3
1. Standard Utility theory ............................................................................................................................... 3
2. Utility theory in finance.............................................................................................................................. 7
3. Practice questions ...................................................................................................................................... 9
Mean-variance portfolio theory ........................................................................................................................ 10
1. Introduction ............................................................................................................................................. 10
2. Combining one risky asset with a risk-free asset (CAPITAL ALLOCATION) ............................................... 11
3. Combining two risky assets (asset allocation problem) ........................................................................... 14
4. Combining N risky assets.......................................................................................................................... 17
5. Consequences and extensions ................................................................................................................. 21
Equilibrium asset pricing: The CAPM ................................................................................................................ 27
1. Introduction ............................................................................................................................................. 27
2. Capital Asset Pricing Model (CAPM) ........................................................................................................ 30
3. Formal derivation of the CAPM formula .................................................................................................. 34
4. Model analysis ......................................................................................................................................... 35
5. Extensions !!! ........................................................................................................................................... 38
6. Conclusions .............................................................................................................................................. 43
Factor Models ................................................................................................................................................... 44
1. Motivation................................................................................................................................................ 44
2. Factor models........................................................................................................................................... 46
3. Multifactor model .................................................................................................................................... 49
3. Arbitrage Pricing Theory .......................................................................................................................... 50
4. Preview of the Fama-French three-factor model ..................................................................................... 55
5. Conclusions .............................................................................................................................................. 56
Empirical asset pricing ...................................................................................................................................... 58
1. Empirical tests of CAPM ........................................................................................................................... 58
2. CAPM anomalies ...................................................................................................................................... 60
3. The Fama-Fench 3-Factor Model ............................................................................................................. 61
4. Factor investing (≈ investment styles)..................................................................................................... 64
The Efficient Market Hypothesis ....................................................................................................................... 67
1. Understanding the Efficient Market Hypothesis ...................................................................................... 67
2. EMH and the industry .............................................................................................................................. 70
3. Testing the Efficient Market Hypothesis .................................................................................................. 72
4. Conclusion ................................................................................................................................................ 79
Market microstructure ...................................................................................................................................... 81
1. Market mechanism .................................................................................................................................. 81
2. Market liquidity ........................................................................................................................................ 85
3. The economics of market trading ............................................................................................................ 87
4. High-frequency trading (HFT) ................................................................................................................... 90
5. Liquidity and asset pricing ........................................................................................................................ 94
6. Conclusions .............................................................................................................................................. 96
Fixed income assets .......................................................................................................................................... 97
1. Fundamentals of fixed income pricing ..................................................................................................... 97
2. Bond Yields ............................................................................................................................................. 101
3. The yield curve ....................................................................................................................................... 103
4. term-structure of interest rates ............................................................................................................. 109
5. Bond price sensitivity ............................................................................................................................. 115
1
, 6. ActivE and passive bond portfolio management ................................................................................... 121
7. Summary ................................................................................................................................................ 123
Equity Valuation.............................................................................................................................................. 124
1. Equity Valuation ..................................................................................................................................... 124
2. DDM and investment opportunities ...................................................................................................... 127
3. Price-to-earnings ratio ........................................................................................................................... 131
5. Valuation in practice – some comments ................................................................................................ 133
6. Conclusions ............................................................................................................................................ 135
Introduction to derivatives .............................................................................................................................. 136
PART 1. Options .............................................................................................................................................. 136
1. Options - introduction ............................................................................................................................ 136
2. Option strategies .................................................................................................................................... 143
3. Brief introduction to option pricing ....................................................................................................... 147
4. Option-like securities ............................................................................................................................. 150
PART 2: futures and forwards ......................................................................................................................... 152
1. Futures and forwards – Introduction ..................................................................................................... 152
6. Forward/future pricing........................................................................................................................... 156
7. Forward/future trading strategies ......................................................................................................... 158
2
,PORTFOLIO MANAGEMENT
COURSE INTRODUCTION
OVERVIEW
DECISION MAKING UNDER UNCERTAINTY
• In this lecture we build a model of human decision making → utility theory. This is a standard tool to understand decisions of
economic agents, heavily used in all areas of economics.
• Central idea: economic agents are rational in the sense that they are able to rank their consumption opportunities in a sensible
way.
• In finance, agents face a very special decision problem: as investment outcomes are uncertain, we need a model for decision
making under uncertainty.
• The application of the standard utility theory for choices over lotteries (=uncertain outcomes) leads to the so-called mean-
variance preferences.
• The theory we develop in the lecture is fairly abstract, but it is a powerful tool to understand investors’ behavior, and to drive
investment decisions.
1. STANDARD UTILITY THEORY
1.1 CONCEPT OF UTILITY
It is a cliché that investors care about risk and return. But what exactly is the precise meaning of these things?
What is return? What is risk? How should we measure them? And, perhaps most importantly, what do we
mean exactly when we say investors care about certain things? In your introductory Finance course you
probably learned an answer to all these questions: return = expected value, risk = variance, and there is a risk-
return trade-off, which is captured by the investor’s mean-variance utility function, which she wants to
maximize.
The theory starts with some assumptions about how the human brain makes decisions. We say that individuals
have rational preferences over their consumption opportunities, and these preferences can be represented
with utility functions. Higher utility means more “happiness”. Rationality means that your decisions are
sensible in some intuitive sense - precisely, that they satisfy the so-called axioms of rationality (see box). In
fact, about half of microeconomics (the part which studies the theory of customer choice) essentially relies on
the same assumptions.
3
, - Individuals are rational, and they want to maximize their utility (enjoyment, well-
being) derived from consumption (c).
(c is an element of the consumption opportunity set C: c ∈ C)
- Rationality: consumers have preferences over consumption bundles ? they can rank
consumption opportunities in a rational way (see box).
- These preferences can be represented with a utility function:
u(c) : C → R
Þ We can assign a utility score to each consumption opportunity.
Þ The utility function u(c) facilitates convenient mathematical analysis.
Þ Individuals prefer the consumption opportunity which yields higher utility.
The utility function describes the same preferences: w ≺ b ⇔ u(w) < u(b)
- In financial applications the utility function is defined over monetary outcomes
(↔ potential future value of an investment portfolio.)
Þ the Bernoulli utility function.
- St. Petersburg Paradox: it’s a paradox related to probability and decision theory in
economics. It is based on a theoretical lottery game that leads to a random variable
with infinite expected value.
Axioms of rationality:
Completeness: you can rank any two consumption opportunities in the opportunity set.
Transitivity: if you prefer beer over wine and wine over water, then you prefer beer over water.
Monotonicity: more is better.
Continuity: infinitesimally smaller quantity of beer is still preferred over a glass of wine.
4
Portfolio Management ....................................................................................................................................3
Course introduction............................................................................................................................................. 3
Overview ........................................................................................................................................................ 3
Decision making under uncertainty .................................................................................................................... 3
1. Standard Utility theory ............................................................................................................................... 3
2. Utility theory in finance.............................................................................................................................. 7
3. Practice questions ...................................................................................................................................... 9
Mean-variance portfolio theory ........................................................................................................................ 10
1. Introduction ............................................................................................................................................. 10
2. Combining one risky asset with a risk-free asset (CAPITAL ALLOCATION) ............................................... 11
3. Combining two risky assets (asset allocation problem) ........................................................................... 14
4. Combining N risky assets.......................................................................................................................... 17
5. Consequences and extensions ................................................................................................................. 21
Equilibrium asset pricing: The CAPM ................................................................................................................ 27
1. Introduction ............................................................................................................................................. 27
2. Capital Asset Pricing Model (CAPM) ........................................................................................................ 30
3. Formal derivation of the CAPM formula .................................................................................................. 34
4. Model analysis ......................................................................................................................................... 35
5. Extensions !!! ........................................................................................................................................... 38
6. Conclusions .............................................................................................................................................. 43
Factor Models ................................................................................................................................................... 44
1. Motivation................................................................................................................................................ 44
2. Factor models........................................................................................................................................... 46
3. Multifactor model .................................................................................................................................... 49
3. Arbitrage Pricing Theory .......................................................................................................................... 50
4. Preview of the Fama-French three-factor model ..................................................................................... 55
5. Conclusions .............................................................................................................................................. 56
Empirical asset pricing ...................................................................................................................................... 58
1. Empirical tests of CAPM ........................................................................................................................... 58
2. CAPM anomalies ...................................................................................................................................... 60
3. The Fama-Fench 3-Factor Model ............................................................................................................. 61
4. Factor investing (≈ investment styles)..................................................................................................... 64
The Efficient Market Hypothesis ....................................................................................................................... 67
1. Understanding the Efficient Market Hypothesis ...................................................................................... 67
2. EMH and the industry .............................................................................................................................. 70
3. Testing the Efficient Market Hypothesis .................................................................................................. 72
4. Conclusion ................................................................................................................................................ 79
Market microstructure ...................................................................................................................................... 81
1. Market mechanism .................................................................................................................................. 81
2. Market liquidity ........................................................................................................................................ 85
3. The economics of market trading ............................................................................................................ 87
4. High-frequency trading (HFT) ................................................................................................................... 90
5. Liquidity and asset pricing ........................................................................................................................ 94
6. Conclusions .............................................................................................................................................. 96
Fixed income assets .......................................................................................................................................... 97
1. Fundamentals of fixed income pricing ..................................................................................................... 97
2. Bond Yields ............................................................................................................................................. 101
3. The yield curve ....................................................................................................................................... 103
4. term-structure of interest rates ............................................................................................................. 109
5. Bond price sensitivity ............................................................................................................................. 115
1
, 6. ActivE and passive bond portfolio management ................................................................................... 121
7. Summary ................................................................................................................................................ 123
Equity Valuation.............................................................................................................................................. 124
1. Equity Valuation ..................................................................................................................................... 124
2. DDM and investment opportunities ...................................................................................................... 127
3. Price-to-earnings ratio ........................................................................................................................... 131
5. Valuation in practice – some comments ................................................................................................ 133
6. Conclusions ............................................................................................................................................ 135
Introduction to derivatives .............................................................................................................................. 136
PART 1. Options .............................................................................................................................................. 136
1. Options - introduction ............................................................................................................................ 136
2. Option strategies .................................................................................................................................... 143
3. Brief introduction to option pricing ....................................................................................................... 147
4. Option-like securities ............................................................................................................................. 150
PART 2: futures and forwards ......................................................................................................................... 152
1. Futures and forwards – Introduction ..................................................................................................... 152
6. Forward/future pricing........................................................................................................................... 156
7. Forward/future trading strategies ......................................................................................................... 158
2
,PORTFOLIO MANAGEMENT
COURSE INTRODUCTION
OVERVIEW
DECISION MAKING UNDER UNCERTAINTY
• In this lecture we build a model of human decision making → utility theory. This is a standard tool to understand decisions of
economic agents, heavily used in all areas of economics.
• Central idea: economic agents are rational in the sense that they are able to rank their consumption opportunities in a sensible
way.
• In finance, agents face a very special decision problem: as investment outcomes are uncertain, we need a model for decision
making under uncertainty.
• The application of the standard utility theory for choices over lotteries (=uncertain outcomes) leads to the so-called mean-
variance preferences.
• The theory we develop in the lecture is fairly abstract, but it is a powerful tool to understand investors’ behavior, and to drive
investment decisions.
1. STANDARD UTILITY THEORY
1.1 CONCEPT OF UTILITY
It is a cliché that investors care about risk and return. But what exactly is the precise meaning of these things?
What is return? What is risk? How should we measure them? And, perhaps most importantly, what do we
mean exactly when we say investors care about certain things? In your introductory Finance course you
probably learned an answer to all these questions: return = expected value, risk = variance, and there is a risk-
return trade-off, which is captured by the investor’s mean-variance utility function, which she wants to
maximize.
The theory starts with some assumptions about how the human brain makes decisions. We say that individuals
have rational preferences over their consumption opportunities, and these preferences can be represented
with utility functions. Higher utility means more “happiness”. Rationality means that your decisions are
sensible in some intuitive sense - precisely, that they satisfy the so-called axioms of rationality (see box). In
fact, about half of microeconomics (the part which studies the theory of customer choice) essentially relies on
the same assumptions.
3
, - Individuals are rational, and they want to maximize their utility (enjoyment, well-
being) derived from consumption (c).
(c is an element of the consumption opportunity set C: c ∈ C)
- Rationality: consumers have preferences over consumption bundles ? they can rank
consumption opportunities in a rational way (see box).
- These preferences can be represented with a utility function:
u(c) : C → R
Þ We can assign a utility score to each consumption opportunity.
Þ The utility function u(c) facilitates convenient mathematical analysis.
Þ Individuals prefer the consumption opportunity which yields higher utility.
The utility function describes the same preferences: w ≺ b ⇔ u(w) < u(b)
- In financial applications the utility function is defined over monetary outcomes
(↔ potential future value of an investment portfolio.)
Þ the Bernoulli utility function.
- St. Petersburg Paradox: it’s a paradox related to probability and decision theory in
economics. It is based on a theoretical lottery game that leads to a random variable
with infinite expected value.
Axioms of rationality:
Completeness: you can rank any two consumption opportunities in the opportunity set.
Transitivity: if you prefer beer over wine and wine over water, then you prefer beer over water.
Monotonicity: more is better.
Continuity: infinitesimally smaller quantity of beer is still preferred over a glass of wine.
4
