Interview
fin_eco
- Course
- Institution
- Book
Interview study book Digital Innovation of Giuseppina Passiante, Valerio Elia, Tommaso Massari - ISBN: 9781783261031 (Study Notes)
[Show more]
Connected book
Book Title:
Author(s):
- Edition:
- ISBN:
- Edition:
Seller
Follow
waseemmirza2262
Content preview
Lecture Notes in Financial Economicsc by Antonio Mele
London School of Economics & Political Science
May 2011
,Contents
Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
I Foundations 14
1 The classic capital asset pricing model 15
1.1 Portfolio selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
1.1.1 The wealth constraint . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
1.1.2 Portfolio choice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
1.1.3 Without the safe asset . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
1.1.4 The market portfolio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
1.2 The CAPM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
1.3 The APT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
1.3.1 A first derivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
1.3.2 The APT with idiosyncratic risk and a large number of assets . . . . . . 25
1.3.3 Empirical evidence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
1.4 Appendix 1: Some analytical details for portfolio choice . . . . . . . . . . . . . . 27
1.4.1 The primal program . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
1.4.2 The dual program . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
1.5 Appendix 2: The market portfolio . . . . . . . . . . . . . . . . . . . . . . . . . . 30
1.5.1 The tangent portfolio is the market portfolio . . . . . . . . . . . . . . . . 30
1.5.2 Tangency condition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
1.6 Appendix 3: An alternative derivation of the SML . . . . . . . . . . . . . . . . . 32
1.7 Appendix 4: Broader definitions of risk - Rothschild and Stiglitz theory . . . . . 33
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
2 The CAPM in general equilibrium 36
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
,Contents c
by A. Mele
2.2 The static general equilibrium in a nutshell . . . . . . . . . . . . . . . . . . . . . 36
2.2.1 Walras’ Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
2.2.2 Competitive equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
2.2.3 Optimality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
2.3 Time and uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
2.4 Financial assets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
2.5 Absence of arbitrage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
2.5.1 How to price a financial asset? . . . . . . . . . . . . . . . . . . . . . . . . 43
2.5.2 The Land of Cockaigne . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
2.6 Equivalent martingales and equilibrium . . . . . . . . . . . . . . . . . . . . . . . 49
2.6.1 The rational expectations assumption . . . . . . . . . . . . . . . . . . . . 49
2.6.2 Stochastic discount factors . . . . . . . . . . . . . . . . . . . . . . . . . . 50
2.6.3 Optimality and equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . 51
2.7 Consumption-CAPM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
2.7.1 The risk premium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
2.7.2 The beta relation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
2.7.3 CCAPM & CAPM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
2.8 Infinite horizon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
2.9 Further topics on incomplete markets . . . . . . . . . . . . . . . . . . . . . . . . 57
2.9.1 Nominal assets and real indeterminacy of the equilibrium . . . . . . . . . 57
2.9.2 Nonneutrality of money . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
2.10 Appendix 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
2.11 Appendix 2: Proofs of selected results . . . . . . . . . . . . . . . . . . . . . . . . 60
2.12 Appendix 3: The multicommodity case . . . . . . . . . . . . . . . . . . . . . . . 63
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
3 Infinite horizon economies 66
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
3.2 Consumption-based asset evaluation . . . . . . . . . . . . . . . . . . . . . . . . . 66
3.2.1 Recursive plans: introduction . . . . . . . . . . . . . . . . . . . . . . . . 66
3.2.2 The marginalist argument . . . . . . . . . . . . . . . . . . . . . . . . . . 67
3.2.3 Intertemporal elasticity of substitution . . . . . . . . . . . . . . . . . . . 68
3.2.4 Lucas’ model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
3.2.5 Arrow-Debreu state prices, the CCAPM and the CAPM . . . . . . . . . 72
3.3 Production: foundational issues . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
3.3.1 Decentralized economy . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
3.3.2 Centralized economy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
3.3.3 Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
3.3.4 Stochastic economies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
3.4 Production-based asset pricing . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
3.4.1 Firms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
3.4.2 Consumers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
3.4.3 Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
2
, Contents c
by A. Mele
3.5 Money, production and asset prices in overlapping generations models . . . . . . 86
3.5.1 Introduction: endowment economies . . . . . . . . . . . . . . . . . . . . . 86
3.5.2 Diamond’s model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
3.5.3 Money . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
3.5.4 Money in a model with real shocks . . . . . . . . . . . . . . . . . . . . . 93
3.6 Optimality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
3.6.1 Models with productive capital . . . . . . . . . . . . . . . . . . . . . . . 94
3.6.2 Models with money . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
3.7 Appendix 1: Finite difference equations, with economic applications . . . . . . . 96
3.8 Appendix 2: Neoclassic growth in continuous-time . . . . . . . . . . . . . . . . . 100
3.8.1 Convergence from discrete-time . . . . . . . . . . . . . . . . . . . . . . . 100
3.8.2 The model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
3.9 Appendix 3: Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
4 Continuous time models 105
4.1 Lambdas and betas in continuous time . . . . . . . . . . . . . . . . . . . . . . . 105
4.1.1 The pricing equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
4.1.2 Expected returns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
4.1.3 Expected returns and risk-adjusted discount rates . . . . . . . . . . . . . 106
4.2 An introduction to continuous time methods in finance . . . . . . . . . . . . . . 108
4.2.1 Partial differential equations and Feynman-Kac probabilistic representa-
tions of the solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
4.2.2 The Girsanov theorem with applications to finance . . . . . . . . . . . . 111
4.3 An introduction to no-arbitrage and equilibrium . . . . . . . . . . . . . . . . . . 113
4.3.1 Self-financed strategies . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
4.3.2 No-arbitrage in Lucas tree . . . . . . . . . . . . . . . . . . . . . . . . . . 114
4.3.3 Equilibrium with CRRA . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
4.3.4 Bubbles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
4.3.5 Reflecting barriers and absence of arbitrage . . . . . . . . . . . . . . . . 118
4.4 Martingales and arbitrage in a diffusion model . . . . . . . . . . . . . . . . . . . 119
4.4.1 The information framework . . . . . . . . . . . . . . . . . . . . . . . . . 119
4.4.2 Viability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
4.4.3 Market completeness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
4.5 Equilibrium with a representative agent . . . . . . . . . . . . . . . . . . . . . . . 124
4.5.1 Consumption and portfolio choices: martingale approaches . . . . . . . . 124
4.5.2 The older, Merton’s approach: dynamic programming . . . . . . . . . . . 126
4.5.3 Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
4.5.4 Continuous-time Consumption-CAPM . . . . . . . . . . . . . . . . . . . 128
4.6 Market imperfections and portfolio choice . . . . . . . . . . . . . . . . . . . . . 129
4.7 Jumps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
4.7.1 Poisson jumps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
4.7.2 Interpretation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
3
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller waseemmirza2262. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $7.49. You're not tied to anything after your purchase.
Can Stuvia be trusted?
4.6 stars on Google & Trustpilot (+1000 reviews)
67474 documents were sold in the last 30 days
Founded in 2010, the go-to place to buy study notes for 14 years now