Summary Investments
1
,Table of Contents
Knowledge Clips – Risk and Return......................................................................... 7
1.1 Expected Returns and Volatility..........................................................................7
Asset Returns ................................................................................................................................... 7
Common Measures of Risk and Return ............................................................................................. 7
Expected Return ............................................................................................................................... 7
1.2 Expected Returns and Volatility..........................................................................8
Average annual return ...................................................................................................................... 8
Variance Estimate using Realized Returns ........................................................................................ 8
Standard Error .................................................................................................................................. 8
1.3 Portfolios ...........................................................................................................8
Expected return of a portfolio ........................................................................................................... 8
1.4 Diversification ...................................................................................................9
1.5 Covariance and Correlation ...............................................................................9
The volatility of a two-stock porfolio ................................................................................................. 9
Knowledge Clips – Diversification ........................................................................ 10
2.1 Volatility .......................................................................................................... 10
2.2 Efficient Portfolio ............................................................................................. 12
The effect of correlation ................................................................................................................. 12
Short sales and leverage ................................................................................................................. 12
Risk versus return ........................................................................................................................... 12
Risk-free saving and borrowing ....................................................................................................... 13
Knowledge Clips – Beta and CAPM ....................................................................... 14
4.1 Beta................................................................................................................. 14
Expected Returns and the Efficient Portfolio ................................................................................... 14
4.2 CAPM .............................................................................................................. 15
The CAPM Assumptions ................................................................................................................. 15
Efficiency of the Market Portfolio .................................................................................................... 15
Market Portfolio .............................................................................................................................. 16
Optimal Investing: The Capital Market Line ..................................................................................... 16
CLM and SML ................................................................................................................................. 16
Knowledge Clips – EMH and factor models ........................................................... 17
1.1 Efficient Market Hypothesis ............................................................................. 17
Implications of EMH ....................................................................................................................... 17
Types of Market Efficiency .............................................................................................................. 17
EMH not many assumptions ........................................................................................................... 18
1.2 Factor Models .................................................................................................. 18
Refresher Slides .................................................................................................. 21
Basic Terms .................................................................................................................................... 21
2
, Common Risk vs Independent Risk ............................................................................. 21
The CAPM ................................................................................................................... 21
The risk premium ............................................................................................................................ 22
The mutual fund theorem ............................................................................................ 22
Matrix Notation: portfolio Variance ................................................................................................. 23
Expected Returns on individual securities ................................................................... 23
Bond Markets .............................................................................................................. 24
Bond Pricing ................................................................................................................................... 25
Yield to Maturity .......................................................................................................... 25
Options Basics............................................................................................................ 25
Financial Options ........................................................................................................................... 25
Call option ..................................................................................................................................... 25
Put option....................................................................................................................................... 25
Week 1 – Chapter 5 Risk, Return and the Historical Record ................................... 26
3.1 Measuring Returns over Different Holding Periods ............................................ 26
3.2 Interest Rates and Inflation Rates .................................................................... 26
3.3 Risk and Risk Premiums ................................................................................... 26
Excess Returns and Risk Premiums ................................................................................................ 27
3.4 Deviations from Normality and Tail Risk............................................................ 27
The reward-to-Volatility (Sharpe) Ratio ........................................................................................... 27
Value at Risk VaR ............................................................................................................................ 27
Expected Shortfall .......................................................................................................................... 28
Lower Partial Standard Deviation and the Sortino Ratio .................................................................. 28
Negative 3-Sigma Returns .............................................................................................................. 29
3.5 Learning from Historical Returns ...................................................................... 29
Expected Returns and Arithmetic Average ...................................................................................... 29
The Geometric (time-weighted) Average Return .............................................................................. 29
3.6 Normality and Long-Term Investments ............................................................. 30
Week 1 – Chapter 6 Capital Allocation to Risky Assets .......................................... 31
4.1 Risk and Risk Aversion ..................................................................................... 31
4.2 Portfolios of One Risky Asset and a Risk-Free Asset .......................................... 31
4.3 Risk Tolerance and Asset Allocation ................................................................. 32
Week 1 – Chapter 7 Efficient Diversification ......................................................... 33
6.1 Diversification and Portfolio Risk...................................................................... 33
6.2 Portfolios of Two Risky Assets .......................................................................... 33
6.3 Asset Allocation with Stocks, Bonds and Bills ................................................... 33
Steps to arrive at the complete portfolio ......................................................................................... 34
3
, 6.4 The Markowitz Portfolio Optimization Model ..................................................... 34
Week 2 – Chapter 8 Index Models ......................................................................... 36
6.1 A Single-Factor Security Market ....................................................................... 36
Systematic versus Firm-Specific Risk ............................................................................................. 36
The Regression Equation of the Single-Index Model ........................................................................ 37
The Expected Return–Beta Relationship (the exposure to market volatility) .................................... 38
Risk and Covariance in the Single-Index Model ............................................................................... 39
The Set of Estimates Needed for the Single-Index Model ................................................................ 40
The Index Model and Diversification ............................................................................................... 41
Week 2 – Chapter 9 The Capital Asset Pricing Model CAPM .................................. 42
The Market Portfolio ....................................................................................................................... 42
Expected Returns on Individual Securities ...................................................................................... 43
The Security Market Line................................................................................................................. 43
Week 2 – Chapter 10 Arbitrage Pricing Theory and Multifactor Models of Risk and
Return ................................................................................................................. 45
Factor Models of Security Returns .................................................................................................. 45
Arbitrage Pricing Theory (APT) ...................................................................................... 45
Arbitrage, Risk Arbitrage, and Equilibrium ....................................................................................... 46
Diversification in a Single-Factor Security Market ........................................................................... 46
Well-Diversified Portfolios .............................................................................................................. 47
The Security Market Line of the APT ................................................................................................ 48
Limitations of APT Compared to CAPM: .......................................................................................... 49
A Multifactor APT ........................................................................................................ 51
The Fama-French (FF) Three-Factor Model ................................................................... 51
Interpreting the Ratio: ..................................................................................................................... 52
Week 2 – Chapter 11 The Efficient Market Hypothesis ........................................... 54
Random Walks and Efficient Markets .......................................................................... 54
Competition as the Source of Efficiency ......................................................................................... 54
Versions of the Efficient Market Hypothesis .................................................................................... 54
Implications of the EMH .............................................................................................. 56
Technical Analysis .......................................................................................................................... 56
Fundamental Analysis .................................................................................................................... 56
Active versus Passive Portfolio Management .................................................................................. 56
Event Studies .............................................................................................................. 56
Week 3 – Chapter 11.4-11.5 The Efficient Market Hypothesis ................................ 60
Are Markets Efficient? ................................................................................................. 60
1. The Issues .................................................................................................................................. 60
2. Weak-Form Tests: Patterns in Stock Returns ............................................................................... 61
3. Predictors of Broad Market Returns ............................................................................................ 62
4. Semistrong-Form Tests: Market Anomalies ................................................................................. 62
5. Strong-Form Tests: Inside Information ........................................................................................ 63
4
1
,Table of Contents
Knowledge Clips – Risk and Return......................................................................... 7
1.1 Expected Returns and Volatility..........................................................................7
Asset Returns ................................................................................................................................... 7
Common Measures of Risk and Return ............................................................................................. 7
Expected Return ............................................................................................................................... 7
1.2 Expected Returns and Volatility..........................................................................8
Average annual return ...................................................................................................................... 8
Variance Estimate using Realized Returns ........................................................................................ 8
Standard Error .................................................................................................................................. 8
1.3 Portfolios ...........................................................................................................8
Expected return of a portfolio ........................................................................................................... 8
1.4 Diversification ...................................................................................................9
1.5 Covariance and Correlation ...............................................................................9
The volatility of a two-stock porfolio ................................................................................................. 9
Knowledge Clips – Diversification ........................................................................ 10
2.1 Volatility .......................................................................................................... 10
2.2 Efficient Portfolio ............................................................................................. 12
The effect of correlation ................................................................................................................. 12
Short sales and leverage ................................................................................................................. 12
Risk versus return ........................................................................................................................... 12
Risk-free saving and borrowing ....................................................................................................... 13
Knowledge Clips – Beta and CAPM ....................................................................... 14
4.1 Beta................................................................................................................. 14
Expected Returns and the Efficient Portfolio ................................................................................... 14
4.2 CAPM .............................................................................................................. 15
The CAPM Assumptions ................................................................................................................. 15
Efficiency of the Market Portfolio .................................................................................................... 15
Market Portfolio .............................................................................................................................. 16
Optimal Investing: The Capital Market Line ..................................................................................... 16
CLM and SML ................................................................................................................................. 16
Knowledge Clips – EMH and factor models ........................................................... 17
1.1 Efficient Market Hypothesis ............................................................................. 17
Implications of EMH ....................................................................................................................... 17
Types of Market Efficiency .............................................................................................................. 17
EMH not many assumptions ........................................................................................................... 18
1.2 Factor Models .................................................................................................. 18
Refresher Slides .................................................................................................. 21
Basic Terms .................................................................................................................................... 21
2
, Common Risk vs Independent Risk ............................................................................. 21
The CAPM ................................................................................................................... 21
The risk premium ............................................................................................................................ 22
The mutual fund theorem ............................................................................................ 22
Matrix Notation: portfolio Variance ................................................................................................. 23
Expected Returns on individual securities ................................................................... 23
Bond Markets .............................................................................................................. 24
Bond Pricing ................................................................................................................................... 25
Yield to Maturity .......................................................................................................... 25
Options Basics............................................................................................................ 25
Financial Options ........................................................................................................................... 25
Call option ..................................................................................................................................... 25
Put option....................................................................................................................................... 25
Week 1 – Chapter 5 Risk, Return and the Historical Record ................................... 26
3.1 Measuring Returns over Different Holding Periods ............................................ 26
3.2 Interest Rates and Inflation Rates .................................................................... 26
3.3 Risk and Risk Premiums ................................................................................... 26
Excess Returns and Risk Premiums ................................................................................................ 27
3.4 Deviations from Normality and Tail Risk............................................................ 27
The reward-to-Volatility (Sharpe) Ratio ........................................................................................... 27
Value at Risk VaR ............................................................................................................................ 27
Expected Shortfall .......................................................................................................................... 28
Lower Partial Standard Deviation and the Sortino Ratio .................................................................. 28
Negative 3-Sigma Returns .............................................................................................................. 29
3.5 Learning from Historical Returns ...................................................................... 29
Expected Returns and Arithmetic Average ...................................................................................... 29
The Geometric (time-weighted) Average Return .............................................................................. 29
3.6 Normality and Long-Term Investments ............................................................. 30
Week 1 – Chapter 6 Capital Allocation to Risky Assets .......................................... 31
4.1 Risk and Risk Aversion ..................................................................................... 31
4.2 Portfolios of One Risky Asset and a Risk-Free Asset .......................................... 31
4.3 Risk Tolerance and Asset Allocation ................................................................. 32
Week 1 – Chapter 7 Efficient Diversification ......................................................... 33
6.1 Diversification and Portfolio Risk...................................................................... 33
6.2 Portfolios of Two Risky Assets .......................................................................... 33
6.3 Asset Allocation with Stocks, Bonds and Bills ................................................... 33
Steps to arrive at the complete portfolio ......................................................................................... 34
3
, 6.4 The Markowitz Portfolio Optimization Model ..................................................... 34
Week 2 – Chapter 8 Index Models ......................................................................... 36
6.1 A Single-Factor Security Market ....................................................................... 36
Systematic versus Firm-Specific Risk ............................................................................................. 36
The Regression Equation of the Single-Index Model ........................................................................ 37
The Expected Return–Beta Relationship (the exposure to market volatility) .................................... 38
Risk and Covariance in the Single-Index Model ............................................................................... 39
The Set of Estimates Needed for the Single-Index Model ................................................................ 40
The Index Model and Diversification ............................................................................................... 41
Week 2 – Chapter 9 The Capital Asset Pricing Model CAPM .................................. 42
The Market Portfolio ....................................................................................................................... 42
Expected Returns on Individual Securities ...................................................................................... 43
The Security Market Line................................................................................................................. 43
Week 2 – Chapter 10 Arbitrage Pricing Theory and Multifactor Models of Risk and
Return ................................................................................................................. 45
Factor Models of Security Returns .................................................................................................. 45
Arbitrage Pricing Theory (APT) ...................................................................................... 45
Arbitrage, Risk Arbitrage, and Equilibrium ....................................................................................... 46
Diversification in a Single-Factor Security Market ........................................................................... 46
Well-Diversified Portfolios .............................................................................................................. 47
The Security Market Line of the APT ................................................................................................ 48
Limitations of APT Compared to CAPM: .......................................................................................... 49
A Multifactor APT ........................................................................................................ 51
The Fama-French (FF) Three-Factor Model ................................................................... 51
Interpreting the Ratio: ..................................................................................................................... 52
Week 2 – Chapter 11 The Efficient Market Hypothesis ........................................... 54
Random Walks and Efficient Markets .......................................................................... 54
Competition as the Source of Efficiency ......................................................................................... 54
Versions of the Efficient Market Hypothesis .................................................................................... 54
Implications of the EMH .............................................................................................. 56
Technical Analysis .......................................................................................................................... 56
Fundamental Analysis .................................................................................................................... 56
Active versus Passive Portfolio Management .................................................................................. 56
Event Studies .............................................................................................................. 56
Week 3 – Chapter 11.4-11.5 The Efficient Market Hypothesis ................................ 60
Are Markets Efficient? ................................................................................................. 60
1. The Issues .................................................................................................................................. 60
2. Weak-Form Tests: Patterns in Stock Returns ............................................................................... 61
3. Predictors of Broad Market Returns ............................................................................................ 62
4. Semistrong-Form Tests: Market Anomalies ................................................................................. 62
5. Strong-Form Tests: Inside Information ........................................................................................ 63
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