Finance Lecture Notes
1
25721
INVESTMENT MANAGEMENT
SESSION 2, 2012
Lecture 5: The Capital Asset Pricing Model
Last Week
2
Index models
Systematic and idiosyncratic risks Calculating covariance
Case study
Calculating systematic and idiosyncratic risks Investment strategies Required return Reward-to-risk ratio
Today
3
Asset pricing models: what and why The Capital Asset Pricing Model (CAPM)
Assumptions The claim Implications The economic mechanism The reality check Applications Extensions
Asset Pricing
4
Central issue: what is the “fair” or “required” return of a risky asset?
Sarah Wolfe of BMC Macro economy:
Why do we care?
Efficient capital allocation for growth Bubbles and crashes
Social welfare: Pension investments Firms’ cost of capital Performance evaluation:
Fund managers, trading strategies
Equilibrium Asset Pricing
5
E(Ri), i, ρij, i,j = 1,…N
Markowitz Portfolio Optimization
The minimum variance set (MVS) and the optimal risky portfolio
Capital Asset Pricing Model
The CAPM Assumptions
6
All investors are price takers, meanvariance optimisers, and have identical information and holding periods. All assets are marketable and divisible. The market portfolio includes ALL assets There is a single risk-free rate at which one can borrow or lend any amount No market imperfections (no taxes, short selling restriction, transaction costs, etc)
CAPM Conclusion
7
The market portfolio is the tangency portfolio on the efficient frontier:
Investors: Same model (Markowitz) + same input parameters = same tangency portfolio (The Separation Property) Equilibrium: supply = demand Total shares issued by firms (market portfolio) = aggregate holdings of all investors (tangency portfolio)
CAPM Implications
8
The optimal portfolio for all investors is a combination of the risk-free asset and the
25721
INVESTMENT MANAGEMENT
SESSION 2, 2012
Lecture 5: The Capital Asset Pricing Model
Last Week
2
Index models
Systematic and idiosyncratic risks Calculating covariance
Case study
Calculating systematic and idiosyncratic risks Investment strategies Required return Reward-to-risk ratio
Today
3
Asset pricing models: what and why The Capital Asset Pricing Model (CAPM)
Assumptions The claim Implications The economic mechanism The reality check Applications Extensions
Asset Pricing
4
Central issue: what is the “fair” or “required” return of a risky asset?
Sarah Wolfe of BMC Macro economy:
Why do we care?
Efficient capital allocation for growth Bubbles and crashes
Social welfare: Pension investments Firms’ cost of capital Performance evaluation:
Fund managers, trading strategies
Equilibrium Asset Pricing
5
E(Ri), i, ρij, i,j = 1,…N
Markowitz Portfolio Optimization
The minimum variance set (MVS) and the optimal risky portfolio
Capital Asset Pricing Model
The CAPM Assumptions
6
All investors are price takers, meanvariance optimisers, and have identical information and holding periods. All assets are marketable and divisible. The market portfolio includes ALL assets There is a single risk-free rate at which one can borrow or lend any amount No market imperfections (no taxes, short selling restriction, transaction costs, etc)
CAPM Conclusion
7
The market portfolio is the tangency portfolio on the efficient frontier:
Investors: Same model (Markowitz) + same input parameters = same tangency portfolio (The Separation Property) Equilibrium: supply = demand Total shares issued by firms (market portfolio) = aggregate holdings of all investors (tangency portfolio)
CAPM Implications
8
The optimal portfolio for all investors is a combination of the risk-free asset and the