Modern portfolio theory and beyond
The importance of diversification
Key tenets of modern portfolio theory
The investors should focus on how securities are reacting to one on other
Priced risk
Systematic risk should be the only risk
Statistics
Variance
Covariance
Risk of the portfolio
Capital allocation line
Graphe
Formula
Expected return of a portfolio with a risky et riskfree assets
Correlation ⚠Graphe
Efficient frontier ⚠Graphe
CAL & Optimal portfolio ⚠Graphe
In reality
Short selling
Interest rate
The pitfalls of modern portfolio theory
Mean-variance analysis assumptions
Returns are normally distributed
Market = efficient
Assumptions
investors’ utility functions are quadratic
or joint distribution of asset returns is normal
MPT = single period model if:
utility functions are myopic
Or independant returns over time
Reality
Investors are risk adverse
Inconsistent with MTP
Undiversified
Trade too much
Don't be stocks
The capital asset market pricing model
Optimal risky portfolio=
combine risk-free and risky assets
CAL
Superimpose utility curves on the CAL
Combine risk-free and risky assets ⚠ graphe
Several optimal portfolios?
Identical expectations: single optimal
Different expectations: different optimal portfolios
CAPM ⚠ Formula ⚠Graphe
Beta
Assumption
Investor= risk-averse, utility maximizing, rational
Market are frictionless (= no transaction costs or taxes)
Investors plan for the same single holding period
Investors have homogeneous expectation or beliefs
All investments are infinitely divisible
Investors are price takers
SML : ⚠Graphe
Application of the CAPM
Estimates of expected return
Performance appraisal
Security selection
Limitation of the CAPM
Single-factor model
Single-period model
Extensions to the CAPM
APT
4 factors model