Lecture 6 Flashcards
Assumptions of CAPM (6)
- Many investors, each with small wealth in comparison to overall wealth
- All investors plan for identical holding period
- Investments limited to publicly traded financial assets
- Investors pay no taxes
- Investors are rational, mean variance optimisers
- All investors analyse securities in the same way
CAPM theory
All investors chose to hold a portfolio of risky assets in the proportions that duplicate the representation of assets in the market portfolio
Market portfolio under CAPM
On the efficient frontier and tangency portfolio to optimal CAL
The risk premium on the market portfolio is
Proportional to its risk and the degree of risk aversion of the representative investor
The risk premium on an individual’s assets is
Proportional to the risk premium of the market portfolio (M) and the beta coefficient of the security relative to the market portfolio
When aggregated, portfolios of all individual investors lending and borrowing
Cancel out
Value of the aggregate risky portfolio =
Entire wealth of the economy
Proportion of each stock in the portfolio formula =
Market value of the stock / Sum market value all stocks
CAPM implies that
As individuals attempt to optimise person portfolios, they arrive at the same portfolio with equal weightings. Therefore if investors use identical Markowitz analysis applied to same securities in same time horizons, will arrive at same composition
Optimal risky portfolio of all investors =
Share of market portfolio
Price adjustment process ensures
All stocks are included in the market portfolio, only issue is price at which investors willing to include stock in their portfolio
CML =
Graphs the risk premiums of efficient portfolios as a function of the portfolio standard deviation
M =
Optimal tangency portfolio on the efficient frontier
Assuming all investors chose to hold market index mutual fund, portfolio selection depends on (2)
- Technical problem > creation of mutual funds by professional managers
- Personal problem > investor’s risk aversion
CAPM built the insight that
The appropriate risk premium of an asset is determined by its’ contribution to the risk of the investor’s overall portfolios
Stock’s contribution to the risk of a market portfolio depends on
The covariance of that portfolio
Basic principle equilibrium =
All investors should offer the same risk to reward (balances out if they offer different)
Beta measures
The contribution of the stock to the variance of the market portfolio
Beta = 1
Weighted average value of beta across all assets (market’s beta)
Beta > 1 =
Aggressive > above average sensitivity
Beta < 1 =
Defensive > below average sensitivity
Security market line graphically portrays
The expected return-beta relationship (for individual assets)
Slope of SML =
Risk premium of the market portfolio
SML provides a benchmark
For the evaluation of investment performance (then can use sensitivity analysis)
Fairly priced assets
Plot onto the SML
In the market equilibrium
All securities lie on the SML
If the stock’s expected return is greater than the fair return stipulated by the SML
Stock is underpriced, will plot above SML line
If the stock’s expected return is less than the fair return stipulated by the SML
Stock is overpriced, will plot below the SML line
Difference between the fair and actual expected return on a stock =
Alpha
Positive alpha =
Underpriced
Negative alpha =
Overpriced
