Portfolio Theory and CAPM Flashcards
The basic idea of portfolio theory which links risk and return
the CAPM postulates a linear relationship between a stock’s market risk (beta) and the expected return (SML).
Basic intuition: combine various assets in portfolios that offer the highest expected return for a given level of risk. For a given level of risk, portfolio theory identifies the highest expected return possible (efficient portfolios)
The efficient frontier and the identification of efficient portfolios
Markowitz’s efficient portfolio is one where no added diversification can lower the portfolio’s risk for a given return expectation.
The efficient frontier is a set of portfolios that will give the highest expected return for each given level of risk. These concepts of efficiency were essential to CAPM development.
The red curve is the efficient frontier, assets not on it aren’t efficient
why investors use the sharpe ratio to evaluate investments
With a tangency portfolio one maximizes the ratio of risk premium to standard deviation (= the Sharpe ratio).
At the efficient frontier, you can lend (less risk exposure) and borrow (more risk exposure) at the same risk-free rate (to leverage or de-leverage the investment)
What is the Tobin separation theorem?
The Tobin separation theorem shows the decision for the best portfolio and if one should lend or borrow to match the risk appetite
The relationship between risk and return: SML
If we replace the standard deviation by beta, the tangent line is called Security Market Line (SML)
the capital asset pricing model (CAPM) and its assumptions
The CAPM transforms the expected risk premium of the market into an expected risk premium of the asset i. It proposes a linear relationship between the expected return of the asset and the systematic risk of beta
Empirical tests of the CAPM have shown that the model shows validity for some time periods and in particular for low- to medium-beta assets, while empirical data does not confirm such a relationship for high-beta assets
Implications of the CAPM
underperformance: assets below the SML, excess supply of underperformers, their prices decline, and expected returns increase
overperformance: assets above the SML, excess demand for outperformed, their prices increase, and expected returns decrease
The calculation/ estimation of beta
To empirically estimate beta = testing CAPM, we use the testable version.
Historical betas are often good indicators for future betas. Historical betas are not constant. Historical beta < 1 implies a higher beta in the future and vice versa
Empirical tests of the CAPM
- choose a starting point
- divide all stocks that are traded at exchange into 10 portfolios according to betas
- calculate the yearly performance of the 10 portfolios
- rebalance the portfolio at the end of the year and calculate the performance of this rebalanced portfolio at the year-end
- plot the results against the theoretical prediction of the CAPM, the SML
Why is there contradicting evidence?
- all relevant risk is market risk
- unlimited lending and borrowing is possible at the risk-free rate
- investors are risk averse and concerned with the maximization of expected utility over a single period
- all investors have homogenous expectations with respect to the necessary inputs to the portfolio decision
- all assets are infinitely divisible
- all information is available to all investors free of charge
- there are no taxes, transaction costs, and market frictions
the arbitrage pricing theory (APT)
factor models which are based on the APT, describe the return of a stock by its sensitivity towards a number of factors and the respective factor risk premia - they generally explain returns better than the CAPM but lack theoretical foundations of the CAPM
CAPM assumes all investors hold the same (market) portfolio and choose the amount of investment in this portfolio depending on their risk profile
APT assumes that stock returns depend on various factors and that each stock has a different sensitivity with respect to these factors
