Portfolio Theory and CAPM Flashcards
(30 cards)
The distribution of returns: Normal distribution –> short run
The return distribution is close to normally-
distributed
The distribution of returns: Normal distribution –> long run
Returns are log-normally distributed
The normal distribution has a convenient property
It only requires the first two moments (mean and variance) of the distribution to describe the whole distribution
The basic intuition behind portfolio theory is simple
Combine various assets in portfolios that offer the highest expected return for a given level of risk
efficient portfolios
For a given level of risk (which will be determined by “investor risk appetite”) portfolio theory then identifies the highest expected return which is possible
lend money at the risk free rate
want to have less risk exposure than the market portfolio (e.g., a portfolio of 40% risk free asset, and 60% market portfolio)
we borrow money to “over”-invest
in the market portfolio in order to get more risk exposure (e.g., 150% market portfolio, which is
financed by borrowing 50% of the amount)
Construction of the tangency portfolio: In which
portfolio to invest in?
- Lines 1 & 2 are too steep
to touch the efficient
frontier. - Line 4 is too flat to be a
tangent. - Line 3 goes through the
tangent portfolio: This is
the market portfolio. - Since this is the steepest
line that one can
construct, this portfolio
offers the highest return
per unit of risk
page 16 –> graph
Sharpe Ratio
maximizes the ratio of risk premium to standard
deviation
Tobin separation theorem
1) identify the best portfolio of common stocks (e.g., “S”)
2) decide on whether to borrow or lend to match the risk appetite
Security Market Line (SML)
replace the standard deviation by beta
The Capital Asset Pricing Model (CAPM): definition
the relation between expected returns and risk in this (security market line) framework
transforms the expected risk premium of the
market into an expected risk premium of the asset i
proposes a linear relationship between the
expected return of the asset i and the systematic risk of i, i.e., the “beta”
The Capital Asset Pricing Model (CAPM): calculation
E (ri) = rf + Bi x (E (rm) - rf)
Implications of the CAPM : Underperformance
- Assets below the SML
- Excess supply of underperformers
–> Prices of underperformers decrease, expected returns increase
Implications of the CAPM : Outperformance
- Assets above the SML
- Excess demand for outperformed
–> Prices of outperformers increase,
expected returns decrease
“defensive” assets
B < 1
- less sensitive to market fluctuations
- tend to protect value in downturns
“aggressive” assets
B > 1
- more sensitive to market movements
- tend to outperform in bull markets but suffer more in downturns
- They are riskier, but can offer higher expected returns
Historical beta < 1 implies
higher beta in the future
Historical beta > 1 implies
lower beta in the future
Measurement errors beta
A very low beta estimate is more likely
to be contaminated by negative measurement error and a high beta estimate is more likely to be contaminated by positive measurement error
This higher leverage will tend to increase the firm’s…
equity beta toward unity
–> Firms with low systematic risk are able to take on more debt
Beta adjustement calculation
betak = 1/3 + 2/3 x Bk (historical)
A simple empirical test of the CAPM
- Choose a starting point
- Divide all stocks that are traded at the exchange into 10 portfolios according to their betas
- Calculate the yearly performance of the ten portfolios
- Rebalance the portfolio at the end of the year (as the betas of the stocks have changed) and calculate the performance of this rebalanced portfolio at the year end.
- Plot the results against the theoretical prediction of the CAPM, i.e., against the Security Market Line
(explicit and implicit) assumptions of the CAPM and its limitations
- All relevant risk is market risk: Hence, beta is the only risk measure
- Unlimited lending and borrowing is possible at the risk-free rate
- Investors are risk averse and concerned with the maximization (mean-variance framework) of expected utility over a single period
- All investors have homogeneous expectations with respect to the necessary inputs to the portfolio decision (i.e., returns, variances, and correlations)
- All assets are infinitely divisible
- All information is available to all investors free of charge
- There are no taxes, transaction costs, and market frictions (e.g., no short-sale restrictions, individuals cannot affect the price of an asset by their buying or selling action, etc.)
