When do we choose the “average arithemtic mean” to calculate our return?
If we Rebalance our Portfolio
When do we choose the “geometric arithemtic mean” to calculate our return?
If we dont rebalance our Portfolio, we choose the “Buy & Hold” Strategy. It takes the compounding into account
What is the continuously compounded return (CCR)?
It is the logaretmic price change and takes the compunding interest affect in to account.
It is Additive to the monthly return.
Which statement can be made if the correlation between 2 assets is less than 1?
For a given Risk (standard deviation), there is a possibility for a better return. The combination of both assets is better than a single asset.
Which Statement can we made on the portfolio variance formular?
The Avergage Covariance is independet from the Number of Assets while the term (1/N)*(Average Variance-Average Covariance) depends on the number of assets. We can diversify our Risk by increasing the number of assets
Which specific features does the utility function have?
Utility functions are concave
Utility functions increase with wealtch
Define the Risk Aversion from Investors
If Investor prefer certain outcome over uncertain outcome -> Risk avers
If Investor is indifferent -> Risk neutral
If Investor prefer uncertain outcome oder certain outcom -> Risk Loving
Where is the optimal portfolio of an invester on the efficient frontier line?
The Tangent of the utility function and the Efficient frontier line
Why does a linear risk return arises if we introduce a risk free rate
Risk free asset has zero volatilty
Correlation between the risk free asset and risky portfolio is zero
What are the CAPM assumptions?
Risk averse and utility maximizing investors
Perfect capital markets (no taxes or transactions costs)
Risk free rate exists
Investors have homogennous expectation of volatilites, correlations an expected return of securites
Define the Capital Market Line
The set of possible combinations of the risk free asset and the efficient portfolios.
When can we use the capital market line?
It can only be used to price efficient portfolios whre the total risk equal systematic risk
How can we interpret a low stocks beta?
The lower the beta, the lower the correlation the stock has with the market portfolio. Thus we have higher diversification. Low Beta stocks are less risky
What are main CAPM lessons?
Dont hold individual assets, hold the market
Each investor has his own optimal market risk
Average investors holds the market
Systematic risk is beta
Why can Assets not paying off in bad times?
They have high risk premiums:
High betas are more risky, dont offer diversification and require high expected values
What is a pure factor portfolio?
It is a portfolio whith one factor sensitivity of 1 against all other factor
Which types of multi factor models exist?
Macroeconomic factor (inflation, war, interest rate)
Fundemental factor (Attributes of firms or stocks like investemnt styl or book-to-market size
In which case are the geometric mean and the arithemtic mean equal?
If there is no variation in return.
What does happen with the portfolio variance, if the number of assets in a portfolio increases?
The Portfolio Variance converges to the average covariance. So the the diversifiable risk equals the systemtic risk.
Does every Investor has the same optimal portfolio?
What is the optimal Portfolio for an Inestor?
No, due to the fact that every Investor has his own risk tolerance.
The individually optimal portfolio is the one with the highest mean-variance utility
What does the “two fund speretation theorem” state?
The composition of the optimal risky portfolio does not depend on the risk preferences of the investor
the mix of the tangent portfolio and the risk free assets does depend on the risk preferences
What is the equilibrium in the CAPM?
In equilibrium the investor holds a combination of the market portfolio and the risk free asset.
Please describe which role the tangency portfolio will take in the CAPM equilibrium?
All investors hav homogenous expectation. -> Investors will hold an identical risky portfolio. If all investors hold the same portfolio, in equilibrium it will contain all assets.
Tangecy Portfolio = Market Portfolio
Who do riskavers people need a higher Expected Value in the “Mean-Variance” utility function and why?
Risk avers people need a higher expected return to be compesated otherwise their utility would not match with lower risk avers people
What is the “Arbitrage Pricing Theory”?
It is based on the “law of one price” and assumes that invesotrs have homogenous expectations without relying on the utility maximation or mean variance model
What is the “synthetic” risk-free portfolio” in the APT model?
We weight our assets to delete the factors impact. As a result the factor is immune to our portfolio. There is a arbitrage against the risk free rate possible
What is the difference between CAPM and APT?
CAPM has only one driving factor, where APT has more factors. The Risk Premium of each facotr reflects the exposure of the asset and the factor. Each factor has its own definition on bad times.
Which Sharpe Ratio does the effecient frontier has?
The efficient frontier has the highest sharpe ratio
What are the empirical results from Black, Jensen and Scholes (1972)
Time series regression
It violates the CAPM, High Beta -> Low Returns and Low Beta -> High returns
Confirm the linear relationship between excess return and beta, but in some period it was not consistent with the capm
What are the Empirical Results Ferson and Harvey (1994) (Factors)
World Market Portfolio is the most important factor
Every Country has its own factor sensitivity
State the regression of a cross sectional test of the CAPM and please state the Null-Hypothesis
Y0 = 0
Y1 = 1 = Market-Risk