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

What is the efficient portfolio?

The highest return of a given risk.

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

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 is the MVP Portfolio?

It is the efficient Portfolio with the lowest variance

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

Define the formula for the portfolio variance

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

Define the APT-Multifactor Modell

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

How can we calculate the risk premium in the APT?

Define the Formula for the expected Return in the APT Model

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

Cross Sectional

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

What are the empirical results from Fama & MacBeth (1973) and please state the regression

Relationship between Expected Return and Beta is positive

But Y0 is > Rf and Beta < Market-Risk

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