Lecture 2 Flashcards
Portfolio Theory Components
What are the three main components of portfolio construction?
- Security Selection: Analyse individual assets to estimate expected returns and covariance.
- Asset Allocation: Determine the optimal risky portfolio composition.
- Capital Allocation: Allocate funds between risky and risk-free assets based on risk aversion.
Portfolio Return and Variance
What is the formula for portfolio return and variance for two assets?
Normal Variance and Return
Minimum Variance Portfolio Weights
How are the weights for the minimum-variance portfolio calculated?
Correlation and Risk
How does the correlation coefficient ρ affect portfolio risk?
ρ=1: Perfect positive correlation, no diversification.
ρ=0: Partial diversification benefit.
ρ=−1: Perfect negative correlation, maximum diversification.
Complete Portfolio Composition
How is the return of a complete portfolio calculated?
Capital Allocation Line (CAL)
What does the Capital Allocation Line (CAL) represent?
The CAL shows all risk-return combinations for different portfolio weights. Its slope, called the Sharpe Ratio, is given by:
Optimal Risky Portfolio
How are the weights for the optimal risky portfolio determined?
Incldue Risk free asset
Utility and Risk Aversion
What is the utility function for risk-averse investors?
This takes into account the risk aversion of investors in capital allcoation
if A > 0 risk averse
if A < 0 risk lvoer
if A = 0 neutral
Separation Principle
What is the Separation Principle in portfolio theory?
Portfolio construction is divided into:
- Identifying the optimal risky portfolio (common for all investors).
- Allocating capital between the risk-free asset and the risky portfolio based on individual risk preferences.
Efficient Frontier
What is the efficient frontier?
It represents the set of portfolios offering the maximum expected return for a given level of risk, derived from the minimum-variance frontier.
Capital Allocation
How is the optimal proportion invested in the risky portfolio determined?
links to the utility function also here * means it is the optical compelte protfolio Return
Markowitz Model
What is the purpose of the Markowitz Model in portfolio selection?
To determine the efficient frontier by solving:
- Variance minimization for a given return.
- Return maximization for a given variance
Risky Portfolio
What is a risky portfolio?
A risky portfolio (P) is a combination of multiple risky assets (e.g., stocks, bonds) selected to maximize return for a given level of risk or minimize risk for a given level of return. It is characterized by:
Expected return (Erp): The weighted average return of its constituent assets.
Variance (σ): Depends on the variances and covariances of the assets in the portfolio.
Objective: Optimize the Sharpe Ratio for the portfolio.
Complete Portfolio
What is a complete portfolio?
A complete portfolio (C) combines a risky portfolio (P) with a risk-free asset (F), allowing the investor to achieve a desired risk-return tradeoff based on their risk aversion.
Expected return (Erc) : Weighted average of the risky portfolio and risk-free asset
Variance (σ^2c): Directly proportional to the proportion of wealth in the risky portfolio.
Connection Between Risky and Complete Portfolios
How are the risky portfolio and complete portfolio connected?
- The risky portfolio represents the optimal combination of risky assets.
- The complete portfolio includes the risk-free asset and adjusts the investor’s overall risk level by varying the proportion (y) invested in the risky portfolio.
- The expected return and risk of the complete portfolio are influenced by the properties of the risky portfolio and the proportion of wealth allocated to it.
