Homework for Week 10
Math 408 Section A, March 8
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Reading Assignment:
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Homework Assignment:
- Markowitz Mean-Variance Theory
- Be able to state what the Markowitz QP is.
- Be able to write the KKT conditions for the Markowitz QP.
- Under the assumption that the covariance matrix is nonsingular,
be able to derive the solution to the Markowitz QP.
- Under the assumption that the covariance matrix is nonsingular,
be able to derive the solution to the Markowitz QP when it assumed that
there is a risk free asset.
- Complete the exercises in the notes.
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Vocabulary List:
- Markowitz Mean-Variance Portfolio Theory
- return and rate of return on an asset
- short selling
- the Markowitz risk measure
- the Markowitz theory QP
- KKT conditions for the Markowitz theory QP
- the derivation of the solution to the Markowitz theory QP
- the minimum variance portfolio
- the feasible region for the Markowitz theory
- the efficient frontier for the Markowitz theory
- the Two Fund Theorem
- the risk free asset Markowitz problem
- the derivation of the solution of the risk free asset problem
- the one fund theorm
- the capital market line
- the price of risk
- the asset pricing theorem in CAPM
- the beta of an asset
- the CAPM pricing formula
- the certainty equivalent pricing formula
Key Concepts:
- Markowitz Mean-Variance Portfolio Theory
- rate of return on and asset
- a portfolio as a weighted sum of assets
- variance of a portfolio as a measure of risk
- the Markowitz QP and its solution
- the efficient frontier
- the minimum variance solution and the market solution
- the Two Fund and One Fund theorems
- the asset pricing theorem in CAPM
- the beta of an asset
- the CAPM pricing formula and the certainty equivalent pricing formula
Skills to Master:
- writing down and solving the Markowitz QP using the KKT conditions
- using the CAPM to price assets
Quiz:
The quiz will have two questions. The first will be a vocabulary
word from the notes on
Markowitz portfolio theory and the second will be to solve a
Markowitz QP.