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CM2: Financial Engineering & Loss Reserving
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Module 3
Mean-Variance Portfolio Theory
1
Portfolio Expected Return and Variance
Calculate the expected return and variance of a portfolio of two risky assets.
2
Efficient Frontier for Two Correlated Risky Assets
Plot and interpret the efficient frontier for two correlated risky assets.
3
Minimum Variance Portfolio: Matrix Approach
Determine the minimum variance portfolio for N risky assets using matrix notation.
4
The N-Asset Efficient Frontier: A Lagrange Multiplier Approach
Formulate the optimisation problem for finding the N-asset efficient frontier using Lagrange multipliers.
5
Building the Capital Market Line with a Risk-Free Asset
Incorporate a risk-free asset to derive the Capital Market Line (CML).
6
Tobin's Separation Theorem and Optimal Portfolios
State and apply the Tobin Separation Theorem to construct optimal portfolios.
7
Portfolio Optimization: Constrained and Unconstrained
Solve numerical portfolio optimisation problems with and without constraints like no short-selling.
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Utility Theory and Investment Risk
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Asset Pricing Models