PORTFOLIO THEORY AND RISK MANAGEMENT

Aims:
The idea is to develop the skills and knowledge necessary to apply modern riskmeasures and portfolio management tools to balance investment risk and return. Theemphasis will be on employing the concept of diversification to manage investmentin stock. A more general approach involves utility functions and the construction ofportfolios using expected utility optimisation.
Topics:

• Mean and variance as measures of return and risk.
• Risk and return of a portfolio of two assets, diversification. Construction of the feasible set.
• Risk minimisation for two assets. Finding the market portfolio in two-assetmarket. Discussion of the separation principle (single fund theorem).
• Market imperfections: different rates for borrowing and lending.Non-linear optimisation: Lagrange multipliers.
• General case of many assets, risk-minimization, efficient frontier and its char-acterization (reduction to the two-assets case: two-fund theorem). The role ofrisk-free asset, Capital Market Line, market portfolio.
• Market imperfections: no short-selling.
• Capital Asset Pricing Model, Security Market Line, practical applications andequilibrium theory.
• Value-at-Risk (VaR). (if possible, time allowing)
• Expected utility maximisation. (if possible, time allowing)