### MA311-_-SP : Mathematics of Portfolios

The module introduces modern financial economic theories and methods on portfolio management to construct asset models to assist risk management of financial services firms.

Syllabus

1. Utility Theory and Investment Risk
Utility function, expected utility theorem, measures of investment risk – variance of return, downside semi-variance of return, shortfall probabilities and Value-at-Risk (VAR) / Tail VaR.

2. Mean Variance Portfolio Theory
Short sales and portfolios of assets, diversification, the Markowitz model, the two-fund theorem, inclusion of a risk-free asset, the one-fund theorem.

3. The Capital Asset Pricing Model (CAPM)
Capital asset pricing model, betas and CAPM for portfolios, security market line, CAPM as a pricing formula, the Efficient Market Hypothesis (EMH)

4. Factor Models
Single factor models, multi-factor models, construction of the different types of multifactor models and perform calculations using both single and multi-factor models.

5. Arbitrage Pricing Theory
Simple APT, compatibility of APT with CAPM, More on compatibility of APT with CAPM, two-factor model, diversifying the portfolio, arbitrage pricing on the diversified portfolio

On completion of the module students should be able to:
- Describe and discuss the application of utility theory to economic and financial problems.

- Discuss the advantages and disadvantages of different measures of investment risk.

- Describe and discuss the assumptions of mean-variance portfolio theory and find mean-variance optimal portfolios.

- Describe and discuss the properties of single and multifactor models of asset returns.

- Describe asset pricing models, perform calculations and appreciate the limitations of the models studied.