2.1 The modern portfolio theory: background of the theory; portfolio expected return; the actual and weighted portfolio risk; derivation of efficient sets; the capital market line (CML) model and its applications, the mean variance dominance rule; short comings of portfolio theory

The Modern Portfolio Theory (MPT) is a financial framework developed by Harry Markowitz in the 1950s. It provides a mathematical approach to constructing investment portfolios that aim to optimize the tradeoff between risk and return. The key principles and concepts of the Modern Portfolio Theory include:

1. Diversification: MPT emphasizes the importance of diversifying investments across a variety of assets to reduce risk. By combining assets with different risk profiles and correlations, investors can achieve a more efficient portfolio that reduces the impact of individual asset fluctuations.
2. Efficient Frontier: The efficient frontier is a graphical representation of all possible portfolios that maximize expected returns for a given level of risk or minimize risk for a given level of expected returns. Portfolios that lie on the efficient frontier are considered optimal because they provide the highest return for a given level of risk or the lowest risk for a given level of return.
3. Risk and Return: MPT recognizes that investors are risk-averse and seek higher returns for taking on higher levels of risk. The theory quantifies the relationship between risk and return and provides a framework for selecting portfolios that offer the best risk-return tradeoff based on an investor’s risk tolerance.
4. Asset Allocation: MPT emphasizes the importance of asset allocation in portfolio construction. It suggests that the majority of investment returns can be attributed to the asset allocation decision rather than individual security selection. MPT provides a method for determining the optimal mix of asset classes based on their risk and return characteristics.
5. Risk Measurement: MPT uses statistical measures such as variance and standard deviation to quantify the risk of individual assets and portfolios. These measures help investors assess the level of risk they are exposed to and compare different investment options.
6. Capital Market Line (CML): The Capital Market Line is a line that represents the risk-return tradeoff for a portfolio that combines a risk-free asset (such as Treasury bonds) with a risky portfolio. It helps investors determine the optimal allocation between risk-free and risky assets based on their risk tolerance.