Review on Modern Portfolio theory

Historical development and current state of theory:

Modern Portfolio theory is developed by Markowitz (1952, 1959). Portfolio problem has been formulated as an option of the variance and mean of an asset portfolio. If investors concern on the return distributions for a single period, the mean and variance portfolio theory need to be developed to find the optimum portfolio. Then the investors need to find out the mean and the variance of return for each asset in the portfolio for that single period. Markowitz also has proved the fundamental theorem of mean variance theory, which are holding variance constant, maximize the expected return, as well as holding constant the expected return minimize variance. Based on these principles and individual risk return preferences, investors could choose their preferred portfolio and form the optimum efficient frontier.

Issues in estimating the key inputs for portfolio theory

There are two different models are used, which are index models and covariance estimates. The single-index model was developed and popularized by Sharpe (1967). However, multi-index model was developed to better explain the theory. Multi-index models can be used to provide inputs for a portfolio optimization technique; it also can be used to understand the sensitivity of the portfolio to various economic influences.

If we make additional assumption that Capital Asset Pricing Model (CAPM) holds and ignore insight of Fama ( 1968) that the residuals from the market model cannot be uncorrelated and we allow short sales, then Elton et al.(1976) solution reduces to Treynor and Black(1973) solution that the investment in any stock should be proportional to the ratio of alpha to variance of residual risk. When returns are generated by a multi-index model, the portfolio problem can be viewed as choosing among