OPTIMAL PORTFOLIO BASED ON OPTIMAL CRITERIA

Optimal Portfolio Based On Optimal Criteria

CHAPTER I: PORTFOLIO OPTIMIZATION

Introduction

The fundamental question of portfolio optimization - How do we trade in the stock market in the best possible way? - is as challenging today as ever. Classical strategies, such as Markowitz' mean-variance portfolio, applied with parameters estimated from data are known to give exceptionally volatile portfolio weights. This is primarily due to the difficulty of estimating expected returns with sufficient accuracy; In this paper we develop a new approach to circumventing this difficulty.

Several different methods for resolving this difficulty have been published. For example, Black and Litterman proposed to estimate the expected returns by combining Capital Asset Pricing Model (CAPM) equilibrium with subjective investor views. A drawback with this approach is that the investor's beliefs must be quantified by specifying numbers for both the expected returns and the uncertainty in them. The Arbitrage Pricing Theory (APT), is another acclaimed approach. The APT models the discrete time returns of the stocks as a linear combination of independent factors. The APT relies on statistical estimates of the expected returns that are constructed to fit historical data and hence again may lead to unstable portfolio weights.

Yet another popular method for dealing with the difficulty of estimating expected returns is simply to ignore them. This idea is pursued in the classical 1/n strategy, which puts 1/n of the investor's capital in each of n available assets. Intuitively, this strategy should be well diversified. However, this may not be the case due to covariation between different stocks. Since it is possible to obtain good estimates of covariances between stock returns, we want to use this information in our portfolio construction. Recently, it has been proposed to let expected returns depend on ranks. These ranks could, for example, be based on the capital distribution of the market, assigning rank 1 to the stock with the highest market capitalization, rank 2 to the second highest, and so on.

Modern portfolio optimization was initialized by Markowitz in . Markowitz measured the risk of a portfolio by the variance of its return. He then formulated a one-period quadratic program where he minimized a portfolio's variance subject to the constraint that the expected return should be greater than some constant. Merton ( and ) was the first to consider continuous time portfolio optimization. He used dynamic programming and stochastic control to maximize the expected utility of the investor's terminal wealth. The first results on continuous time versions of the Markowitz problem were published rather recently;

The securities markets changes rapidly on National level. However, the portfolio management is a new practice for the Bulgarian investors. The portfolio is a combination of various securities selected by a certain criteria so that diversification in a portfolio reduces an investor's risk and optimises the return. Therefore, the investment decision can be described as a tradeoffs between market risk and expected return. For the portfolio optimisation investors need to know how the market is changing, by means to make forecasts and analyses ...