Markowitz Portfolio Model

Harry Markowitz opened new vistas to modern portfolio selection by publishing an article in the journal of Finance in March 1952. His publication indicated by the importance of correlation among the different stock's returns in the construction of a Portfolio. Markowitz also showed that for a given level of expected return in a group of securities, one security dominates the other. To find out this, the knowledge of the correlation coefficient between all possible securities combination is required.

After the publication of his paper, numerous Investment firms and Portfolio managers developed "Markowitz Algorithms" to minimise the portfolio variance i.e. risk. Even today the term Markowitz diversification is used to refer to the portfolio construction accomplished with the help of security covariances.

Simple diversification 
Portfolio risk can be reduced by the simplest kind of diversification. Portfolio means de group of assets an investor owns. The assets may vary from stocks to different types of bonds. Sometimes the portfolio may consist of securities of different industries. When different assets are added to the portfolio, the total risk tends to decrease. In the case of common stocks, diversification reduces the unsystematic risk or unique risk. Analyst opine that if 15 stocks are added in a Portfolio of the investor, the unsystematic risk can be reduced to zero. But at the same time if the number exceeds 15, additional risk reductions cannot be gained. But diversification cannot reduce systematic or an diversifiable risk.

The naive kind of diversification is known as simple diversification. In the case of simple diversification, securities are selected at random and no analytical procedure is used.

Total risk of the portfolio consist of systematic and unsystematic risk and total risk is measured by the variance of the rates of returns over time. Many studies have shown that is systematic risk forms one quarter of the total risk. 

The simple random diversification reduces the total risk. The reason behind this is that the unsystematic price fluctuations are not correlated with b markets systematic fluctuations. This describes how the simple diversification produces in portfolio management. The following graph shows how the simple diversification reduces the risk. The standard deviations of a portfolios are given in y axis angle number of randomly selected portfolio securities in the x axis.


The standard deviation was calculated for each portfolio and plotted. As the portfolio size increases, the total risk line starts declining. Its flattens out after a certain point. Beyond that limit, risk cannot be reduced. This indicates that spreading out the assets beyond certain level cannot be expected to reduce the portfolios total with below the level of undiversifiable risk. 

Problems of vast diversification: spreading the investment on too many assets will give rise to problems such as purchase of poor performers, information adequacy, high research cost and transaction cost.

Purchase of poor performers: while buying numerous stocks, sometimes investors also buy stocks that will not yield adequate return.

Information inadequacy: if there are too many securities in a Portfolio, it is difficult for the portfolio manager to get information about their individual performance. The portfolio manager has to be in touch with the details regarding the individual company performance. Get all the information simultaneously is quite difficult.

High research cost: if a large number of stocks are included, before the inclusion itself the return and risk of the individual stock have to be analysed. Towards this end, lot of information has to be gathered and kept in store and these procedures involve high cost.

High transaction cost: when small quantity of stocks are purchased frequently, the investor has to Inka transaction cost then the purchase of large blocks at less frequent intervals. In spite of all these difficulties big Financial institutions purchase hundreds of different stocks. Likewise, mutual funds also invest in different stocks.



The Markowitz model 
Most people agree that holding two stocks is less risky than holding one stock. For example, holding stocks from textile, banking and electronic companies is better than investing all the money on the textile company's stock. But building up the optimal portfolio is very difficult. Markowitz provides the answer do it with the help of risk and return relationship. 

Assumptions: the individual investor estimates risk on the basis of variability of return that is the variance of returns. Investors decision is solely based on the expected return and variance of return only.

For a given level of risk, investor prefers higher return to lower return. Likewise, for a given level of return investor prefers lower risk than higher risk.

The concept: in developing his model, markowitz had given up the single stock portfolio and introduced diversification. The single security portfolio would be preferable if the investor is perfectly so that his expectation of highest return would turn out to be real. In the world of uncertainty, most of the risk averse investors would like to join Markowitz rather than keeping a single stock, because diversification reduces the risk. 

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