markowitz and capital asset pricing

Markowitz model

This model is used to trace locus and identify the portfolios. It used quadratic programming where a number of securities not less than two are calculates in consideration of their expected returns and risks. This method assists in identifying in calculating the expected value of return of least risk portfolio. All portfolios that are to be calculated are prepared from available list of securities into possible portfolios. Only those portfolios which can possibly provide a higher return at a given level of risk will be considered in each category. This model is very demanding because of the data that is required for computation. Although this method is considered as the best for return optimization since all portfolios are considered for their returns, standard deviations, correlation and other risk measurement tools. The method will give a frontier with a wide of risk return options analysis.

Single index model

This model is used to simplify the data inputs and tabulations while reaching a solution for the Markowitz model. Therefore, meaning that it reduces the data that is used for computation purposes as compared to Markowitz model. The model assumes that fluctuations in the value of a security is relative to that of another but does not depend on the characteristics of the two securities. This means that the relationship between securities occurs in business in the same industry. The method considers additional inputs apart from Markowitz inputs and this is the indices of returns of each security.

Capital asset pricing model.

The model we built up as important applications that field of capital budgeting where it is known as the capital asset pricing model. It is operated by determining for each project an appropriate discount rate for use in calculating its net present value. This rate is the risk free cost of capital plus a risk premium where the premium is determined according to the degree of risk attaching to the project in the content of its addition to an existing portfolio. The existing portfolio has a rate of return which is regarded as being a risk free rate of return plus a risk premium appropriate to that portfolio.

Arbitrage Pricing Model.

Arbitrage price model assumes that there are four factors that affect the risk relationship of a security. And the formula used in this case is as follows:


The equation above which have four items that represent a specific economic factor and a given stock sensitivity to that factor are used in arriving at a more accurate answer to the return of a portfolio as compared to capital pricing model. These factors that are considered by these models include economic forces which influence the activity of the stock market and they include inflation, unexpected change in demand, and unexpected increase in production, unexpected swift in risk premiums and unexpected change or movement in the interest rate. All these factors must be unexpected in any market.

In conclusion the best tool among the four discussed tools for choosing the best equity portfolio with adequate diversification is Markowitz. This tool provides an optimization level where risk and return are taken into account. It also considers the portfolio risk as well as the investors’ risks tolerance.

2. Market efficiency

            The recent happening in the market that is the collapse of banks leading to global financial crisis has lead to a number of unexpected activities on the efficiency of the market. In a nutshell the current happenings in the market have introduced some information that affects the efficiency of the market. To begin with, the efficiency of the market is determined by the information that is available in the market. It assumes that the stock prices reflect all the relevant information that is available in the market. This means that any new information will be definitely incorporated into the share prices of a security as quick as possible. This is what has happened in the current situation in markets. Take for example, the information of collapsing of the mortgage industry as well as the near collapsing of three major financial institutions in the United States, introduced new information. This information was filtered quickly into various stock prices in New York stock exchange leading to a downward movement of Dos Jones index as well as New York stock price index.

In the market efficient prices of securities are determined by forces of demand and supply. If the demand of a stock goes up, the share prices go up and vice versa. Thus the current price of each security at any given moment represents the best estimates of its true value as per  all the available information. The current price of any security represents a consensus view of the security’s current worth – its price is the result of the action of buyers and sellers, each with different perceptions of the value of the security. There are three forms of market efficiency including;

Weak Form efficiency- this exist if it were not possible to make abnormal profits from security investing relying on past security price movements  or technical rules to indicate when to buy and sell. The other form of market efficiency is called semi – strong market efficiency. This a form of efficiency where all relevant publicly held information is impounded or included in the share prices. The last form of market efficiency is strong form where all relevant information including the information held by privileged individuals Is reflected in the share prices of he company in the stock exchange. However the current happenings in the market is due to information that is publicly held and was not reflected inintially in the share prices. Making the market looks like a semi – strong form. I describe as a semi –strong market because the information of collapsing of banks and the mortgage industry was trickled to the market and the market collapsed.

In my opinion the market efficiency currently is in semi – strong form and the downward trend of share prices world wide is due to the information relating to collapsing of the mortgage industry.


Fischer D. E.and Jordan R.J. (2006) Security analysis and Portfolio management, Prentice-Hall, India.

Ghetti A. (2008); Terrific introduction to financial management; Amazon


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