Portfolio Management  An Overview 

The basic objective of any investor is to reduce risk to minimum and maximize the return. Investments can be in form of Bank deposit, Post office, Shares and in any other form but all investments involve risk. As an investor the various strategies for investments are 1. To look for the economic, industry and company fundamentals to find out the intrinsic value of the stock and see weather the stock is selling cheap in the market or not. 2. To look at various statistical graphs and historical price movements to identify trends for future. 3. Go for the noise as following what others are doing in the market. 4. Believing that the prices are moving in random and then try to pick stocks on random. A professional investor generally go for more then one investment i.e. the investor go for a collection of investment, which is known as a portfolio. Investor by construction of portfolio tries to use the effect of diversification and reduces the unsystematic risk to a great extent. Portfolio theory was originally proposed by Harry Markowitz in 1950`s was the first formal attempt to quantify the risk of a portfolio and developed a model for determining optional portfolio. Prior to the development of portfolio model investors dealt with the concept of risk and return somewhat loosely. Intuitively smart investors knew the benefit of diversification which reflected in the traditional edge "Do not put all your eggs in one basket". Harry Markowitz was the first person to show quantitatively why and how diversification reduces risk. In recognition of its seminal contribution in this field he was awarded the Nobel Prize in economics in 1990. Markowitz model was highly information intensive. If one is considering a portfolio of n securities it requires n expected returns, n variances, n(n1)/2 covariance and in total it requires n(n+3)/2 information. In his contribution Markowitz had suggested that an index, to which securities are related, may be used for the purpose of generating the covariance terms. Taking clue from this William sharpe developed his single Index model. The number of information required reduces significantly i.e. to (3n+2) in total from n (n+3)/2 in the model suggested by William sharpe. A major breakthrough in the field of portfolio management was the development of CAPM (Capital asset pricing model) which is concerned with 1. What is the relationship between risk and return of an efficient portfolio? 2. What is the relationship between risk and return for individual security? The CAPM in essence, predicts the relationship between the risk of a security and its return. This relationship is useful in producing a benchmark. It also helps us to make an informed guess about the return that can be expected from a security that has not yet been traded in the market. Although the empirical evidence on the CAPM is mixed, it is widely used because of the valuable insights. William Sharpe its principal originator was awarded the Nobel Prize in economics for his work. Once the portfolios are constructed the optimal and the efficient portfolios are selected. This is done through construction of efficient frontier. All the superior portfolios lie on the efficient frontier. The selection of best portfolio is done on the basis of indifference curves of investor's choice. Indifference curve represents a set of risk and expected return combinations that provide an investor with the same amount of utility. The investor is indifferent about the risk –expected return combinations on the same indifference curve. The portfolio which suits the requirement of investor is selected even though all portfolios on the efficient frontier are best ones. The above presented methods of selecting portfolio need investor to calculate expected returns and variances for all the securities under consideration. Furthermore, all the covariances among these securities need to be estimated, and the risk free rate needs to be determined. Once this is done, the investor can identify the composition of the tangency portfolio as well as its expected return and standard deviation. The investor can then identify the optimal portfolio by noting where one of his or her indifference curves touches but does not intersect the efficient frontier. This portfolio involves an investment in the tangency portfolio along with a certain amount of either risk free borrowing or lending because the efficient set is linear. Such an approach to investing is an exercise in normative economics, wherein investors are told what they should do. Thus, the approach is prescriptive in nature. In the realm of positive economics a descriptive
model is presented, how assets are priced? CAPM is widely used model in this. The CAPM reduces the situation to an extreme case. Everyone has the same information and agrees about the future prospectus for securities. Implicitly
this means that investors analyze and process information in the same way. There are perfect markets for securities because potential impediments such as finite divisibility, taxes, transaction costs, and different risk free
borrowing and lending rates have been assumed away. This approach allows the focus to shift from how an individual should invest to what would happen to security price if everyone invested in a similar manner. Examining the
collective behavior of all investors in the market place enables one to develop the resulting equilibrium relationship between each security's risk and return. 

Source: Email December 13, 2005 
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