Construction of the Optimal Portfolio

CONSTRUCTION OF THE OPTIMAL PORTFOLIO The optimal portfolio concept falls under the modern portfolio theory. The theory assumes (among other things) that investors fanatically try to minimize risk while striving for the highest return possible. The theory states that investors will act rationally, always making decisions aimed at maximizing their return for their acceptable level of risk. The optimal portfolio was used in 1952 by Harry Markowitz, and it shows us that it is possible for different portfolios to have varying levels of risk and return. Each investor must decide how much risk they can handle and then allocate (or diversify) their portfolio according to this decision.

Steps in constructing optimal portfolio : 

Determination of objectives

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Selection of securities based on the objectives

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Choose a suitable approach for construction portfolio

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Apply the approach and construct the portfolio

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Assessment of risk and return.

Various methods of constructing optimal portfolio: Some of the famous methods for constructing optimal portfolio are:  

Markowitz model Sharpe’s single index model

Methodology : Step 1: A brief profile of each of the 30 companies of sensex index is chosen. Step 2: For a period of 5 years data of the each companies have been recorded. Step 3: For applying Sharpe’s index model Ri,Rm, σ ei

2, βi, σ

m2,Rf values are required. so all these data are collected and calculated for proceeding further. Step 4: The cut-off point C* is calculated using the formula: Ci= ( σm2∑(Ri-Rf) β i / σei ) / (1+ σm2 ∑ βi2/ σei2)

Step 5: After Ci for the companies are calculated the value got were put in a table and then the interpretations were made. Step 6: The Ci values go on increasing up to a certain point and then start decreasing. the highest point is called cut-off point(C*).the securities which are above C* point are chosen to the portfolio. Step 7: Once the portfolios are chosen,the proportion in which they should be invested is to be determined.This can be done using a formula where Xi denotes the proportion Xi=Zi / ∑Zi Where Zi =

βi / σei2

( [Ri-Rf/βi ] -C* )

Step 8: Return on portfolio can be made known with the formula Rp=∑XiRi Step 9: σp2 gives the risk associated with portfolio.

Strengths and weaknesses The Sharpe ratio has as its principal advantage that it is directly computable from any observed series of returns without need for additional information surrounding the source of profitability. Other ratios such as the bias ratio have recently been introduced into the literature to handle cases where the observed volatility may be an especially poor proxy for the risk inherent in a time-series of observed returns. While the Treynor ratio works only with systemic risk of a portfolio, the Sharpe ratio observes both systemic and idiosyncratic risks. The returns measured can be of any frequency (i.e. daily, weekly, monthly or annually), as long as they are normally distributed, as the returns can always be annualized. Herein lies the underlying weakness of the ratio - not all asset returns are normally distributed. Abnormalities like kurtosis, fatter tails and higher peaks, or skewness on thedistribution can be a problematic for the ratio, as standard deviation doesn't have the same effectiveness when these problems exist. Sometimes it can be downright dangerous to use this formula when returns are not normally distributed. López de Prado shows that Sharpe ratios tend to be "inflated" in the case of hedge funds with short track records. Because it is a dimensionless ratio, laypeople find it difficult to interpret Sharpe Ratios of different investments. For example, how much better is an investment with a Sharpe Ratio of 0.5 than one with a Sharpe Ratio of -0.2? This weakness was well addressed by the developed Modigliani Risk-Adjusted Performance.

Conclusion: When looking to invest,you need to look at both risk and return.While return can be easily quantified,risk cannot.Today Standard deviation is

the most commonly referenced risk measure,while the Sharpe ratio is the most commonly used risk/return measure.The Sharpe ratio has been around since 1960,but its life has not passed without controversy.Even its founder William Sharpe has admitted the ratio is not without its problems. Thus Sharpe ratio is a good measure of risk for large,diversified,liquid investments but for others such as hedge funds,it can only be used as one of a number of risk/return measures.