construction of the optimal portfolio

8/2/2019 Construction of the Optimal Portfolio

1/4

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 tominimize 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 theycan handle and then allocate (or diversify) their portfolio

according to this decision.

Steps in constructing optimal portfolio :

Determination of objectives Selection of securities based on the objectives Choose a suitable approach for construction portfolio Apply the approach and construct the portfolio Assessment of risk and return.

Various methods of constructing optimal portfolio:

Some of the famous methods for constructing optimal portfolio are:

Markowitz model Sharpes single index model


2/4

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 Sharpes index model Ri,Rm, ei 2, i,

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= ( m2(Ri-Rf) i / ei ) / (1+ m2 i2/ ei2)

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 = i / ei2 ( [Ri-Rf/i ] -C* )

Step 8: Return on portfolio can be made known with the formulaRp=XiRi

Step 9: p2 gives the risk associated with portfolio.


3/4

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. Otherratios such as thebias ratiohave 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 theTreynor ratioworks 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 arenormally distributed, as thereturns can always be annualized. Herein lies the underlying weakness

of the ratio - not all asset returns are normally distributed.

Abnormalities likekurtosis,fatter tailsand higher peaks,

orskewnesson thedistributioncan 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.

Lpez de Prado shows that Sharpe ratios tend to be "inflated" in thecase 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
http://en.wikipedia.org/wiki/Bias_ratio_(finance)http://en.wikipedia.org/wiki/Bias_ratio_(finance)http://en.wikipedia.org/wiki/Bias_ratio_(finance)http://en.wikipedia.org/wiki/Treynor_ratiohttp://en.wikipedia.org/wiki/Treynor_ratiohttp://en.wikipedia.org/wiki/Treynor_ratiohttp://en.wikipedia.org/wiki/Normal_distributionhttp://en.wikipedia.org/wiki/Normal_distributionhttp://en.wikipedia.org/wiki/Normal_distributionhttp://en.wikipedia.org/wiki/Kurtosis_riskhttp://en.wikipedia.org/wiki/Kurtosis_riskhttp://en.wikipedia.org/wiki/Kurtosis_riskhttp://en.wikipedia.org/wiki/Fat_tailhttp://en.wikipedia.org/wiki/Fat_tailhttp://en.wikipedia.org/wiki/Fat_tailhttp://en.wikipedia.org/wiki/Skewness_riskhttp://en.wikipedia.org/wiki/Skewness_riskhttp://en.wikipedia.org/wiki/Skewness_riskhttp://en.wikipedia.org/wiki/Probability_distributionhttp://en.wikipedia.org/wiki/Probability_distributionhttp://en.wikipedia.org/wiki/Probability_distributionhttp://en.wikipedia.org/wiki/Skewness_riskhttp://en.wikipedia.org/wiki/Fat_tailhttp://en.wikipedia.org/wiki/Kurtosis_riskhttp://en.wikipedia.org/wiki/Normal_distributionhttp://en.wikipedia.org/wiki/Treynor_ratiohttp://en.wikipedia.org/wiki/Bias_ratio_(finance)


4/4

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.

construction of the optimal portfolio

Documents