APPLICATION OF MARKOWITZ PORTFOLIO ANALYSIS IN INDIAN STOCK MARKET

description of application of Markowitz portfolio analysis to a group of shares recomended by a broker (India)


Sources of Data:

Valueline is a monthly bulletin published by Sharekhan (2005) a broking firm in India. The bulletin contains the target price information and the market price on the date of publication for various stocks researched and recommended by the firm. The data from the bulletin of July 2005, which was made available on the website of the firm for public access, is selected for getting the data of expected returns. Target price data was available for 43 companies. Covariance is to be calculated using 25 months closing price data. The monthly closing price data was taken from Prowess, an electronic data base of balance sheet and share price data of Indian companies published by Centre for Monitoring Indian Economy (CMIE, Mumbai). Out of the total 43 companies, for two companies, data was not available for the full 25 months. These two companies were dropped from the set of securities considered for forming the portfolio. Hence, the final list of stocks considered for portfolio analysis contains 41 companies.

Calculation of Input Variables:

The expected returns were calculated as the difference between target price and current market price of each security, expressed as a percentage of current market price. Monthly returns, required to determine the covariances, were calculated for each company from the monthly closing prices. The covariance matrix for the 41 stocks was calculated using excel covariance function. The monthly covariance between each pair of securities was converted into annual covariance by multiplying it with 12. The input data of expected returns and covariance matrix were thus made ready for the next step in the analysis.

Portfolio Analysis: The software used is the excel optimizer by Markowitz and Todd (2000) described in the book ‘Mean Variance Analysis and Portfolio Choice’. The software was supplied by Todd on request by the author. The software can handle up to 256 securities.

The software requires as input the expected returns of each security, covariance matrix for the set of securities from which the portfolio is to be formed, lower and upper bounds for the proportion of each security in the portfolio and additional constraints if any.

In the first alternative, the portfolio analysis was done with lower and upper boundary for investment in a single security as zero (zero percent) and one (100 percent) respectively. The additional constraint specified is that the sum of the proportions of all securities has to be one or 100%, the amount available for investment. In the second alternative, the analysis was done with the constraint for individual security holding for mutual funds in India, which is a maximum of 10% of the portfolio in a single security. In this case, the lower and upper bounds are 0 and 0.1. The constraint that the sum of all proportions add to 1 or 100% remains.

RESULTS AND FINDINGS



Corner portfolios describe the efficient frontier. Between any two adjacent corner portfolios, the efficient frontier is a straight line, a weighted average of the two corner portfolios. For alternative 1, the analysis returned 23 corner portfolios. The minimum return portfolio has an expected return of 13.54% and standard deviation of 14.35%. The maximum return portfolio has an expected return of 95.96% and standard deviation of 36.12%.

Investor has to decide the risk level (standard deviation) he wants to bear to select the optimal portfolio from this efficient frontier. This action involves consultation with financial planners. For illustration, if the investor chooses a risk level of 20.27%, the corner portfolio number ‘9’ becomes the optimal portfolio. The expected return of this portfolio is 55.98%. The portfolio is a combination of 9 shares. The proportion or percentage recommended for investment in various securities being:

1. X(2) = 3%
2. X(3) = 13%
3. X(9) = 30%
4 X(14) = 3%
5. X(16) = 35%
6. X(17) = 4%
7. X(34) = 9%
8. X(38) = 2%
9. X(40) = 1%

The total adds up to 100%.

In the second case, the restriction is that upper bound, the proportion invested in any single company’s equity shares, is to be less than 10% of the NAV of the scheme. Accordingly lower bound is specified as zero and upper bound is specified as 0.10. 52 corner portfolios form the efficient frontier in this alternative. The minimum return portfolio has an expected return of 14.02% and standard deviation of 15.59%. The maximum return portfolio has an expected return of 50.64% and standard deviation of 29.35%. It is interesting to compare risk-return characteristics of the maximum return portfolio of alternative 2 with the portfolio selected as an illustration in alternative 1 (55.98% and 20.27%). The expected return is more and standard deviation is lower in the latter case. Thus the constraints imposed through regulation on mutual fund investment are generating an inferior or suboptimal portfolio in this case.

The performance of these two portfolios is compared over one year period from July 05 to June 2006. The mutual fund portfolio (Exp. Ret: 50.64% and Risk: 29.35%) shows a return of 58.4% with 23.13% standard deviation. The other portfolio (Exp. Ret: 55.98% and Risk 20.27%) shows a return of 21.25% with a standard deviation of 21%. As the returns are expected to be more unstable and risk measures are expected to be relatively more stable, the observed performance can be rationalized in such a simple comparison of performance of the two portfolios over one period. Empirical studies to evaluate the superiority of one-year horizon optimal portfolios formed using quantitative methods have to use number of one year periods in the sample.

CONCLUSION AND FUTURE SCOPE FOR RESEARCH

Markowitz’s portfolio analysis can be operationalized and applied to real life portfolio decisions. The 12-month ahead target prices being published for various securities by security analysts can be used as the input for determining expected returns over the next 12 months. The optimal portfolios generated by the portfolio analysis represent the optimal policy for the investor who wants to use the target price estimates rationally.

Acceptance of the methodology for developing and revising portfolios based on target prices provides scope for further research into improving the estimates of the inputs used for portfolio analysis. Also research is to be done to evaluate the performance of the optimal portfolios, in comparison to portfolios formed without using quantitative portfolio analysis models, over a long period of time.

Review of literature reveals that research into the utility of target prices is initiated. Research needs to be extended to find out which target price finding methods are working better. Regarding covariance estimates, Grinold and Kahn (2004) have mentioned that there is possibility of estimation errors in case historical data over a lower number of monthly periods in comparison to number of securities considered for portfolio analysis are used. They suggest structural models. Researchers have to come out with useful models which investors can use on the basis of published data.

Regarding the software for portfolio analysis, the Todd’s program can handle 256 companies. In any particular country, brokers do not normally come out with more than 256 buy recommendations at any point in time. Hence, the software program may not be a limitation. But certainly there will be scope to improve the software, as more and more investors use the methodology, and thereby need efficient and easy to use software with more facilities to come out with various measurements.

For full paper
http://docs.google.com/View?docid=dg3h8m78_2hqm5bkdf