Using the normalized monthly returns of the top 10 companies based on volume, this paper compares the optimum portfolio for an investor from the stock markets of Abu Dhabi, Muscat, Qatar, Saudi Arabia and Kuwait. Markowitz model of efficient frontier has been used with an extension of short selling. It has been found that Abu Dhabi stock market gives the best portfolio return for both short selling and without it. Out of the five markets only Abu Dhabi and Muscat allow feasible returns when short selling is not allowed. It has also been found that the minimum variance portfolio and the optimum risky portfolio are same for all the markets. This throws light on the effect of recession which has made the market extremely risky in nature.
Keywords: Markowitz Model, Efficient Portfolio, Assets, Risk, Return, risk-free rate, CAL, ORP, MVP, Short Selling,
This paper deals in the comparison of different Middle East markets by utilizing efficient portfolio concept according to the Markowitz's principle. In the portfolio investment the investors are mainly worried about the balance of assets so that there should be proper return for the given risks associated with the market. Risk and Return are two major terms that make investors very much tense in managing their financial resources. Both these terms are very much related to each other, as the assets having high risks have generally very high rate of return. So it depends upon the type of investor whether she is interested in taking risk or averting it or to the extent to which she appreciates either of the two. Risk aversion factor plays a major role in classifying the investor behavior and her preferred assets for making portfolio.
An efficient portfolio is one which provides highest return for a given value of risk or provides minimum risk for the required rate of return of investor. Efficient Portfolio is the best balance of the assets and it optimizes the portfolio performance by reducing risk adhered to individual assets. In efficient portfolio variance is minimum (minimum standard deviation) among the feasible portfolios.
This paper takes into account five Middle-East stock markets comprising Abu Dhabi Securities Market (ADSM), Qatar (Doha Securities Market, DSM), Muscat Securities Market (MSM), Kuwait Stock Exchange (KSE), and Saudi Stock Exchange (Tadawul). These markets are chosen because they represent oil dependent markets and in the time of recession oil prices were the best indication of market situations. These markets showed a lot of activity in one year but they were still very attractive markets in the aversive investor's prospects.
The consideration time for the present research is of 12 months ranging from Dec'08 to Nov'09. The current paper analyzes five portfolios made of 10 top companies of the respective stock markets on the basis of volume. The research has taken both short term selling and buying for long term, according to investors' interests. This paper presents the step by step analysis of portfolio by determining correlation, covariance, weighted distribution, and then applying utility function to determine Optimum Risky Portfolio (ORP), Minimum Variance Portfolio (MVP).
This paper will be very helpful to the investment professionals who are looking for the prospects in Middle East markets. It provides very analytical information about the type of risk and return associated with various types of portfolios in the five markets under consideration. Here these five markets are taken separately for making the portfolio. Inter-market distribution is not introduced here otherwise it could have made the analysis more complex and main point of consideration would have got deviated. The given analysis is much generalized and it could be made a basis for any type of portfolio performance estimation.
This section will be followed by Literature Review, which will give insight to the previous works done in this field and relevance of the research in respect to the conceptual understanding. After that there is Methodology description and conceptual explanation of different related terms. This section is followed by the Data Collection and Analysis part which will give details about the implementation of methodology in getting to the results. Finally the results and their support discussion are summarized in the Conclusion Section. Future related research prospects and the limitations of current research are also mentioned in the last section of the paper.
Portfolio optimization is mainly done for the risk management in the financial world. Major goal for any investor is to get major returns with minor risks involved. This is what the working of Mean-Variance Model does. It measures risk through the returns of the future variance (Harry Markowitz, 1952)[i].
Set of efficient combination of risk and return is a straight line including risk free asset and optimal risky portfolio of risky assets. This means that all the investors would select optimal risky portfolio at the point where the straight line of risk free rate is becoming tangent to the curve of efficient frontier (Tobin, 1958).[ii]
But with this method, there are few shortcomings involved according to various authors.
During the short duration of time ( like one year in our case), risk and return may be negatively correlated, in the earlier time, between 1957 to 1965, securities having higher risk produced lower return as compared to low Beta securities.
Considering the challenges of risk in investment, returns to the stocks are associated with various factors according to various authors; with size of the market (Banz, 1981);[iii] with earning to price ratio (Basu, 1983)[iv]; and with winners and losers in the market in past (De Bondt and Thaler, 1985)[v];
Varian (1993)[vi] concisely appraises the history of modern portfolio theory in the following manner:
Markowitz's innovative research on portfolio optimization was in print in March 1952 in an article titled 'Portfolio Selection' in the Journal of Finance. After Thirty-eight years of the innovation, he was jointly awarded the Nobel Prize for Economics with Merton Miller and William Sharpe (Varian, 1993). Markowitz resolved the difficulty of reducing a portfolio's variance up to a certain minimum level, when expected return and covariance matrix of securities in a portfolio are given, and verified the significance of this to shareholders or the investors.
There are some possibilities of improvement in classical form of Efficient Frontier with a view that "optimized portfolios are 'error maximized' and often have little, if any, reliable investment value. Indeed, an equally weighted portfolio may often be substantially closer to true MV optimality than an optimized portfolio" (Scheel and Blatcher, 1998)[vii].
The efficient frontier, for any given set of securities, gives the best possible risk-return trade off, which a portfolio can provide. (Schirripa and Tecotzky, 2000)[viii]. The Efficient Frontier involves the methodology of determining combination of minimum risk of securities or classes of assets for a given return.
The covariance matrix used in the process of calculation of optimization may have large amount of noise (Kondor and Pafka, 2003)[ix].
Keeping in mind that market factors may influence the price of the securities, market forecast can be considered as an important component for determining risk and return features of the securities and for the chosen portfolios (Jacob and Smith)[x].
Mean-Variance method for portfolio selection has got an outstanding place in finance because of it simplicity and computational ease. This method authentically approximates the expected utility (Jacobs, Levy and Markowitz, 2005)[xi].
Risk measurement is done only through variance of return which is very less complicated as compared to original risk (Chen, 2009)[xii].
High covariance points out that a rise in the return of stock will give rise to the other stock and similarly a low covariance means rate of returns are independent and negative covariance leads to the increase of one stock with the decrease of the other (Chen, Chung, Yu Ho and Ling Hsu)[xiii].
Methodology & Data Collection
Firstly, it is not possible to make a comparison if the prices available are present in different domains. It was due to this reason that there is a need for normalization of data in order to make them comparable and increase the effectiveness of discussion. Min-Max Normalization technique will be used in this case. This will bring all the stock market prices between 0 and 1 which can then be compared. It will also be helpful in making an analysis over risk and return factor associated with company's stock prices. Further correlation between different companies' stock prices will be calculated using MS excel, which will provide us with a 10x10 matrix depicting inter-dependency of different companies over functioning of other companies. This value range from -1 to 1, where -1 represents completely reverse correlation and 1 represents very high correlation.
This will be followed by co-variance matrix that will depict variability and diversification of stock prices of all the companies that will be taken into consideration for the purpose of assigning appropriate weight age to different companies along with defining their corresponding risk factor.
Further this weight age is the primary concern for us as this is the basic criterion that makes it possible to define Minimum Variance Portfolio (MVP) and Optimum Risky Portfolio (ORP) using Markowitz model under unrestricted and restricted categories. These two categories are defined on the basis of values that different weights are allowed to take which is decided with the help of solver in accordance with the return value that has to be achieved. For different values of return, different values of weights and risk associated with it will be achieved. This return value will be mentioned in appendix as portfolio mean along with respective weights as company weights and risk value as portfolio standard deviation. Return value and risk value are presented in the form of percentages while weights are presented as absolute values. Effectiveness of weight distribution is observed by the diversity in their value for stock of different companies. This will be taken care with the help of Cell Formulae that are also defined in a matrix format for all the companies present in the vicinity along with taking contemplation of various other companies that may or may not affect its working.
Values of risk and return along with weight help in determining unrestricted and restricted efficient frontier. These frontiers will be found with the help of cell formulae for different values of return that an investor expects to obtain from its initial investment. Next, we will analyze the standard deviation or risk associated with both unrestricted and restricted portfolios along with defining MVP and ORP with the help of values of CAL using below mentioned formula,
CAL = E (rp) - rf /δ
Next, utility function is defined that along with two other factors, i.e. risk aversion rate and risk free rate characterize Optimal Complete Risky Portfolio in an explicit format. Risk aversion rate in this case is taken to be 6% as the conditions are highly fluctuating in the Middle-East which can be considered as a post recession affect. Initially this part of the world was safe from most of the ill impacts of economic recession but now it has encountered an intense effect due to which risk free rate is also taken as 1%. Base for risk free rate comes from American Depository that offers risk free rate varying from 1% to 4% depending upon external situation. Thus Optimal Risky Portfolio and Optimal overall portfolio will be obtained from ORPs and standard deviation or risk factor associated with it. This process will finally provide us with return % along with risk associated with it for both the cases, i.e. unrestricted and restricted which makes it possible for an investor to channelize her investment in best possible manner. From obtained results, this approach seems to be highly efficient by taking present market situation into account. Another fact that has to be taken into consideration is that this approach has become highly inevitable in current circumstances. This can also be stated by considering stock values of various companies that will be scrutinized.
Most elementary data that is required for the analysis purpose is stock prices of top ten companies present in different stock markets chosen for the purpose of analysis keeping volumetric trade as the basis. Some of the websites that were highly useful in obtaining the required data are www.sharewaadi.com, www.gulfbase.com, www.ameinfo.com.
Stock prices that were taken into consideration were of five different countries of Middle East. GDPs of most of these countries are highly dependent over crude oil prices which retained an element of synchronization. Stock Markets chosen are Saudi Arabia, Abu Dhabi, Qatar, Muscat, and Kuwait. These prices started from December '08 and were extended till November '09. Main aim of choosing this specific period was to take the factor of global recession into account that raised the need for optimizing of a portfolio in order to sustain investor's interest even in extreme adversity. Also the fact that crude oil prices being a macro factor in deciding the fate of economy made it inevitable to ignore the role of these stock markets in functioning of global economy as crude oil can be considered as prime factor defining their pace and slowdown. Companies chosen from five different stock markets are,
Results & Data Analysis
As we have seen, there are five stock markets that have been taken into account. Starting with the analysis of the stock market of Saudi Arabia, on keeping the portfolio mean around the 15 mark, Solver has given the respective standard deviations and Capital Allocation Line (CAL) slopes. As it was expected, the portfolio means for the unrestricted portfolio is lesser as compared to the restricted portfolio. As short selling is allowed in the case of restricted, one can calculate the ORP and MVP of Saudi Arabia stock market to be 14. Similarly for the unrestricted part, it is 34.9. The five values have been selected after Solver found them as most suitable for the respective stock market. This gives an indication that recession has hit the market to such as extent that the optimal risk portfolio is the one which has the minimum variance. This suggests the instability in the market. On using the values of risk aversion rate of 6% and a risk free rate of 1%, one can obtain the optimal position for the risk. In the Saudi Arabian Market it has been found that for a restricted portfolio, it is wise to make an investment of about 80% in the risk free assets and about 20% in the risky assets. This would give an optimal return of 3.5% with a risk of about 6%. This is the lowest amongst the other stock markets which have their economic base as oil. As far as the unrestricted portfolio is concerned, it is not possible as one can't get a feasible return. So, it is only with short-selling that investors can hope to get a return in Saudi Arabia.
Moving on to the Abu Dhabi stock Exchange, one can invest in both restricted and unrestricted portfolio. The market carries the risk associated with the oil-governing nations. Here again, value of ORP is the same as that of MVP for both the types of portfolios. For the restricted part it is 15 and for the unrestricted part it is 23.7. These are once again the optimized values given by Solver. Again using the same values of 6% and 1% respectively for risk aversion rate and risk-free rate, the percentage of investment recommended in the risk-free assets has been found to be about 60% and that in the risky assets has been found to be about 40% in the restricted portfolio. Here the return on investment has been calculated to be 6.5% with a risk of 9%. This is better than the market of Saudi Arabia. In case of unrestricted portfolio, the respective percentages are 30% and 70%. This means that with short-selling not permitted, one can invest 70% in the optimal risky portfolio. This gives a return of about 17% with a risk of 16%. It is a positive indication considering the other competitive markets.
Next in line is the Qatar Stock Market. Here again, the MVP and ORP for the unrestricted portfolio has been found to be the same with a value of 15%. This suggests that about 66% of the investment can be made in the risk-free asset and 34% in the optimal risky portfolio, thereby giving a return of 5.8% with a risk of 9%. This concludes that the market of Qatar is not worth investing as compared to the others in the league. Investment in the restricted portfolio is not feasible in the case of this stock market.
Similarly for Kuwait Stock Market, it has been found that investing in the restricted portfolio would not be possible. For the unrestricted portion, MVP, ORP has been found to be 15%. This allows 63% investment in the risk-free assets and 37% in the optimal risky assets, thereby giving a return of 6.1% with a risk of 9%. It stands a better position in front of Qatar Stock market but on the whole, it does not provide a great value for money.
Finally, the stock market of Muscat allows both restricted and unrestricted investment. In the case of unrestricted, with a MVP, ORP of 15%, one can get a return of about 6% by investing 63% in the risk-free assets and 37% in the optimal risky free assets. This would be risky to an extent of 9%. In the restricted portfolio, with a MVP, ORP of 19.8%; one can get a return of 12.7% by reversing the percentage of investment in the risk-free and optimal risky assets. This would be risky to an extent of 14%.
So, from the data one can infer that the amongst the oil-governing nations, the best market to make an investment for both restricted and unrestricted portfolio is Abu Dhabi Stock Market. As far as the other stock markets are concerned, there has been a wider effect of recession as shown by their returns and viability of taking risk.
- Number of companies taken is only ten to avoid complexity. Higher is the number of companies higher will be the accuracy.
- We have taken a period of only one year for evaluating the efficient portfolio for both restricted and unrestricted.
- We have taken top 10 companies on the basis of trading volume where we could take other factors like P/E ratio or 52 weeks high.
A lot of work can be done in this direction further extending the scope of research. There are several restrictions that are considered during this research and some assumptions are also made. Future research can be based upon following issues:
- Markets of other than Middle East countries which are of similar based economy can be taken.
- Portfolio diversification can be increased by taking companies from different markets in a single portfolio where we took only 5 different markets here.
This paper has used the concept of Markowitz model of efficient portfolio in determining the amount of investment an investor would need to make in risky and risk-free assets. One basic fact that needs to be realized here is that the optimal risky portfolio and minimum variance portfolio have been found to be the same for all the stock markets. This is an indication of the effect of recession on these stock markets which has lowered the capacity of taking risk for the investors. The results have been calculated in MS-Excel with Solver playing a key role in determining the feasible rate of return. Short-selling concept which includes the use of negative weight was also tested for the stock markets. It has been found that out of the five markets taken only Abu Dhabi and Muscat allow this concept to be used in the recession-hit era. We can also conclude that Abu Dhabi Stock Market is the best amongst the five for investment in both restricted and unrestricted portfolio.
- Markowitz, M. H. (1952). Portfolio Selection. Journal of Finance, 77-91
- Tobin, J. (1958). Liquidity Preference as Behavior Towards Risk. Review of Economic Studies, 65-86
- Banz. (1981). The Relationship Between Return and Market Value of Common Stock. Journal of Finacial Economcs, 3-18
- Basu. S. (1983). The Relationship between Earning Yield, Market, and Return for NYSE Common Stocks: Further Evidence. Journal of Financial Economics. 129- 156.
- DeBondt, W. F. M. and Thaler, R. (1985). Does the Stock Market Overact? Journal of Finance. 793-805
- Varian, H. (1993). A Potfolio of Nobel Leureates: Markowitz, Miller and Sharpe. Journal of Economic Perspectives, 159-169
- Scheel, William. Blatcher, William. Denman, John. (1998). Is Efficient Frontier efficient? Book section, 236-286
- Schirripa, Felix, and Nan D. Tecotzky. (2000) An Optimal Frontier. Journal of Portfolio Management. 29-40
- I. Kondor and S. Pafka (2003). Noisy covariance matrices and portfolio optimization ii. Physica A.
- Jacob, Nancy. Smith, Keith. (n.d.) The value of perfect market forecast in Portfolio Selection. Journal of Finance, 16
- Levy, Kenneth. Jacobs, Bruce. Markowitz, Harry. (2005). Portfolio Optimization with factors, scenarios, and Realistic Short Positions. Published in Operation Research, 586-599
- Wei Chen (2009). Risk-based portfolio optimization using sas. SAS Institute Inc. Paper, 127
- Cheng, Wei-Pend. Chung, Huimin. Yu Ho, Keng, Ling Hsu, Tsui. (n.d.) Portfolio optimization models and mean-variance spanning tests. 36