Proper asset allocation in Six different scenarios....
Portfolio Construction and performance evaluation
Portfolio Construction and performance evaluation
Course code: F-407 Course name: Portfolio management and investment analysis
Submitted To: Pallabi Siddiqua
Md. Sajib Hossain
Department of Finance
Department of Finance
University of Dhaka
University of Dhaka
Submitted By: Robin Kumar Saha Roll-16-039 16th Batch Department of Finance University of Dhaka
Date of Submission: February 9, 2014
February 9, 2014 Md Sajib Hossain Lecturer Department of Finance University of Dhaka
Subject: Submission of report on “Portfolio Construction and performance evaluation”
Dear Sir, Here is a report on “Portfolio Construction and performance evaluation”. In this report I have included the various tools and techniques to find out efficient portfolio and optimum weight allocated to each security to find out efficient portfolio. I acknowledge the contributions to our course teacher for the guidance he rendered. I have tried to use my academic knowledge on real life. I am pleased to be granted this vital opportunity and grateful for your versatile assistance. I hope that my work will please you .I shall be available in the presentation for further explanations.
Robin Kumar Saha ID – 16 -039 Finance 16th batch Department of finance University of Dhaka
Executive Summary We were assigned to make a report on portfolio construction. For this purpose we collected data from DSE. We know, portfolio is the combination of securities of an individual. the goals of investment vary with man to man, institutions to institutions based on their financial conditions, economic stability, and risk tolerance, need of income stream, age, and job status. Regardless of the ultimate goal, all face the same set of challenges that extend beyond just the choice of what asset classes to invest in. Here our main objective is to find out optimum portfolio convergence with individual and institutions investment policy objectives. By portfolio approach I mean evaluating individual securities in relation to their contribution to the investment characteristics of the whole portfolio. Here we have taken 10 companies that are listed in Dhaka stock exchange from different industries. We want to maximize the theta and want to minimize risk. We use solver function through excel worksheet to find out portfolio weight to be complied with given six situation. These are, 1. 2. 3. 4. 5. 6.
Maximizing Theta allowing short sell Maximizing Theta by not allowing short sell Minimizing Risk (Standard Deviation) by allowing short sell Minimizing Risk (Standard Deviation) by not allowing short sell Minimizing Risk (Standard Deviation) by allowing short sell for a given return Minimizing Risk (Standard Deviation) by not allowing short sell for a given return
After doing different mathematical and statistical tools and techniques finally I get that portfolio weight for each situation. Here I have seen that if short selling is allowed individual can get highest theta with minimum risk than that of any other combinations
Portfolio Construction at Equal weight
Maximizing Theta allowing short sell
Maximizing Theta by not allowing short sell
8 9 10
Minimizing Risk (Standard Deviation) by allowing short sell Minimizing Risk (Standard Deviation) by not allowing short sell Minimizing Risk (Standard Deviation) by allowing short sell for a given return Minimizing Risk (Standard Deviation) by not allowing short sell for a given return Efficient Frontier Performance Evaluation Conclusion
14 15 16
11 12 13 14
17 18 19 21
Introduction Portfolio management is the process of making decisions about investment mix and policy, matching investments to objectives, asset allocation for individuals and institutions. Portfolio management is all about strengths, weaknesses, opportunities and threats in the choice of debt vs. equity, domestic vs. international, growth vs. safety, and many other tradeoffs encountered in the attempt to maximize return at a given appetite for risk. When an investor invests in one security, he can use expected returns as the measure of securities return and standard deviation or variance as the measure of risk. An investor, who holds a diversified portfolio, cares about the contribution of each security to the expected return and the risk of the portfolio. An investor can maximize the returns of a portfolio by choosing securities with high returns and minimize the risk by diversification of securities. By using completely diversified portfolio, an investor can eliminate most or all unsystematic risk. So the goal of an investor when he invests in portfolio of securities is to choose a portfolio with high expected return and low risk. Portfolio management performs this job.
Macro Analysis Stock markets are representative of economy of a country and investors belief. They are able to capture macroeconomic movements in the economy as well as idiosyncratic factors related to each company or industry. As Stock prices are real time and are more frequent than macroeconomic releases they are better reflector of changes in domestic and global economy and can predict the movement of macroeconomic indicators. In other words stock markets are a leading indicator of the economy. Markets respond to different macroeconomic indicators in different ways. The response of Stock markets to any macroeconomic news is dependent on how the news wills effect the proﬁts and interest rates. Macro economic factors that project brighter times and more proﬁt for the companies like, increasing Industrial production, Increasing money supply, good consumer conﬁdence levels will have a positive effect on the stock prices. Whereas, macro news that point to economic recession or slow growth like, decreasing Industrial production coupled with rising interest rates, rising inflations, rise in unemployment, etc. will have a downward effffect on stock prices. GDP growth rate and stock market performance in Bangladesh: Real GDP growth rate of Bangladesh is almost stable in fact increasing although at a slow rate but stock market index (DGEN) fell significantly at the year of 2011 although the economic growth measured by real GDP growth rate increased from 6% in 2010 to 6.1% in 2011.
Inflation and stock market performance in Bangladesh: The point to point inflation saw a drop of about 18% in 2012 compared to surge of 29% in 2011. A drop on government spending from domestic sources, low import and growth in agriculture helped the inflation to come down to a single digit number. Interest rate and stock market performance in Bangladesh: After comparing Lending interest graph of Bangladesh and DGEN graph from 2008 to 2012 it is found that there is an inverse relationship between lending rate and stock market. From 2008 to 2009 lending rate is showing decreasing trend whereas DGEN is showing increasing trend. In the year of 2011 lending rate increased and but DGEN is showing a decreasing trend at that year.
Asset Allocation For the construction of efficient portfolio 10 companies from 07 industries have been selected from the securities of Dhaka Stock Exchange (DSE). While selecting the industries I took into account industry growth rate and market capitalization. Banking Industry: The financial system in Bangladesh is mainly composed of two types of institutions: banks and non-bank financial institutions (NBFIs). The total stock exchange P/E ratio is 17.19 where the bank industry’s P/E multiple is only 11.68 which is the lowest among all industries. That means I will can cover or get our principle investment within 11.68 years if I invest in banking industry and which is locative also. Moreover there is high growth potentials for the banking industry and here there is no threat of entry as government impose restriction upon new entry. Cement Industry: Bangladesh cement industry is the 40th largest market in the world. Currently capacity of the industry is about 20 mn tonnes (MT). Heidelberg, Holcim and Lafarge are the leaders among multinational cement manufacturers and Shah and Meghna are the leading domestic manufacturers. Textiles Industry: The textile and clothing (T&C) industries provide the single source of economic growth in Bangladesh's rapidly developing economy. Exports of textiles and garments are the principal source of foreign exchange earnings. Square Textile is one of the pioneer companies in this RMG sector. The face value of the share is Tk. 10 which current price is TK. 183 and P?E multiple is 23 and last EPS is TK. 8. As the textile industry is the key of our economy, the attraction of investors are increasing day by day towards the industry. I invest here in the long run I can expect a handsome return from it. Engineering Industry: Light engineering is the capital intensive industry. Due to lack of capital, small manufacturing enterprises dominate the sector. These are scattered throughout the country in various clusters. The light engineering has a large domestic market and their quality and price are reasonable. Pharmaceutical Industry: Pharmaceuticals companies are producing inelastic goods which are also the important contributor to our economy as we export drugs throughout the world. Pharmaceuticals Industries is one of the most stable profitable Industry. The number of firms in an in an industry and their relative sizes and dominance determine the degree of concentration in an industry. The pharmaceutical industry of Bangladesh is very much concentrated as top 5
firms capture on average 45% of the aggregate market. Adding 5 more to the list brings on average 66% of total market to Top 10. The Square Pharmaceutical Company is the top most Pharmaceutical Company in Bangladesh. The face value is Tk. 100 which is currently being traded at Tk. 3240 Power and Fuel Industry: Bangladesh has initiated a Power and Energy Sector Development Roadmap (2010-2021) which targeted to produce 8,500 MW by 2013, 11,500 MW by 2015 and 20,000 MW by 2021. Only 47% of the total population of Bangladesh is enjoying the electric facilities. Per capita generation is 220 KW hr which is comparatively lower than other developed countries in the world. Public and private sector produces 63% and 37% of electricity respectively. Govt. encourages Foreign Investors in this sector with different incentives.
Security Analysis For selecting companies for my portfolio I also conducted company analysis as the final step. In this report I basically focused on financial analysis of the companies.
Market Value (2013) 53
Portfolio Construction Equal Weight: If I put equal weights in each company. The excel outcome is shown below-
Sharpe Ratio Company EHL ABBANK CITYBANK IDLC PRIMEFIN AFTABAUTO DESCO SQUARETEXT SQURPHARMA HEIDELBCEM
Weight .1 .1 .1 .1 .1 .1 .1 .1 .1 .1
If I put equal weight in each of the stock my return will be 49% and risk will be 9.5%. The sharpe ratio is 4.44 indicates that I will be receive 4.44 tk. return for taking 1 tk. additional risk.
Minimum Risk, No Short Sale: When short sale is not allowed I have got the following resultReturn
ABBANK CITYBANK IDLC PRIMEFIN
0 0.23217249 0.004361006 0.00114067
I should not invest any of my funds in AB Bank, Aftab Auto, Heidelberg Cement and invest most of my funds 24% in Square Textiles, 23% in City Bank, 21% in DESCO and then rest of the fund in others respectively. Here the sharpe ratio is 3.27 which means that I can achieve 3.27 tk. returns for assuming 1 tk. additional risk.
Minimum Risk, Short Sale: After running the solver tools to find the weight at which risk will be minimized when short sale is allowed I have got the following result
Return Excess Return Variance SD
0.27828741 0.20555182 0.00644998 0.08031174 2.55942436
Sharpe Ratio Company
IDLC PRIMEFIN AFTABAUTO
-0.009929911 0.01422616 -0.096904032
The above results suggest that if I want to achieve minimum risk with short selling approach I have to short sale the securities of AB Bank, IDLC, Aftab Auto, Heidelberg Cement and invest most of my funds in DESCO. The sharp ratio of 2.55 indicates that under this strategy I can achieve 2.55 tk. returns for assuming 1 tk. additional risk.
Maximum Theta, no short sell After running the solver tools to find the weights at which theta will be maximized when short sale is not allowed I have got the following results Return Excess Return Variance SD Sharpe Ratio
0.66853299 0.5957974 0.01396717 0.11818277 5.04132209
The above result suggests that if I want to maximize theta (sharp ratio) without using short selling approach I have to invest nothing in the stock of DESCO, City bank, Square Pharma, Square textile and Heidelberg Cement and most of my funds (35%) in IDLC. Doing so will generate a return of approximately 60% at a risk of 12%. The sharp ratio is 5.04 here indicating that I can achieve 5.04 tk returns for assuming 1 tk. additional risk.
Maximum theta, Short sell: After running the solver tools to find the weights at which theta will be maximized when short sale is allowed I have got the following result
Return Excess Return Variance SD Sharpe Ratio Company
0.94362 0.87088441 0.02732733 0.16530979 5.26819632 Weight
The above result suggests that if I want to maximize theta (sharp ratio) using short selling approach I have to short sale the securities of City bank, Square textile and DESCO. and invest most of my funds in IDLC and AB bank. Doing so will generate a return of approximately 87% at a risk of 16.5%. The sharp ratio is 5.27 here indicating that I can achieve 5.27 tk. returns for assuming 1 tk. additional risk.
Minimum Risk, Short sell, given return: Then I tried to find the weights in which I will get minimum .3 returns. I have allowed short sell. Constraints are1. ∑Wi = 1 Her we assume given return is .3. Then through solver function I get allocated weight for each security. To get this return I have to invest in securities with following weight, Return Excess Return Variance SD Sharpe Ratio Company EHL ABBANK
0.3 0.22726441 0.00647221 0.08045008 2.8249123 Weight 0.129150063 -0.094190802
The above result suggests that if I want to minimize risk with using short selling approach and want to achieve a return of 30% I have to short sale the securities of Aftab Auto and invest most of my funds in DESCO, Square Textile, Square Pharma. The sharp ratio is 2.82 here indicating that I can achieve 2.82 tk. returns for assuming 1 tk. additional risk.
Minimum Risk, No Short Sale, Given Return: Then finally I have tried to find the weights in which I will get minimum .3 returns. I have not allowed short sell. Constraints are1.∑Wi = 1 2. Wi >= 0 Her we assume given return is .3. Then through solver function I get allocated weight for each security 0.3 Return Excess Return Variance SD Sharpe Ratio
0.2272644 0.00840472 0.09167726 2.47896166
and to get .3 return I have to invest to securities with following weights, Company EHL ABBANK CITYBANK
Weight 0.08139105 0 0.420974761
The above result suggests that if I want to minimize risk without using short selling approach and want to achieve a return of 30% I have to invest most of my funds in Square Textiles and City Bank respectively and nothing at others. The sharp ratio 2.47 here indicates that I can achieve 2.47 tk. returns for assuming 1 tk. additional risk.
Efficient Frontier The efficient frontier is a concept in modern portfolio theory introduced by Harry Markowitz and others. A combination of assets, a portfolio, is referred to as "efficient" if it has the best possible expected level of return for its level of risk (usually proxied by the standard deviation of the portfolio's return). Here, every possible combination of risky assets, without including any holdings of the risk-free asset, can be plotted in risk-expected return space, and the collection of all such possible portfolios defines a region in this space. The upward-sloped (positively-sloped) part of the left boundary of this region, a hyperbola, is then called the "efficient frontier". The efficient frontier is then the portion of the opportunity set that offers the highest expected return for a given level of risk, and lies at the top of the opportunity set or the feasible set. For further detail see modern portfolio theory. The return and risk series of the portfolio produces the efficient frontier below: Risk 8.03% 8.05% 8.33% 9.47% 11.82% 16.53%
Return 27.83% 30.00% 34.52% 49.38% 66.85% 94.36%
Efficient frontier 100.00% 90.00% 80.00%
70.00% 60.00% 50.00% 40.00% 30.00% 20.00% 10.00% 0.00% 1
Performance Evaluation Good investment performance depends on being in the right asset (e.g. stocks vs. bonds etc) and in the right securities at the right time. Performance attribution separates over / under performance into these two components (or more), so you can see how much asset allocation added / subtracted from your portfolio’s performance, and likewise how much security picking added / subtracted. Decomposing overall performance into components Components are related to specific elements of performance Example components
Broad Allocation Industry Security Choice Up and Down Markets
Treynor Measure If portfolio is combined with other actively managed small portfolios that make up a larger investment fund (i.e., a fund of funds approach). Since the large investment fund is completely diversified, systematic risk is all that is relevant for portfolio – i.e., how much risk it adds to the larger fund
RP = Portfolio’s average risk premium over the measurement period
P = Estimate of portfolio’s beta
Sharpe Index If portfolio is the entire risky investment that is being considered. Essentially, the Sharpe Index involves calculating the CAL slope of portfolio, and then comparing it to other funds / portfolios. Selecting portfolios based on the Sharpe measure is the same thing as choosing the highest sloped CAL.
RP P where
RP = Portfolio’s average risk premium over the measurement period (return minus risk free rate)
P = Standard deviation of the portfolio’s risk premium.
Jensen Alfa Jensen's alpha) is used to determine the abnormal return of a security or portfolio of securities over the theoretical expected return. The security could be any asset, such as stocks, bonds, or derivatives. The theoretical return is predicted by a market model, most commonly the capital asset pricing model (CAPM). The market model uses statistical methods to predict the appropriate risk-adjusted return of an asset. The CAPM for instance uses beta as a multiplier. Jensen's alpha = Portfolio Return − [Risk Free Rate + Portfolio Beta * (Market Return − Risk Free Rate)]
Performance of my portfolio: Treynor ratio
Actually, Treynor and Sharpe ratio are measured to compare between two or among some portfolios. But Jensen Alfa measures the performance of portfolio out of the overall market performance. Here, we can easily notice that Treynor and Sharpe ratio is positive but in this case we have no other portfolios to compare. Jensen Alfa is .33. My portfolio has beat the market.
Conclusion From above calculation I have shown that by allocating different weights to different securities the investor can maximize his return. He can also keep his risk at desire level as well as he can achieve expected return. Here I have show that if short selling is possible the theta and return can be maximized than if short selling is not allowed. But there is also disadvantage of short selling that is when market falls, short selling mechanism creates pressure to price fall which is not expected for share market. That’s why in Bangladesh short sell is not allowed.