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Quantitative Techniques for Equity portfolio constructionanalysis
- 1. Quantitative Techniques Equity Portfolio Construction
- 2. 19 February 2019 Equity Portfolio Construction Page 2 Problem Introduction • Construction of Equity portfolio with Rs. 10 Lakh containing 10 stocks selected from 15 stocks • 15 stocks are selected by using Delphi Method and • Out the 15 selected stocks 10 should be Large Cap and 5 should be mid Cap stocks • At least 5 large cap and 3 mid cap stocks must be part of the portfolio • At least 6.5 Lakhs to be invested in large cap stocks (>= 65%) • At least 2 lakhs to be invested in mid stocks (>= 20%) • All funds are to be invested for a period of 30 years • No switch between stocks in allowed during the period of 30 years
- 3. 19 February 2019 Equity Portfolio Construction Page 3 Methodology 1. Selecting 15 stocks based on Delphi method, Heuristics 2. Calculating yearly returns for the 15 selected stocks 3. Using the Return(Mean) and risk (Std. Dev.) for simulation of returns for the next 30 years 4. Forming the Linear programming equation for maximization of returns. 5. Applying various constraints as per the problem definition to maximization of return 6. Calculation of overall returns and portfolio returns
- 4. 19 February 2019 Equity Portfolio Construction Page 4 Selected Stocks Sr. No Company Name Size Historical Returns (10 Years) Historical Risks (10 Years) 1 Eicher Motors Large 0.7868038 0.650164346 2 Kotak Mahindra Bank Large 0.3075782 0.36770514 3 MRF Large 0.5257487 0.615998476 4 Balkrishna Industries Large 0.6219221 0.777776877 5 TCS Large 0.314042 0.471978505 6 Natco Large 0.5293815 0.672489971 7 Bosch Large 0.2640151 0.375577924 8 Dr Reddy Large 0.2364526 0.43692798 9 HDFC Large 0.1967285 0.222159787 10 HDFC Bank Large 0.2739559 0.223778391 11 Divis Lab Mid 0.4009718 0.551633959 12 Escorts Mid 0.57276 0.939241288 13 Pfizer Mid 0.2253158 0.367372493 14 Exide Mid 0.2203103 0.453193568 15 Voltas Mid 0.2219007 0.795116252
- 5. 19 February 2019 Equity Portfolio Construction Page 5 • Assuming returns to be constant • As we know Present Value (PV) and Time period (n) is constant i.e. 10 lakhs, n is 30 years. • Therefore Setting the Objective functions max(𝐹𝑉) = max(𝑃𝑉 1 + 𝑟 𝑛 ) max 𝐹𝑉 = 10 lakhs X max( 1 + 𝑟 30 )
- 6. 19 February 2019 Equity Portfolio Construction Page 6 Constraints - Linear Programming No. of Large Cap Stocks 7 >= 5 No. of Mid Cap Stocks 3 >= 3 Investment in Large 700000 >= 650,000 Investment in Mid 300000 >= 200,000 Constraints
- 7. 19 February 2019 Equity Portfolio Construction Page 7 Results - Linear Programming Stocks Return (1+r)^30 Present Value Include Investment Amt Future Value Eicher Motors 78.68% 36501091.77 200000 1 200000 7.30022E+12 Kotak Mahindra Bank 30.76% 3119.10888 50000 1 50000 155955444 MRF 52.57% 319514.0764 200000 1 50000 15975703821 Balkrishna Industries 62.19% 1999398.506 200000 1 200000 3.9988E+11 TCS 31.40% 3616.407153 50000 1 50000 180820357.7 Natco 52.94% 343142.6563 200000 1 100000 34314265632 Bosch 26.40% 1128.673471 50000 0 0 0 Dr Reddy 23.65% 582.5375528 50000 0 0 0 HDFC 19.67% 218.7104519 50000 0 0 0 HDFC Bank 27.40% 1427.68219 50000 1 50000 71384109.48 Voltas 40.41% 26431.03549 50000 1 50000 1321551775 Escorts 57.28% 794096.544 200000 1 200000 1.58819E+11 Pfizer 22.53% 444.0588849 50000 1 50000 22202944.24 Exide 22.36% 425.7894416 50000 0 0 0 Divis Lab 22.19% 408.3925677 50000 0 0 0 Actual 1500000 10 1000000 7.91096E+12 = = Constraints 10 1000000
- 8. 19 February 2019 Equity Portfolio Construction Page 8 Simulation Results CAGR = 55% Market Cap Company Present Value Future Value Return Based on Simulation Weight Weighted Return Eicher Motors 200000 543,707,098,269 64% 0.2 12.77% Kotak Mahindra Bank 50000 70,654,973 27% 0.05 1.37% MRF 50000 364,852,335 35% 0.05 1.73% Balkrishna Industries 200000 75,296,536 22% 0.2 4.37% TCS 50000 20,646,746 22% 0.05 1.11% Natco 100000 68,360,924 24% 0.1 2.43% HDFC Bank 50000 72,507,029 27% 0.05 1.37% Voltas 50000 7,709,935 18% 0.05 0.91% Escorts 200000 3,278,146,864 38% 0.2 7.64% Pfizer 50000 8,401,681 19% 0.05 0.93% 1000000 547,673,675,294 55% 35% Large Cap Mid Cap Total
- 9. 19 February 2019 Equity Portfolio Construction Page 9 Visualization
- 10. 19 February 2019 Equity Portfolio Construction Page 10 Visualization
- 11. 19 February 2019 Equity Portfolio Construction Page 11 Visualization
- 12. 19 February 2019 Equity Portfolio Construction Page 12 Assumptions • All earnings such as Dividends are not considered. • Returns will follow a historic trend • No issue of new shares/rights takes place during the period of 30 years • All 10 Companies continue to operate for the next 30 years • Return of a stock is normally distributed • Factors like economic changes, government rules and regulations will not affect Equity risks and returns.
- 13. 19 February 2019 Equity Portfolio Construction Page 13 Limitations • Limited availability of resources i.e. Rs. 10 Lakhs • All investments are made according to the historical risks and returns. • Does not provide a holistic view of the Equity market (Returns are maximized considering only 15 stocks)