Equity portfolio
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Quantitative Techniques Equity Portfolio Construction 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 Page 2 01 February 2019 Equity Portfolio Construction 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 Page 3 01 February 2019 Equity Portfolio Construction Selected Stocks Sr. No Company Name 1 Eicher Motors 2 Kotak Mahindra Bank 3 MRF 4 Balkrishna Industries 5 TCS 6 Natco 7 Bosch 8 Dr Reddy 9 HDFC 10 HDFC Bank 11 Divis Lab 12 Escorts 13 Pfizer 14 Exide 15 Voltas Page 4 01 February 2019 Size Large Large Large Large Large Large Large Large Large Large Mid Mid Mid Mid Mid Historical Returns (10 Years) 0.7868038 0.3075782 0.5257487 0.6219221 0.314042 0.5293815 0.2640151 0.2364526 0.1967285 0.2739559 0.4009718 0.57276 0.2253158 0.2203103 0.2219007 Equity Portfolio Construction Historical Risks (10 Years) 0.650164346 0.36770514 0.615998476 0.777776877 0.471978505 0.672489971 0.375577924 0.43692798 0.222159787 0.223778391 0.551633959 0.939241288 0.367372493 0.453193568 0.795116252 Setting the Objective functions • Assuming returns to be constant 𝑛 max(𝐹𝑉) = max(𝑃𝑉 1 + 𝑟 ) • As we know Present Value (PV) and Time period (n) is constant i.e. 10 lakhs, n is 30 years. • Therefore max 𝐹𝑉 = 10 lakhs X max( 1 + 𝑟 Page 5 01 February 2019 Equity Portfolio Construction 30 ) Results - Linear Programming Stocks Return Eicher Motors 78.68% Kotak Mahindra Bank 30.76% MRF 52.57% Balkrishna Industries 62.19% TCS 31.40% Natco 52.94% Bosch 26.40% Dr Reddy 23.65% HDFC 19.67% HDFC Bank 27.40% Voltas 40.41% Escorts 57.28% Pfizer 22.53% Exide 22.36% Divis Lab 22.19% Actual (1+r)^30 36501091.77 3119.10888 319514.0764 1999398.506 3616.407153 343142.6563 1128.673471 582.5375528 218.7104519 1427.68219 26431.03549 794096.544 444.0588849 425.7894416 408.3925677 Present Value 200000 50000 200000 200000 50000 200000 50000 50000 50000 50000 50000 200000 50000 50000 50000 1500000 Include 1 1 1 1 1 1 0 0 0 1 1 1 1 0 0 10 Constraints No. of Large Cap Stocks 7 >= No. of Mid Cap Stocks 3 >= Investment in Large 700000 >= Investment in Mid 300000 >= = Constraints Page 6 01 February 2019 10 Equity Portfolio Construction Investment Amt 200000 50000 50000 200000 50000 100000 0 0 0 50000 50000 200000 50000 0 0 1000000 = 1000000 5 3 650,000 200,000 Future Value 7.30022E+12 155955444 15975703821 3.9988E+11 180820357.7 34314265632 0 0 0 71384109.48 1321551775 1.58819E+11 22202944.24 0 0 7.91096E+12 Simulation Results Market Cap Company Present Value Eicher Motors Kotak Mahindra Bank MRF Large Cap Balkrishna Industries TCS Natco HDFC Bank Voltas Mid Cap Escorts Pfizer Total Future Value 200000 543,707,098,269 50000 70,654,973 50000 364,852,335 200000 75,296,536 50000 20,646,746 100000 68,360,924 50000 72,507,029 50000 7,709,935 200000 3,278,146,864 50000 8,401,681 1000000 547,673,675,294 CAGR = 55% Page 7 01 February 2019 Equity Portfolio Construction Return Weighted Based on Weight Return Simulation 64% 0.2 12.77% 27% 0.05 1.37% 35% 0.05 1.73% 22% 0.2 4.37% 22% 0.05 1.11% 24% 0.1 2.43% 27% 0.05 1.37% 18% 0.05 0.91% 38% 0.2 7.64% 19% 0.05 0.93% 55% 35% Visualization Page 8 01 February 2019 Equity Portfolio Construction Visualization Page 9 01 February 2019 Equity Portfolio Construction Visualization Page 10 01 February 2019 Equity Portfolio Construction 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. Page 11 01 February 2019 Equity Portfolio Construction 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) Page 12 01 February 2019 Equity Portfolio Construction Thank you Questions?
