The Solution for the Investment Problem

Introduction

Before, investing, it is important to evaluate the risk-return profile of an individual security and entire portfolio. Further, when selecting a stock to include in a portfolio, it is important to take into account the concept of diversification. Diversification lowers the overall risk of a portfolio (Brigham & Michael 2009). The paper seeks to advise an investor who intends to spend a sum of $500,000 in a portfolio that is made up of shares from three sectors. In the end, the investor will be advised on the amount of money to invest in each stock, the resulting portfolio risk, and return. The targeted sectors are industrial, finance, and health sectors. Further, 5 companies are selected from each industry and this brings the total number of shares in the portfolio to 15. A summary of the companies selected is presented in appendix 1. Historical monthly share prices for the companies are collected for 5 years. This is equivalent to 60 months. The expected return and beta for each portfolio will be calculated using the data for monthly share prices. Further, the data for the S&P 500 index will be collected to represent movement in the market.

Discussion

The results in appendix 2 show that the companies have different values of expected return and risks. Companies operating in the industrial and financial sectors tend to have a low of both expected return and standard deviation. This can be an indication that the two industries are less volatile. On the other hand, companies in the health sector have a large range of both risk and return. Thus, risk-averse investors might prefer to invest in the industrial and financial sectors while investors who are risk-takers will prefer to invest in the health sector because they offer high returns. Under the industrial sector, Apple, Inc. had the highest value of the expected return while Hewlett Packard Corporation had the least amount of return (Simon 2012). The calculations show that the stock of Hewlett Packard Corporation had the highest risk level risky while that of Deere & Company had the least amount of risk. Under the health sector, Achillion Pharmaceuticals, Inc. had the highest value of the expected return while American Caresource Holdings, Inc. had the least amount of return. Further, the stock for Achillion Pharmaceuticals, Inc was most risky while that of Cooper Companies, Inc. was the least risky. Further, in the case of the Finance sector, Prudential Financials, Inc. had the highest value of the expected return while Bank of America had the least amount of return. In terms of risk, Bank of America was the most risky while Wells Fargo was the least risky in this category. In the entire portfolio, Achillion Pharmaceuticals, Inc. had the highest return with the highest amount of risk. The company also had the highest value of systematic risk (beta). A review of risk and return is important because investors have different attitudes towards risk (Shepherd 2008). The total return for the entire portfolio is 0.0174.

After the estimation of risk and return for individual security and for the portfolio, a model will be built to solve the puzzle of the amount to invest in each security. The model is built on various assumptions. First, the maximum amount available for investment is $500,000. Secondly, the beta for the entire portfolio should be 1.1. Further, the minimum expected return of the portfolio should be 0.08. Also, not more than 12% of the entire capital should not be allocated to one stock and not more than 15% of the total capital should be allocated to all companies that the value of beta exceeds 1.2. Some limitations are put on the amounts allocated for each industry; at most 15% of the entire capital should be in the health sector, at least 10% in the industrials and a minimum of 20% in the financial sector. A spreadsheet model is constructed to solve the problem. The model is presented in appendix 3. All these assumptions are taken into account in the model (Falkenstein 2009).

Solution and recommendation

The solution for the investment problem is presented in appendix 4. The goal of the investor is to maximize the expected return and minimize risk. An efficient portfolio gives a combination of securities that offers the highest return at a given level of risk or the least amount of risk for a given level of return (Block & Hirt 2007; Damodaran 2008). The solution shows that two companies should be dropped, these are 3M Company and American Caresource Holding, Inc. These two companies were not attractive. The results also show that the maximum possible allocation will be made to companies such as Apple, Inc., Deere, and Company, and Wells Fargo among others. The solution is made up of companies from all the three sectors Besides, they have different amounts of risk and return. The portfolio will satisfy the customer’s need for an 8% return and 1.10 for systematic risk.

References

Block, S & Hirt, G 2007, Foundations of financial management, McGraw-Hill/Irwin, USA.

Brigham, E & Michael, J 2009, Financial management theory and practice, South-Western Cengage Learning, USA.

Damodaran, A 2008, Strategic risk taking: a framework for risk management, Pearson Education Inc., US.

Falkenstein, E 2009, Finding alpha: the search for alpha when risk and return break down, John Wiley & Sons, US.

Shepherd, S 2008, Cash holdings, stock split, and mergers: examining risk and return in the equity markets, ProQuest, US.

Simon, A 2012, CAPM vs behavioural finance: risk and return – does behavioural finance provide better explanations than the CAPM?, GRIN Verlag, Germany.

Appendices

Industrial Companies Share price ($)
1 Apple Inc. 126.32
2 Hewlett Packard 33.7
3 Ford Motor Company 15.65
4 General Electric Company 26.92
5 John Deere 91.14
Health
1 3M Company 159.5
2 Acadia Healthcare Company, Inc. 68.46
3 Achillion Pharmaceuticals, Inc. 9.62
4 American Caresource Holdings, Inc. 1.91
5 Cooper Companies, Inc. 179.33
Finance
1 Prudential Financial, Inc. 86.77
2 Bank of America 16.49
3 Citigroup Inc. 53.97
4 JP Morgan Chase & Co. 65.45
5 Wells Fargo& Co. 55.51
Market index S&P 500 2105.33
Appendix 1: Summary statistics for the companies selected.
Expected return Standard deviation Variance Covariance between each stock and S&P Beta (variance/cov)
Apple Inc. 0.02739 0.07298 0.00533 0.00123 0.87823
Hewlett Packard 0.00379 0.09963 0.00993 0.00211 1.51207
Ford 0.01115 0.08879 0.00788 0.00213 1.52352
General Electric 0.01263 0.06589 0.00434 0.00201 1.43972
John Deere 0.01409 0.07110 0.00506 0.00173 1.24235
3M Company 0.01551 0.04945 0.00245 0.00153 1.09634
Acadia Healthcare Company, Inc. 0.04911 0.10677 0.01140 0.00051 0.36835
Achillion Pharmaceuticals, Inc. 0.06144 0.31014 0.09619 0.00304 2.17897
Americal Caresoruce Holdings, Inc. -0.00256 0.15637 0.02445 0.00178 1.27924
Cooper Companies, Inc. 0.02821 0.06441 0.00415 0.00012 0.08846
Prudential Financial, Inc. 0.01530 0.07655 0.00586 0.00223 1.59542
Bank of America 0.00851 0.10410 0.01084 0.00224 1.60601
Freedie Mac 0.01241 0.09040 0.00817 0.00256 1.83774
JP Morgan Chase 0.01296 0.07736 0.00598 0.00219 1.57057
Wells Fargo 0.01458 0.05596 0.00313 0.00160 1.14543
S&P 500 0.01178 0.03735 0.00140
Appendix 2: The estimated values of beta and expected return for the companies selected.
Maximize
Shares Apple Inc. Hewlett Packard Ford General Electric John Deere 3M Company Acadia Healthcare Company, Inc. Achillion Pharmaceuticals, Inc. Americal Caresoruce Holdings, Inc. Cooper Companies, Inc. Prudential Financial, Inc. Bank of America Freedie Mac JP Morgan Chase Wells Fargo
Total invested 60000 2500 60000 2500 60000 15000 29500 500 500 29500 25000 60000 55000 40000 60000
Return per share 0.0274 0.0038 0.0112 0.0126 0.0141 0.0155 0.0491 0.0614 -0.0026 0.0282 0.0153 0.0085 0.0124 0.0130 0.0146 0.017422106
Subject to
Apple Inc. Hewlett Packard Ford General Electric John Deere 3M Company Acadia Healthcare Company, Inc. Achillion Pharmaceuticals, Inc. Americal Caresoruce Holdings, Inc. Cooper Companies, Inc. Prudential Financial, Inc. Bank of America Freedie Mac JP Morgan Chase Wells Fargo Total Limit
Beta (variance/cov) 0.8782 1.5121 1.5235 1.4397 1.2424 1.0963 0.3684 2.1790 1.2792 0.0885 1.5954 1.6060 1.8377 1.5706 1.1454 1.253091913 1.1
Industrial 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 185000 50000
Health 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 75000 75000
Finance 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 240000 100000
Individual Constraints
Apple Inc. 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 60000 60,000
Hewlett Packard 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 2500 60,000
Ford 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 60000 60,000
General Electric 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 2500 60,000
John Deere 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 60000 60,000
3M Company 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 15000 60,000
Acadia Healthcare Company, Inc. 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 29500 60,000
Achillion Pharmaceuticals, Inc. 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 500 60,000
Americal Caresoruce Holdings, Inc. 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 500 60,000
Cooper Companies, Inc. 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 29500 60,000
Prudential Financial, Inc. 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 25000 60,000
Bank of America 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 60000 60,000
Freedie Mac 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 55000 60,000
JP Morgan Chase 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 40000 60,000
Wells Fargo 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 60000 60,000
Return 0.0274 0.0038 0.0112 0.0126 0.0141 0.0155 0.0491 0.0614 -0.0026 0.0282 0.0153 0.0085 0.0124 0.0130 0.0146 0.0174 0.08
Beta 0 1 1 1 1 0 0 1 1 0 1 1 1 1 0 306000 75,000
Appendix 3: A spreadsheet model for solving the portfolio problem.
Solution
Apple Inc. 60000
Hewlett Packard 330.4247627
Ford 60000
General Electric 1099.582003
John Deere 60000
3M Company 0
Acadia Healthcare Company, Inc. 36620.08735
Achillion Pharmaceuticals, Inc. 1901.71366
Americal Caresoruce Holdings, Inc. 0
Cooper Companies, Inc. 36478.19899
Prudential Financial, Inc. 13715.8772
Bank of America 60000
Freedie Mac 41548.03867
JP Morgan Chase 28708.22601
Wells Fargo 60000
Industry
Industrial 181430.0068
Health 75000
Finance 203972.1419
Risk level (beta) 0.087200632
Return 1.09
Appendix 4: Solution to the portfolio problem.

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