**Portfolio Optimization using Markowitz model with using r**

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**Methodology**

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In this project, optimal portfolio will be developed by using Markowitz Portfolio Theory (MPT). The underlying concept of MPT is to minimize risk of portfolio while not sacrificing expected return (Sirucek & Kren, 2015). MRT is based on diversification effect (Bhat, 2009). Based on CAPM^{[1]} theory weights of the individual stocks in the different portfolios (exist in the efficient frontier) will be derived. Portfolios will be developed based on the analysis of each stock’ individual risk and return, and covariance with other stocks. These efficient portfolios will be generated based on the assumption of no short selling. Stocks in each portfolio will be put together according to some predefined criteria. The optimal portfolio will be selected from the efficient portfolio that maximize return for given level of risk. The optimal portfolio will be considered with inclusion of risk-free assets and efficient portfolio. The current yield of 1 Year Treasury Bond will be considered as proxy of risk-free rate. The portfolio will be designed with ten stocks from DJIA^{[2]}. The underlying rationale of choosing DJIA is the potential diversification across almost all traded sectors. From twenty stocks from five sectors (financial, insurance, automobile, service, and oil & gas), ten stocks will

In this project, optimal portfolio will be developed by using Markowitz Portfolio Theory (MPT). The underlying concept of MPT is to minimize risk of portfolio while not sacrificing expected return (Sirucek & Kren, 2015). MRT is based on diversification effect (Bhat, 2009). Based on CAPM^{[3]} theory weights of the individual stocks in the different portfolios (exist in the efficient frontier) will be derived. Portfolios will be developed based on the analysis of each stock’ individual risk and return, and covariance with other stocks. These efficient portfolios will be generated based on the assumption of no short selling. Stocks in each portfolio will be put together according to some predefined criteria. The optimal portfolio will be selected from the efficient portfolio that maximize return for given level of risk. The optimal portfolio will be considered with inclusion of risk-free assets and efficient portfolio. The current yield of 1 Year Treasury Bond will be considered as proxy of risk-free rate.

The portfolio will be designed with ten stocks from DJIA^{[4]}. The underlying rationale of choosing DJIA is the potential diversification across almost all traded sectors. From twenty stocks from five sectors (financial, insurance, automobile, service, and oil & gas), ten stocks will

The companies selected

Table 1: List of 20 Companies from Five Industries |
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Sector |
Company |
Symbol |

Financial |
JPMorgan Chase & Co. | JPM |

Bank of America Corp. | BAC | |

Wells Fargo & Co. | WFC | |

Citigroup Inc. | C | |

Insurance |
American Equity Investment Life Holding Co. | AEL |

Universal Insurance Holdings, Inc. | UVE | |

FBL Financial Group Inc. | FFG | |

Prudential Public Limited Co. | PUK | |

Automobile |
General Motors Co. | GM |

Ford Motor Co. | F | |

Honda Motor Co. Ltd. | HMC | |

Tesla, Inc. | TSLA | |

Service |
Amazon.com, Inc. | AMZN |

Apple, Inc. | AAPL | |

Walmart Inc. | WMT | |

The Home Depot, Inc. | HD | |

Oil and Gas |
NextEra Energy, Inc. | NEE |

Duke Energy Corporation | DUK | |

The Southern Company | SO | |

Dominion Energy, Inc. | D | |

Source: Author (2018) |

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**TASK TO DO**

**Analysis of the stocks above from those 20 companies above using data from 2013 to 2017, and analyses their returns and standard deviation- Both analysis of the data graphically and in tabular form and you also test for normality****Optimal Risky Portfolio – Explain both in tabular from and plot the graph****Portfolio Selection process****Optimal Risky portfolio and risk free treasury bearer bonds- graph is needed here and explanation of the graph. Use the stocks above****Efficient Frontier and the capital allocation line…Graph is needed here****Which stocks you will recommend to investors and why. Please don’t forget to include the frontier where the percentage of stock are being 10% risky and 90% risky free****I need both the r codes and the data set that you get from yahoo finance**

[1] CAPM: Capital Assets Pricing Model

[2] DJIA: Dow Jones Industrial Average

[3] CAPM: Capital Assets Pricing Model

[4] DJIA: Dow Jones Industrial Average