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Qant 620 - Non-Linear Project

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Non-linear project

Course: QANT 620

Name: Ruoxi Li

ID: 0882298

  1. Company introduction

I decided to select data from those three companies (1999-2013).




Brief introduction

This is an American multinational technology corporation.

This is an American electronic commerce and cloud computing company.

This is an American multinational automaker.

  1. Data Collection

I collected the data from Yahoo Finance, and the whole data you can find in Excel clearly.

[pic 1]

Then, I calculated the annual return out.

[pic 2]

  1. Defining the decision variables

In this problem, we must determine what percentage of the total funds invested should go toward the purchase of each of the three stocks. Thus, to formulate the model for this problem, we need the following three decision variables:

P1= proportion of total funds invested in Microsoft

P2=proportion of total funds invested in Amazon

P3= proportion of total funds invested in Ford

  1. Defining the objective function

The objective in this problem is to minimize the risk of the portfolio as measured by its variance. In general, the variance of a portfolio consisting of n investments is defined in

Portfolio variance=    [pic 3]

So, using the preceding formula, the objective for our problem is stated as:

MIN: 0.0988 p21 + 0.1132 p2 + 0.07248 p23

+2(0.113212 p1p2 +0.06378 p1p3 +0.46542 p2p3)

  1. Defining the constraints

There are several constraints that apply to this problem. First, this is accomplished by the following constraint:


Next, we must ensure that minimum 12% rate of return while minimizing total risk. The following constraints enforce this restriction:

0.7088P1+0.2243P2+ 0.0669P3>= 12%

Finally, because the decision variables must represent proportions, we also should include the           following upper and lower bounds:

P1, p2, p3 ≥0

P1, p2, p3 ≤1

  1. Implicating the model

MIN: 0.0988 p21 + 0.1132 p2 + 0.07248 p23



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