Calculate the optimum point

Assignment Help Management Information Sys

Reference no: EM131439767

Need to use zynga inc stock data

1 Introduction

The purpose of this assignment is to apply the knowledge you have acquired so far in this module to a real- world scenario. This is a group assignment. It facilitates application of several techniques, namely linear regression, time-series analysis, and linear programming.

2 Financial Data

Buying and selling of stocks (or bonds and other securities) is a potentially profitable business, but without proper analytics, it can lead to big financial losses.
When designing a stock portfolio, some of the decisions to take are:
- The capital to invest;
- The risk the investor is willing to take;
- The time the investor will wait for his/her returns.

The use of analytics methods can help with some of these decisions.

3 Assignment Description

Your task is to allocate an investment portfolio of up to $50,000 (US Dollars) between a set of companies, all trading at either the NYSE or NASDAQ stock exchanges. Your objective is to maximise the expected return of the portfolio, after a two week investment period, from the 6th March 2017 (opening price) until the 17th March 2017 (closing price).

Establish a Portfolio of Companies
Your portfolio must be comprised of as many companies as there are members in your group (four or ftve). The first letter of the Ticker code of each company must match the first letter of each of your team member's names (e.g. Aaron, Marie, Anne and Francis can choose AAPL, MSFT, AMZN and FB). The companies must trade at the NASDAQ or NYSE stock exchanges only.

Data Gathering
Download daily data for each of your companies, for the period from 2nd December 2016 until the 3rd March 2017 (inclusive). Choose companies likely to give a positive return on investment. Acquire your data from Yahoo Finance:

https://finance.yahoo.com/ 1

Data Modelling and Prediction

For each company, calculate the 5-day moving average (MA(5)) for its daily Close Price. Then perform linear regression on the MA(5) data. Using the resulting model, extrapolate a predicted close price for the 17th March 2017. The predicted return of that stock is then calculated as:

PR = (PCP - LCP )/LCP

where LCP is the last closing price (3rd March 2017), and PCP is the predicted closing price (17th March 2017). You can ignore transaction costs.

Risk Measure

Calculate an investment risk figure for each company. We will use the Coefficient of Variation (CV) as the risk measure; it is calculated as:

CV = σ/µ

where σ is the standard deviation of the (raw) close price data for each company, and µ its mean close price, for the training period stated above.

Portfolio Optimisation

Formulate this problem as an integer linear programming problem:

- The objective is to maximise the return of investment;

- You can invest up to $50,000;

- Do not allow the total weighted risk to go above $2,000 (the total weighted risk is calculated by multiplying each dollar invested in each company by the risk (CV) associated with that company, and adding it for all companies);

- To minimise risk, do not invest more than $20,000 on a single company.

Calculate the optimum point, using Excel Solver. Calculate the expected return, and the expected profit. Once closing price data for the 17th March 2017 becomes available, calculate the actual return. Compare both figures.

Reference no: EM131439767

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Reviews

len1439767

3/25/2017 2:07:18 AM

3. Include Sensitivity Analysis in your report. State which are the binding and non-binding constraints, and shadow prices. Refer to these concepts in layman’s terms, which someone that does not understand linear programming could understand. 4. Include alternative measurements of risk in your portfolio optimisation. 5. Extend your portfolio from four companies to eight (or from five to ten), using the same (first letter) restriction as before. For this case alone, your page limit is increased from 8 to 12 pages (or from 9 to 13); ensure the extra pages are used for new company analysis only (one page per company).

len1439767

3/25/2017 2:07:00 AM

You can also attempt extra credits for your project with the following objectives: 1. Instead of calculating a MA(5) on raw Close prices before applying linear regression, choose a custom approach for each stock. Try out different approaches (e.g. different MAs, WMAs (Weighted Moving Averages), log/exponential transformations, etc), and train your linear regression model with data. Then use the remaining ten days to obtain a Test RMSE. Choose the modelling approach that minimises the test error, for each stock. 2. To further minimise risk, do a pair-wise correlation analysis of all the stocks comprising your portfolio. For each pair of stocks, calculate the correlation between their raw prices for the training period. Include an extra constraint in your optimisation, not allowing more than $20,000/r to be spent between the pair of stocks with the highest correlation (r) between then.

len1439767

3/25/2017 2:06:33 AM

2. The document should be up to eight pages long: this does not include cover page and reference list, but includes all graphics; 3. No table of contents and appendixes of any form are allowed. You must also submit a Microsoft Excel spreadsheet: 1. Include all your data and calculations; 2. Separate data and linear programming calculations using separate Excel sheets; 3. Label cells carefully, to make it clear where objective function, constraints, and solution are. Please note that only your PDF document will be evaluated (but we will check your Excel spreadsheet for the consistency of your calculations, plot generation, etc.) Criteria for evaluation include clarity of presentation, capacity to succinctly describe all findings, justification for portfolio composition (apart from naming constraint mentioned above), and critical analysis of results and methodology.

len1439767

3/25/2017 2:06:21 AM

1. At least the following is expected: (a) An appropriate cover page; (b) An introduction page, detailing the contents of the document; (c) One page analysis per stock composing your portfolio, including a short introduction to the company, a time-series plot, a verbal analysis of its market behaviour for the analysed period (and possible causes), the used variable transformations, the resulting model, the predicted return, and the risk measured. (d) A description of your optimisation setup, including objective function and all constraints; (e) A comparison of your predicted profit and the observed profit on the (f) An analysis of the difference between predicted and observed profit, including a description of the limitations of the analytics methods applied.

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