3 Assignment Description This project is a (simple) simulation of modelling and optimising an investment portfolio, stated as follows: After a year of 2022 marked by the conflict in Ukraine, resulting energy and cost of living crisis, and followup hyper inflation, which led to a severe contraction of financial markets, 2023 proved to be a remarkable recover period. To exploit this period and recover from losses from the previous year, a group of investors tasked you with setting up a portfolio of companies, modelling their price behaviour, and optimising a two-week investment strategy, from the 15th May 2023 to the 26th May 2023, while subject to specific risk constraints.

3.1 Establish a Portfolio of Companies Your portfolio must be composed of twice as many companies as there are members in your group (e.g. eight companies for a group of four members). The first letter of the Ticker Code of each company must match the first letter of each of your team members first (given) name, as registered with UCD. For example, Grace Hopper can choose GOOGL (Alphabet Inc.) and GILD (Gilead Sciences, Inc.), while Alfred Kinsey can choose AAPL (Apple Inc.) and AMZN) (Amazon.com, Inc.). All companies must trade on the NASDAQ Stock Exchange.

3.2 Data Gathering Download daily data for each of your companies, for the period from the 10th April 2023 until the 12th May 2023 (inclusive). Based on performance during this period, choose companies likely to give a positive return on investment. Acquire your data from Yahoo Finance: http://finance.yahoo.com/

1 3.3 Descriptive Analytics For each company, start by sequentially numbering each daily entry as a Trading Day (TD) (i.e. data for the 10th April 2023 is T D = 1). Next, you must calculate the 5-day Least Squares Moving Average (LSMA(5)) of the Closing Price (CP). The LSMA(5) at day t is calculated as follows: LSMA(5)t = LR(CP :TD,5)(t) (1) where LR(CP :TD,5) is a linear regression model of CP given TD, for the 5 previous days. In other words, to calculate the LSMA(5) for day t, build a linear regression predicting CP given TD, using data from t 5 to t 1, and make a prediction for day t using the model2 . Finally, to visualise the data, create a line plot of TD versus CP, for the period from TD=1 until TD=25, with a second line (in the same plot) showing the calculated LSMA(5) data from TD=6 until TD=25.

3.4 Predictive Analytics For each company, perform linear regression on the Closing Price (CP) data, using TD as the predictor. Use the whole data (from the 10th April 2023 until the 12th May 2023) as your training data. Report the predicted Daily Price Increase (DPI) of each company, as the slope of the calculated model, along with the train RMSE and R2 of the model. 1Once you have found the main page of a stock, choose Historical Data, choose your dates range (make sure all required days are included), select Daily and Historical Prices, click Apply, then choose Download Data. 2The easiest way to achieve this is to use the =FORECAST.LINEAR() formula.

2 3.5 Prescriptive Analytics

The strategy you will employ relies on deciding how many days to invest in each company. The objective is to maximise the expected return of the investment: The expected return of each company is calculated by multiplying the predicted DPI of that company by the number of shares bought for the company, and multiplying the result by number of days of investment in the company. Add the expected return of investment figures for all companies, to obtain the total expected return of the investment. You will optimise how many days to invest in each company: Ensure that the number of days of investment is a whole number, through the use of Integer Linear Programming in Excel. In order to control the risk of your investment strategy, use the following constraints: Invest no more than 10 * R2 days in each company, where R2 is the training Coefficient of Determination, calculated in Section

3.4. Invest as close to $20,000 (US Dollars) per company as possible. Calculate the number of shares bought for each company based on this constraint and its latest CP figure. For example, if company ABCDEs closing price on the 12th May 2023 was $900, then you can buy 22 shares of that company. For a portfolio with P companies, invest no more than an average of $7,500 * P per day, across all 10 days of investment. Calculate the optimum point (number of days to invest in each company), using Linear Programming. Report your solution, along with the total amount invested, and the total expected return. Report the actual return of the investment using real data: Download the actual market data for the investment period (15th May 2023 to 26th May 2023), and calculate the actual return for the investment period. Use the Open Price of the 15th May 2023 as the stock price for each company, while ensuring that you are still investing as close to $20,000 per company3 . Use the Closing Price corresponding to the last investment day (e.g. 22nd May 2023 for a company in which you invested 6 days). The profit per company is then simply calculated as (CP OP)#shares bought. Compare and analyse the difference between both figures.