You need to use your business domain knowledge and make some reasonable
assumptions to derive business rules. The skills needed to complete this assignment are introduced in the
lecture slides, videos and tutorial in this week. This assignment builds on the examples in the lecture
videos but asks you to extend the techniques. Understanding the examples in the lecture part is key for
success but you will also have to think and explore.

Automata Inc. produces specialty vehicles by contract. The company operates several departments, each of
which builds a particular vehicle, such as a limousine, a truck, a van, or an RV.
Before a new vehicle is built, the department places an order with the purchasing department to request
specific components. Automata’s purchasing department is interested in creating a database to keep track
of orders and to accelerate the process of delivering materials.
The order received by the purchasing department may contain several different items. An inventory is
maintained so that the most frequently requested items are delivered almost immediately. When an order
comes in, it is checked to determine whether the requested item is in inventory. If an item is not in inventory,
it must be ordered from a supplier. Each item may have several suppliers.

1. Recently, an analysis of Caterpillar Inc. found that it’s equity beta (the beta on its stock) is 1.03. The most recent annual dividend is $4.12/share. A survey of economist finds that the perceived market risk premium is around 6.5%. As of Oct 1, 2020, the yield on a 30-year U.S. Treasury was 1.45%. Given this information, answer the following questions.
   a. Assuming dividends are NOT expected to grow in the future. What is the expected current share price given this information?
   b. Assume dividends are expected to grow by 4% in perpetuity. Given this assumption, what is the expected current share price?
   c. Assume that dividends are expected to grow abnormally for the next 3 years at a rate of 10%. Then, long-term dividend growth is expected to stabilize at 4% annually. Given this information, what is the expected current price?
   d. The actual current price in mid-October is $168.75. Given this information and assuming a constant growth rate, what is the implied growth rate given this price?
   e. Provide one or more possible explanations of why the actual price ($168.75) is so far above the prices calculated in parts (a), (b), and (c).
2. Think of three publicly traded (meaning they have stock prices) U.S. firms, which we will call A, B, and C. A & B should be firms in the same industry and ones you expect to be very similar. Firm C should be a company in a completely different industry. As an example, you could choose Coca-Cola, PepsiCo, and Microsoft. Extract the monthly prices and determine the monthly returns of each of these securities over a 60-month period (From Jan 1, 2015-Dec 31, 2019). If you do not know how to do this, please watch the brief tutorial Getting Stock Returns. Enter all of these returns in a single spreadsheet and do the following.
   a. Determine the mean, variance, and standard deviation of each security’s returns.
   b. Determine the covariance and correlations of each pair’s returns with one another. Briefly discuss each correlation (i.e. does it make sense given the (lack of) similarities?).
   c. Create two portfolios (AB and AC). Begin with $1,000 to invest and evenly distribute into each investment at the beginning of the first month.
3. Determine the value of each investment at the end of the first month, and then evenly divide the total amount into the same to investments at the beginning of the second month. Continue doing this for all 60 months (this is called rebalancing an equally-weighted portfolio).
4. Determine the monthly returns of these two portfolios.
   Speculate which of the two portfolios should have the lower standard deviation and why.
5. Calculate each portfolio’s standard deviation and compare to your expectations in (ii). How do the portfolios’ standard deviations compare to the standard deviations of the individual securities that comprise the portfolios? Discuss any lessons/insights.

In the above graph, portfolios are formed using an increasing number of securities. Sketch the expected “Total Portfolio Risk” dotted-line if

a. Each additional stock was from the same industry as A&B.
b. Each additional stock was from a different industry than the other stocks.

• Explain why your two graphs are either similar or different from one another.