# Long Dong Chinese Man

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This assignment is about applying statistics in finance. Before starting this assignment, it is important to review the Note on Review of Statistics. It is also recommended to use statistical functions in Excel or Spreadsheets for calculations. In accordance with the Coursera Honor Code, I, Amanda Milligan, verify that the answers given are solely my own work.

Exxon Oil Company shareholders are exposed to various risks associated with holding its shares, particularly in relation to the demand for Exxon’s fuels from the airline industry. If the economy weakens, there is typically a decrease in travel, resulting in lower demand for Exxon’s fuels. Such risks are categorized as Specific/Idiosyncratic Risk for Exxon’s shareholders.

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There are three securities (X, Y, and Z) available for selection. The next year’s economy will experience an expansion, normal, or recession state with probabilities of 0.30, 0.35, and 0.35 respectively. The returns (%) on these securities in each state are as follows: Security X {expansion = +10, normal = +8, recession = +6}; Security Y {+25,+10,-10}; Security Z {+7.5,+7.5,+7.5}. Assuming the investor is risk neutral, they must choose between investing in Security Y or Security Z. In this case, the investor is indifferent between Y and Z.

Your grandfather is seeking your investment advice because he values your expertise in finance and statistics. He is concerned about the recent financial turmoil and wants a low-risk portfolio recommendation. There are three portfolio options (A, B, and C) to consider for the upcoming year, which is expected to have an expansionary, normal, or recessionary state with probabilities of 0.40, 0.40, and 0.20 respectively. The corresponding returns (%) for these portfolios in each state are as follows:

• Portfolio A: Expansion = +13, Normal = +9, Recession = +8.5
• Portfolio B: Expansion = +10, Normal = +9, Recession = +5
• Portfolio C: Expansion = +13, Normal = +8, Recession = +7.5

You must determine which investment option best aligns with your grandfather’s needs.

Investors typically demand a risk premium when holding a security, regardless of the source of the additional risk.

The covariance between the returns of a stock and its own return is always one, but calculating covariances among the returns of multiple stocks can be complex.

As a CEO, you are considering providing smartphones to your employees in order to improve their availability for clients and sales. However, you have concerns about potential work distractions such as gaming and social media updates. To investigate this issue, you conducted an experiment where 6 employees were randomly selected. Three of them received smartphones while the other three continued using their existing technology. The table below shows the changes in sales for each employee. Your goal is to determine the correlation between having a smartphone and an increase in sales. You can use the correl spreadsheet function to calculate this correlation. Please provide the correlation percentage without including the % sign.

Employee Smartphone Sales Change
Anthony Yes 60
Kira No/<>/</>
/>
Michael/t/>No/
Scarlett/t/>Yes/<-20/-20/ <>Yes

-5/-5/
<>No

-35/-35/

Investors typically avoid taking on risk, resulting in a higher price for government bonds compared to corporate bonds that are otherwise similar.

Your client has three securities to choose from: X, Y, or Z. The world can fall into one of three categories: expansion, normal, or recession. Each category has probabilities of 0.40, 0.40, and 0.20 respectively.

During the expansion state:
– Security X offers returns of +14%
– Security Y offers returns of +11%
– Security Z offers returns of +13%

In the normal state:
– Security X provides returns of +10%
– Security Y provides returns of +9%
– Security Z provides returns of +8%

In the recession state:
– Security X has returns of +7%
– Security Y has returns of +8%
– Security Z has returns of +7.5%

Based on this information, which security should you discourage your client from investing in?

You have recently become the fund manager at a brokerage firm. Thomas, your assistant, is giving you an update on the current portfolio. He suggests transferring some funds from Alpha to Gamma for better diversification. Here is the data on all three stocks:

Beta\$27.50 20%\$27.50\$26\$25

Stock Current Price Current Weight Next Year’s Price (Expansion) Next Year’s Price (Normal) Next Year’s Price (Recession)
Alpha 40 80% 48 44 36

Based on this information, Thomas believes that reallocating some of our funds from Alpha to Gamma will help improve diversification. Do you agree?

Suppose there are two mortgage bankers. Banker 1 has two \$1,000,000 mortgages to sell. The borrowers live on opposite sides of the country and face an independent probability of default of 5%, with the banker able to salvage 40% of the mortgage value in case of default. Banker 2 also has two \$1,000,000 mortgages to sell, but Banker 2’s borrowers live on the same street, have the same job security and income. Put differently, the fates and thus solvency of Banker 2’s borrowers move in lock step. They have a probability of defaulting of 5%, with the banker able to salvage 40% of the mortgage value in case of default. Both Bankers plan to sell their respective mortgages as a bundle in a mortgage-backed security (MBS) (i.e., as a portfolio).

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