Financial Math

Homework 8

Due November 8, 2022

For this week’s homework, please write about a project and come up with a group. You’re allowed to change your project, group, and any other details, but I want you to come up with a plan early. Even if you are working in a group, please submit this homework individually–you may come up with questions and methods together with your group, though.

1. Write down 5 questions that you would like to answer regarding your project (for instance, does salary level in baseball predict home run production?), and

2. In complete sentences, talk about the methods you will use to solve each one (ex. linear regression on salary to predict homeruns, algebraic calculations, literature re- view).

More on the project below.

As the major part of your remaining work this semester, you will be working on a class project, either individually or as a group. For individual projects, you will submit a 4-page single-spaced report. For each additional member of the group, your report should have an additional page for each member of the group (up to 4 people). Thus, a 4-person group should submit 7-page report. Below are some suggested projects; you can find others in the slides for the class on November 1.

You may pick one or choose your own—you’re encouraged to pick anything that you are interested in, as long as it has financial and math components. Each report should also contain some concrete mathematical calculations or data analysis whenever appropriate. You may find references discussing some of these ideas. You can use these as references (and cite them!), but you are also expected to contribute some original ideas or calculations.

Project 1 Junk bonds. What are junk bonds? Why would anyone want to invest in such bonds, given that their risks are higher? Analyze the historical performance of some historical junk bond funds in comparison with mutual funds, the overall stock market index, etc. Give some concrete calculations; for example, compare the Sharpe ratio of different assets. How do junk bonds perform relatively to other assets during downturns?

Project 2 Correlation in the stock market. Analyze the correlation of different sectors or stocks in the stock market. For example, compare consumer staples, energy, health care, technology, etc. You can analyze the historical prices of sector ETFs like XLP, XLE, XLV, XLK. During economic downturns, which sectors are best? What about when the economy is doing well?

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Project 3 Gamestop and wallstreetbets. How did the wallstreetbets reddit group bring down Melvin Capital and other short sellers? As part of their strategy, they did a “short squeeze” on Gamestop. You may also want to comment on the “gamma squeeze” which was an even more powerful version of the short squeeze.

Project 4 US historical worker salaries. You can discuss historical trends in salaries in the US. You can consider ideas such as salaries in specific industries, along class lines, along racial lines, executive salaries vs. workers, etc.

Project 5 Inflation. There are many directions to go with this. How does inflation affect bond prices, or how does it affect stock prices? You can look at different sectors of the market. Or you can look at how inflation affects the consumer or worker.

Project 6 Bond prices around the world. Why do some countries need to pay a higher yield on their bonds? How does the US’s status as the global reserve currency affect its bond prices?

Project 7 Predict actuarial claims. Kaggle is a website that has a lot of data analysis projects (and competitions). One project is to predict actuarial claim values given demo- graphic information and injury type. This may be a more challenging project, but one where you will get experience doing real actuary work! Here is the webpage with more information: https://www.kaggle.com/c/actuarial-loss-estimation.

Project 8 Predict house prices. Similar to the previous project, you can predict house prices. https://www.kaggle.com/competitions/house-prices-advanced-regression-techniques

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