Financial Mathematics- Writing Assignment

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timer Asked: Jun 24th, 2018
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Question description

You are an actuary providing your services as a consultant for a bank. The bank has an opportunity to make a package of loans totaling 500 million (500M). This package of loans will be repaid by level end of year payments totaling 50M for 30 years.

In order to o↵set some of the bank’s initial liability and generate capital for this invest- ment the bank asks you to structure a bond for them. The purchase price must be 200M and it will have annual coupons. It is your goal to set the face value (F) nominal coupon rate (↵(1)) and redemption amount (C).

Notice, if the bank had not packaged up the debt into a bond, and just made the package of loans through its own capital, then the bank’s APY would have been 9.3%. You should try and find a set of values for F, C, ↵(1) which get the bank’s APY as close to the original 9.3%, or higher. as you can. Also, to make the bond a worthwhile investment to the investor you should ensure that the APY to the investor is at least 1%.

Writing Assignment Instructor Tyler Mayer Due in class 6/28/2018 This assignment is in the fulfillment of the AMS department technical writing requirement. It is designed to test your ability to communicate ideas of a technical nature from your field with a layperson or another direct member of your field. 1 Question You are an actuary providing your services as a consultant for a bank. The bank has an opportunity to make a package of loans totaling 500 million (500M). This package of loans will be repaid by level end of year payments totaling 50M for 30 years. In order to o↵set some of the bank’s initial liability and generate capital for this investment the bank asks you to structure a bond for them. The purchase price must be 200M and it will have annual coupons. It is your goal to set the face value (F) nominal coupon rate (↵(1) ) and redemption amount (C). Notice, if the bank had not packaged up the debt into a bond, and just made the package of loans through its own capital, then the bank’s APY would have been 9.3%. You should try and find a set of values for F, C, ↵(1) which get the bank’s APY as close to the original 9.3%, or higher. as you can. Also, to make the bond a worthwhile investment to the investor you should ensure that the APY to the investor is at least 1%. 2 Assignment Create a technical report to the bank detailing your recommended bond structure. 1. State clearly the values for the three parameters described above 2. Briefly explain what the bank’s net cash flow will be as a result of making this package of loans and issuing this bond. 3. State the new APY a↵orded to the bank in this situation. 4. Briefly explain the cash flow, generated by the bond, for the investor. 1 5. State the APY a↵orded to the investor. 6. Briefly outline the tradeo↵ between APY a↵orded to the bank and APY a↵orded to the bond investor. 3 Grading This project is to assess weather or not you can create a short concise technical report able to communicate with Professionals/laypersons in/out of your field. The report should be no more than 2 pages double spaced including figures (if any). It should: • Be self contained. That is define any interest terms you use (such as coupon, face value, nominal coupon rate, etc.) and not require someone to have taken an interest theory class to understand. For example do not include your calculations, just the final results with explanations. 30% • Contain a (brief) mathematically correct analysis of your recommended investment strategy. Outline the bank’s resulting cash flow, and the investor’s resulting cash flow and their corresponding APY’s as well as a simple explanation (single equation, or explanation in terms of the three values calculated above) of the relationship between the bank’s APY and the investor’s APY. (For example if you increase C per unit what is the relationship between the bank’s and investor’s APY?) 30% • Be neatly laid out optionally including figures/charts/visuals pertinent to your analysis/decision for the Bank and use proper conventions of the english language (spelling, grammar etc.) 40%. 2

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Robert F
School: New York University

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