ECON483B SUM2019 Mini-Cases PDF

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YOUR FULL NAME: _________________________________________________________________

ECON 483B: Economics of Fixed Income Markets, Summer 2019 Dr. Charles Sebuharara

END-OF-TERM MINI-CASES [10 points in total] Due Date: No later than 11:59PM E.T. on TUESDAY, August 6, 2019. (Some Final Exam may be drawn from these mini-cases!).

IMPORTANT GENERAL NOTES ABOUT DUE DATE AND SUBMISSION FORMAT:

1. Due date: 11:59 PM E.T. on TUESDAY, August 6, 2019. 2. There are TWO (2) short mini-cases in this assignment. Each mini-case is worth 5 points, for a total of 10 points. Please, solve each mini-case and present your work of each on a separate page. 3. Please clearly type or mark your answers to avoid any ambiguity and to facilitate grading. Double check your answers! 4. Please, UPLOAD your completed typed assignments (in Microsoft WORD or PDF) to the course site on Blackboard in MyCourses. Please, print your attached file before submission to make sure it is completely legible and its prints exactly as you intended. 5. Please, make sure you rename the file to include your Full Name, Course number (ECON483B) and Term (Summer2-2019) before you upload it; the same information, as well as the title of the assignment, must be included in the paper (WORD or PDF and EXCEL). Refer to the syllabus for the other submission details. 6. You should consider working on these mini-case assignments as seriously as you would on an exam, with the difference that these assignments are “open-book,” giving you the opportunity to go back and check the material covered in the text and other related posted documents. Thus, they are also a good preparation for the final exam. 7. Please bring to my attention any typo/mistake you notice, which I might have overlooked after I had gone over the assignment. Let me know if you have any question or concern.

©2019 Charles Sebuharara

pg. 1

MINI-CASE 1: ESTIMATING REQUIRED RATE OF RETURN (Interest Rate) USING RISK PREMIUMS. [5 points] (References: See essentially Schedule of Classes Units 1, 3 and 6) A. Preliminary Remarks: The purpose of this mini-case is to demonstrate how the required rate of return on a fixed-income security can be determined, using the risk premium perspective. The mini-case brings together, in a simple model, several of the various risks associated with fixed-income securities. From a corporation perspective, the nominal interest rate to be determined in this mini-case can serve as a basis for estimating the firm’s before-tax cost of debt. At the issue of the security, if the nominal interest rate is set as the coupon rate that is equal to the yield to maturity (so that the price equals the par value), then one could interpret the obtained rate as a discount rate. From the perspective of investors (buyers of the security), the rate could be interpreted as the investor’s nominal required rate of return. B. The Mini-Case Assignment: 



Your company, Binghamton Truck, Inc., is about to offer a new issue of corporate bonds to the investing marketplace. You have been asked by your CFO to provide a reasonable estimate of the nominal interest rate (nominal yield), Rd, for a new issue of Aaa-rated bonds to be offered by Binghamton Truck. Some agreed-upon procedures related to generating estimates for key variables in the relevant equation, Rd = R*rf + IRP + DRP + MP + LP, are as follows: (1) The current (mid-2008) financial market environment is considered representative of the prospective tone of the market near the time of offering the new bonds to the investing public. This means that current interest rates will be used as benchmarks for some of the variable estimates. All estimates will be rounded off to hundredths of a percent; thus, 6.288 becomes 6.29 percent. (2) The real risk-free rate of interest, R*rf, is the difference between the calculated average yield on 3-month Treasury bills and the inflation rate. (3) The inflation-risk premium, IRP, is the rate of inflation expected to occur over the life of the bond under consideration. (4) The default-risk premium, DRP, is estimated by the difference between the average yield on Aaa-rated bonds and 30-year Treasury bonds. (5) The maturity premium, MP, is estimated by the difference between the calculated average yield on 30-year Treasury bonds and 3-month Treasury bills.

©2019 Charles Sebuharara

pg. 2

(6) Binghamton Truck’ bonds will be traded on the New York Exchange for Bonds, so the liquidity premium, LP, will be slight. It will be greater than zero; however, because the secondary market for the firm’s bonds is more uncertain than that of some other truck producers, it is estimated at 3 basis points. Note: A basis point is one one-hundredth of 1 percent. (E.g., 1 basis point = 0.01%; 25 basis points = 0.25%) 

Based on your research, the mid-2008 estimates of the representative interest and inflation rates are as follows: (1) 3-Month T-Bills = 4.89%, (2) 30-Year T-Bonds = 5.38% (use this as proxy for 20-year TBonds), (3) Aaa-Rated Corporate Bonds = 6.24%, and (4) Inflation Rate = 3.60%. Visit online Federal Reserve Bank of St. Louis (Google “Federal Reserve Bank of St. Louis FRED”) and update the above data with the most recently available rates for each of the above fixed income securities and for the inflation rate.



Required Task: Complete the Solution Table below, which is presented in form of a formula required to determine Rd. Place your answers (values) in the cells below the variables in the second row, and show your calculations below the Table, where applicable, of how you obtained the value for each of the variables. Similarly, use your most recent collected rates (May 2019; see source below) to complete the third row of the worksheet below. Briefly comment on the differences between the two results (i.e. results obtained from above old data versus results obtained from recent data you collected).

Solution to Mini-Case 1 (show your work below the table, as appropriate):

R*rf

+ IRP

+ DRP

+ MRP + LRP

=

Rd

Using “old” data in the case above Using “newer” data*

©2019 Charles Sebuharara

pg. 3

Show in this space (add page as necessary) any calculations you performed to find any of the terms in the above table.

_________________________________ * Source of data for part II of Mini-Case 1: FRED – ECONOMIC DATA, by The Federal Reserve Bank of St. Louis https://fred.stlouisfed.org/categories Copy and Paste the above URL into your browser, then look for the following data, under either “Prices” or “Interest Rates.” The “identifier” like TB3MS can be seen when you download the series (download option is provided in the top right corner of the data window of interest. When you click on “Download”, you will be given options for the format, like Excel, etc. I suggest choosing “Excel” if you decide to download the series.) (1) Inflation Rate: PCETRIM12M159SFRBDAL PCETRIM12M159SFRBDA L

Trimmed Mean PCE Inflation Rate, Percent Change from Year Ago, Monthly, Seasonally Adjusted Adjusted

(2) Three (3)-Month Treasury Bill TB3M S

[look under Treasury Bills]

3-Month Treasury Bill: Secondary Market Rate, Percent, Monthly, Not Seasonally Adjusted

(3) 30-Year Treasury Constant Maturity Rate DGS30

30-Year Treasury Constant Maturity Rate, Percent, Daily, Not Seasonally Adjusted

(4) 20-Year Treasury Constant Maturity Rate DGS20

[look under Treasury Constant Maturity]

20-Year Treasury Constant Maturity Rate, Percent, Daily, Not Seasonally Adjusted

(5) Moody’s Seasoned Aaa Corporate Bond Yield AAA

[look under Treasury Constant Maturity]

[look under Corporate Bonds]

Moody's Seasoned Aaa Corporate Bond Yield, Percent, Monthly, Not Seasonally Adjusted

©2019 Charles Sebuharara

pg. 4

MINI-CASE 2: BOOTSTRAPPING METHOD FOR ESTIMATING SPOT RATES. [5 points] A. Introduction: As discussed in the text and the PowerPoints, the Yield Curve should be constructed using theoretical rates, which represent the spot rates corresponding to each maturity. These rates and corresponding calculated prices are referred to as “Spot Rates” (or pure discount rate) and “Implied Zeroes” (or zero-coupon prices). The purpose of this mini-case is to illustrate how to calculate these implied prices and spot rates. Ideally, the calculated spot rates are the rates that should be used to discount the respective cash flows, instead of using for example a single yield to maturity when determining the value of a bond. B. The Problem: Consider the problem of finding the pure discount bond prices from the coupon prices that are available. Table 1 gives data for three bonds for a period of three years. Table 1: Coupon Bond Prices and Coupon Payments. (Notice that the Cash Flows in years 1 through Year 3 already reflect the coupon payments and the par value at maturity.) Bond

Price

Year 1

Year 2

Year 3

1

99.50

105

0

0

2

101.25

6

106

0

3

100.25

7

7

107

1. Let Pi be the price of bond i (e.g., if i=1, then Pi=P1 for bond 1). Let ci denote the dollar coupon associated with bond i, and y1 as a one-year spot rate of interest. Then, we can denote the price of the first bond as

P1=

100 +c 1 (1+ y 1)

Then, using known data, solve for y1. Finally, we can solve for the one-year implied zero price, z1, as follows:

z 1=

1 P1 = ( 1+ y 1 ) 100 + c 1

Note: z1 is also referred to as the “discount factor” or the present value of a $1 to be received at time t in the future. The two terms to the right of the z1 equation are equivalent ways of finding the answer. They should give the same answer.

©2019 Charles Sebuharara

pg. 5

Following the same procedure, we can solve iteratively for y2 and z2, etc …. Note that, after solving for yi in one step it becomes a known value in the next step. For example, when solving for y2 and z2, P1, P2 and y1 are known values that you can just plug in the formula for P2 to find y2 and then solve for z2. 2. Required task: Use the above procedure, called “Bootstrapping” to complete Table 2 below for maturities 2 and 3. (Note: I provided the answers for maturity 1, for illustration. However, show your work, i.e., show the steps you followed to reach the answers, including your work to verify the answers already provided). Table 2: Implied Zeroes and Spot Rates. (Answers for maturity 1 are already given to you for illustration. This will not count in your grade.)

Maturity (Years)

Implied Zero (zi)

Spot Rate (yi)

1

z1 = 0.9476

y1 = 5.53%

2

z2 =

?

y2 =

?

3

z3 =

?

Y3 =

?

©2019 Charles Sebuharara

pg. 6...