Econ 136: Financial EconomicsProblem Set #5

Due Date: October 15, 2015

Please submit the homework in the lecture hall before the lecture starts. Late home-work will not be accepted.

Please put your name, student ID & your GSIs name at the top-right corner of thefront page.

Please staple the pages of your homework together. Homework will be returned in sections.

1. What is the price each of the following risk-free 6-year bonds if the yield is 4%?

(a) A semi-annual compounding zero-coupon bond that pays $1000 at maturity.

(b) A 4% coupon bond that pays a $400 coupon once per year.

(c) A 10% coupon bond that pays the $100 coupon once per year.

2. Using the approach developed in Lecture 9, reproduce the calculations of the discount-factors, spot rates and forward rates we did in class and then extend them for all thematurities shown on Slide 14 of Lecture 9.

3. Briefly describe:

(a) The similarities between option delta and fixed-income duration.

(b) The similarities between option gamma and fixed-income convexity.

4. From the Federal Reserve website1 download data for the Fed Funds rate2, and theConstant Maturity Treasury (CMT) rates shown in the graph on Slide 2 of Lecture 11,but replace the yield curve of 02/28/13 with that of 10/09/15. Create your version ofthe graph on the lecture slide and a table of the interest rates.

5. When the Non-Farm Payroll report is released interest-rates immediately change in theChicago trading pits and in banks worldwide. By what mechanism (i.e. what two keyequations) does an unemployment number change translate into a change in interestrates?

1http://research.stlouisfed.org/fred2/.2The Fed Funds rate is the overnight rate (tenor 1/365.25 years) and appears as the rate closest to a

zero tenor in Slide 2 of Lecture 11.

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6. On January 6, 2010 the financial regulators3 of the United States issued an advisory4

reminding financial institutions of regulatory expectations that included, among otherthings, an interest-rate stress test of 400 basis-point changes to the term-structureof interest rates. Some thought this rate change to be excessive and unnecessary givethe then existing scenarios of 100, 200, 300 basis points. Using the cumula-tive distribution analysis framework from Problem Set #1, analyze the year-over-yearchange (not return) of the monthly 10-year CMT rate5 available at the Federal Re-serve website1. Calculate and plot the cumulative distribution vs. interest-rate changegraph and, referring to it, discuss the merits of the then existing scenarios of 100,200, 300 basis points, and the proposed addition of the 400 basis-point stressscenarios in light of what you know about the CME SPAN system.

7. On Slide 9 of Lecture 11, the final derivation of the price of the perpetuity

P =C

2

i=1

1

(1 + Y/2)i=C

Y(1)

was said to follow from the following sum:

ak=0

xk =a

1 x (2)

where a is a constant. Verify the price of the perpetuity in Eq. (1) by making thesubstitutions a = C/2 and x = 1/ (1 + Y/2) and carrying out the algebra. (Hint: thek = 0 term in the sum in Eq. (2) is equal to a.)

3At that time the financial regulators consisted of the Board of Governors of the Federal Reserve Sys-tem (FRB), the Federal Deposit Insurance Corporation (FDIC), the National Credit Union Administration(NCUA), the Office of the Comptroller of the Currency (OCC), the Office of Thrift Supervision (OTS), andthe Federal Financial Institutions Examination Council (FFIEC) State Liaison Committee.

4See, for example, Office of the Comptroller of the Currency, Washington, DC. Interagency Advisory onInterest Rate Risk Management (OCC 2010-1a), 2010.

5Note, in this case there are no dividends and you are looking at the year-over-year change instead of thereturn.

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