You will work on this assignment in groups of up to four people. Make sure the
names of all group members are on the document you submit and registered on
Canvas, otherwise credit cannot be given. This is a graded exercise, and all groups
must work independently of each other. We will discuss the results during class on
Monday 12/4, so assignments submitted after class will not be accepted.
By 6:00 pm Sunday 12/3 you must submit on Canvas your answers to the
following questions…
- The prices of the individual options comprising the call spread described below.
- The midmarket “breakeven” price of the call spread.
- Given the midmarket “breakeven” price you calculated in question (1) above,
what will be your offered price to the client? Explain your reasoning. - The notional amount of the 1.625% of 3/3/2026 you need initially to hedge your
bank’s position in the call spread, assuming you can transact your hedge at the
5:00 pm price on Thursday March 3rd. Do you need to buy or sell bonds to
hedge? - What happens to your risk exposure if yields move up a lot?
Explain your reasoning for all answers and be sure to clearly state your units in
all numerical answers. You may submit supporting documents and/or spreadsheets
for your answers to the questions above, but please present your answers to the
first four questions in this format…
Midmarket price for 180 bp strike ($)
Midmarket price for 200 bp strike ($)
Midmarket price for the call spread ($)
Offered price for the call spread ($)
Initial hedge
Buy or sell?
Notional amount?
Yale SOM MGT805 Fixed Income Fall 2023
©2023 S.Majd (All Rights Reserved) Page 2 of 6
The assignment:
Pretend that you are in the first few days of March 2016. At 8:30 am on Friday
March 4, 2016, the Bureau of Labor Statistics will release the February Jobs Report.
Arguably this is the most important economic statistic that is released each month.
(Don’t bother to research this past announcement, as our February 2016 Jobs Report
and the subsequent market actions are fabricated and do not correspond to actual
historical events!)
Assume that it is 5:00 pm on Thursday March 3rd, 2016, the day before the release of
the February Jobs Report, and the yield on a ten-year Treasury note (a hypothetical
bond that is on coupon dates so that you can ignore accrued interest), the 1.625% of
3/3/2026, is 1.80%.
Your bank’s syndicate desk has been working with a client on a new ten-year bond
issue that will be brought to market sometime next week. The treasurer of the
company is concerned that rates will rise before the bonds are issued and wishes to
hedge this risk.
The treasurer of the company asks your bank to offer a call spread on the yield of
the Treasury note above. You will be in competition with other banks, so your offer
must be competitive as well as profitable. The call spread has the following
particulars:
- Underlying variable: the yield of the 1.625% of 3/3/2026
- Expiration: one day (i.e., 5:00 pm Friday March 4th)
- Strike 1: customer buys a call on the yield struck at 1.80%
- Strike 2: customer sells a call on the yield struck at 2.00%
- Notional amount: $100 million of the underlying ten-year Treasury note
- The contract specifies cash settlement of the call spread using a fixed DV01 of
0.09034 (the DV01 of the underlying Treasury note at the spot yield of
1.80%)
We will start the class discussion with your pricing of the call spread and your
calculation of the hedge. We then will reveal the February Jobs Report and the
subsequent market reaction (not the actual report or market reaction) and discuss
changes in the price and risk of the call spread based on the market move.
Yale SOM MGT805 Fixed Income Fall 2023
©2023 S.Majd (All Rights Reserved) Page 3 of 6
Background to the current economic climate:
The Fed has been keeping short-term rates close to zero since the economic crisis of
- In December 2015, for the first time, they raised short-term rates 25bp. It was
generally believed at the time that the Fed would be raising rates over most of 2016.
However, at the beginning of the year, triggered by devaluation in China, equity
markets have been skittish and are lower across the globe by 10-20%. This has the
Fed temporarily on hold, and at their last meeting of January 27th they did not raise
rates. Some are even calling for the Fed to lower rates back to zero, but most are
saying that the Fed should hold off on raising rates again until markets stabilize
somewhat.
March 3rd, 2016, 5pm closing interest rates:
Money Market Rates On-the-run Treasuries
Fed Funds 0.32 2-year Note 0.88
Overnight Repo 0.30 5-year Note 1.40
1-month T Bills 0.25 10-year Note 1.80
3-month T Bills 0.29 30-year Bond 2.66
1-year T Bills 0.65
Historical daily changes in the CMT10 (constant maturity ten-year Treasury yield)
from February 2015 to February 2016 exhibit the following:
- The largest one-day upward movement in rates was 24.6 bp
- The largest one-day downward movement in rates was -25.9 bp
- The mean one-day change in rates was 1 bp
- The standard deviation of one-day changes in rates was 4.8bp (or 76.8 bp
annualized using 256 days) - The one-day standard deviation of daily returns was 2.5% (or 40.0%
annualized using 256 days)
Short-dated options on ten-year Treasury bonds have been trading in the market
with a 4-vega bid-offer spread in volatility.
Yale SOM MGT805 Fixed Income Fall 2023
©2023 S.Majd (All Rights Reserved) Page 4 of 6
Graph of the CMT10 yields over the last year:
Table of the last twelve employment-day returns:
Employment Date
CMT10
closing
yield
One-day
raw yield
change
One-day
percent yield
change
Friday, March 6, 2015 2.247 0.133 0.0610
Friday, April 3, 2015 1.848 -0.075 -0.0398
Friday, May 8, 2015 2.161 -0.026 -0.0120
Friday, June 5, 2015 2.407 0.246 0.1078
Friday, July 10, 2015 2.415 0.008 0.0033
Friday, August 7, 2015 2.188 -0.227 -0.0987
Friday, September 4, 2015 2.134 -0.053 -0.0245
Friday, October 9, 2015 2.114 -0.02 -0.0094
Friday, November 6, 2015 2.346 0.232 0.1041
Friday, December 4, 2015 2.272 -0.074 -0.0321
Friday, January 8, 2016 2.121 -0.151 -0.0688
Friday, February 5, 2016 1.862 -0.259 -0.1302
Yale SOM MGT805 Fixed Income Fall 2023
©2023 S.Majd (All Rights Reserved) Page 5 of 6
The recent US employment situation has been somewhat strong. The last
employment report was not as strong as originally anticipated. Highlights of the last
ten employment reports:
Yale SOM MGT805 Fixed Income Fall 2023
©2023 S.Majd (All Rights Reserved) Page 6 of 6
The current consensus for Friday’s employment report by Wall Street economists as
reported by Bloomberg:
