Yields and Bills. 100
(a) Define the following yield concepts:
• Redemption yield
• Par yield
• Yield to put
• Yield to worst
(b) Can a zero and an otherwise identical, maturity-matched level-coupon bond ever have
the same duration?
(c) A 3M T-bill currently sells for 98:08 (what does this quotation mean?). Calculate its
bond equivalent yield.
(d) Calculate the discount yield of the preceding 3M T-bill currently selling for 98:08.
(e) What does convexity measure and how is it used in the assessment of interest rate risk?
2. Rich-Cheap Analysis and Treasury Arbitrage. Working as a quantitative analyst for 100+20
a major Wall-Street firm, you are preparing your daily recommendation for relative value
trades for your desk and their clients. As befits a junior analyst, you focus on the short end
of the yield curve. The date is March 15, 2019.
Type Maturity Coupon Price Spot Yield Disc Factor Fwd Rate
UST Bill 182D 99.9791
UST Note 1.0Y 99.9325
UST Note 1.5Y 0.125 99.9780
UST Note 2.0Y 1.125 96.3470
(a) Using current UST security information from Bloomberg reproduced above, you first
extract the relevant spot rates and fill in the remainder of the table to verify the numbers
displayed by your trading system. Note that the maturities are exactly as stated, all
securities are on-the-run, and the prices midpoint.
You might want to provide the requisite formulae indicating your exact calculations to
convince your boss that your analysis can be trusted.
(b) Next, you analyze a selection of UST notes to detect any mispricing and possible relative-
value trades. From Bloomberg, you identify the following promising candidates on March
15, 2021:
Type Maturity Coupon Actual Price YTM Fair Price Fair YTM
USN 03/15/22 2.375 102-09 0.072949
USN 09/15/22 1.500 102-02 0.100885
USN 03/15/23 0.500 100-20 0.148887
(c) Carry out the requisite rich-cheap analysis for the securities in (b) to identify arbitrage
opportunities in the form of relative-value trades.
2
(d) The FRB has recently raised interest rates four times by 75 basis points. Its most
aggressive tightening cycle in decades has considerably destabilized financial markets.
What are the dangers of the Fed’s current policy stance and what does the market seem
to expect for the foreseeable future? Do you see any benefits? Explain.
(e) Optional. Research the current yield curve as of the date of the exam and compare it 20
to the one at the beginning of the year. Download the data (e.g., from Bloomberg or
www.treasury.gov), generate the requisite charts, and explain. What do you see?
3. Interest-Rate Risk Management. As chief financial officer (CFO) of The California 100+20
Widows & Orphans Insurance Company (“C-WOIC”), one of your primary tasks is the man-
agement of your company’s interest rate exposure. Following best industry practices, you are
currently trying to convince your board to move beyond traditional approaches to interest-
rate risk and actively manage your institution’s rate exposure by relying less on external
consultants but instead implement models based on tried and tested mathematical relations
between fixed-income prices and yields (rates).
(a) State a formula which relates changes in fixed-income price to interest-rate variability
(i.e., changes in yields) using at least one if not two different measures of yield sensitivity.
Illustrate how bond prices are related to yields on the basis of this formula and a diagram.
Why or why not is this approach valid?
(b) The modified duration and convexity of a high-grade corporate bond in C-WOIC’s in-
vestment portfolio are 5.6 years and 34.9, respectively. By what dollar amounts would
you expect its price to change for a 60 bpts rise or fall in interest rates given that the
current bond’s price is $91.65?
(c) At a meeting of C-WOIC’s board you propose to update current A&L management prac-
tices focusing more on interest-rate exposure given the shifting monetary environment.
• Formulate an appropriate objective in terms of a measure of interest-rate sensitivity.
• One of your board members, a retired bank CFO, claims that your approach to
interest-rate exposure measurement and management is fundamentally flawed. What
problems might she referring to? Do you agree with her assessment?
(d) Currently, the average duration of your investment portfolio is 5 years whereas the
average duration of your various fixed income liabilities (life-insurance policies, variable
rate annuities, and savings products) is 15 years. You may assume that the average
yield on assets and liabilities for a company of C-WOIC’s credit quality is around 6.00%.
Calculate C-WOIC’s net rate exposure and propose a strategy to neutralize the effect of
interest-rate changes on your balance sheet which is (in billion USD) as follows:
C-WOIC Simplified Balance Sheet
Assets Liabilities
Fixed-income portfolio 100 Equity 11
Cash and cash equivalent 10 Annuities, policies, saving plans 99
Total 110 Total 110
3
(e) Optional. Should industrial companies engage in active interest-rate management? 20
Why or why not? If so, what would appropriate objectives be in light of your preceding
analysis?
4. Commercial Banking. You are a corporate account officer with the Commercial & In- 100+20
dustrial Bank Corporation (CIBC). One of your major manufacturing clients, who are re-
tooling one of their factories, just bought a piece of customized machinery to be delivered
in six months’ time. The company’s treasurer intends to initially finance the purchase in
the short-term loan market for six months and inquires about the possibilities of locking in
the borrowing cost now. The amount is USD 10m and the loan would be disbursed in a six
months from now to be repaid in exactly one year’s time from now. The current SOFR term
structure is as follows: Maturity (D) SOFR Rate (%)
30 0.15%
90 0.24%
180 0.33%
360 0.55%
(a) What kind of solution to their problem would you suggest to your manufacturing client?
(b) Quote a borrowing cost for the preceding suggestion. Since your MD is of a somewhat
suspicious nature you better indicate your methodology to derive the quote.
(c) What alternative could you suggest to your customer?
(d) What is SOFR and how is it related to LIBOR?
(e) Define and calculate the SOFR forward curve. Why or why not is it a good predictor
for future SOFR rates?
(f) Optional. At expiration, i.e., six months after entering into the agreement, the 180D 20
SOFR stands at 0.90%. Who wins and who loses? Calculate the client’s gain or loss
from your suggestion or the alternative, whichever you prefer.
5. Swap Valuation. The date is January 03, 2019 and you just returned to work from a 100+20
thorough and exhausting celebration of the New Year. As a junior clerk on the USD fixed-
income derivative desk your first transaction of the year involves a 5Y fixed-for-floating swap
with yearly payments on $100m notional. Bloomberg provides you with the following data:
Payment Dates T-Strip Prices
(years) P (0, T )
1.0 95.39
2.0 90.63
3.0 85.78
4.0 80.93
5.0 76.11
4
(a) In terms of cash-replication, the above 5Y plain vanilla swap corresponds to holding
what positions in what type of instruments?
(b) How much is the swap worth at inception?
(c) Calculate the 5Y swap rate for an annual fixed-for-floating USD swap. What is an
appropriate bid-ask spread assuming that the Bloomberg data are midpoints?
(d) You ponder various strategies to hedge the resulting interest-rate exposure. Describe
two different strategies which you could use to hedge the transaction.
(e) Optional. It is still January 03, 2019 and LIBOR has not been replaced by SOFR, yet. 20
Your company has sold a 6Y plain-vanilla swap on 1Y LIBOR precisely one year ago for
a swap rate of 7.15%; as a consequence, you receive fixed and pay floating. What value
should your accounting system attribute to the swap today (notional principal: $40m)?
6. Corporate Bond Issuance and Trading. As a member of the BofA/Merrill Lynch cor- 100
porate bond origination team, you are working on an upcoming transaction on behalf of
Western Digital Corp. (Nasdaq: WDC) which is planning a massive bond offering to fund
the acquisition of SanDisk Corp. (Nasdaq: SNDK). You are in charge of all the fixed-income
analysis and report directly to the lead banker. A lot is on the line for your company because
this deal might become the largest bond offering in 2016 so far. Here is recent press coverage
of the announcement of the bond offering:
Western Digital Readies $5.6B Bond Offering Backing SanDisk Buy
Western Digital this morning launched off the shadow calendar its SanDisk acquisition bond
financing, comprising $1.5 billion of seven-year (non-call three) secured notes and $4.1 billion
of eight-year (non-call three) senior notes, according to sources. Roadshows are scheduled
to run Monday, March 21 through Monday, March 28, with pricing to follow via a Bank of
America–led bookrunner team, the sources added.
While first call premiums have not been outlined for the two series, take note that while par
plus 75% coupon to balance the short schedule is most typical, an issuer-friendly arrangement
at par plus 50% coupon has become more acceptable over the past year. Beyond that, market
sources relay that the equity-clawback feature on both tranches is most typical, as three-year
for up to 35% of the issue, at par plus coupon, and the change-of-control call provisions are
also regular-way, at 101% of par.
Additional bookrunners on the long-awaited effort are J.P. Morgan, Credit Suisse, RBC, and
HSBC. Proceeds, along with those from a TLA, TLB, and an RC draw, will be used to back
the $19 billion acquisition of the rival storage-technology company, and issuance is under Rule
144A for life.
As reported, the company has guided the $4.2 billion U.S. dollar TLB, and $550 million-
equivalent, euro-denominated TLB at L/E+450–475, with a 0.75% floor and OID of 98.5.
The seven-year, covenant-lite term debt will include 12 months of 101 soft call protection,
and at current guidance the term loan would yield roughly 5.64–5.9% to maturity.
Take note that the same bank line up is arranging the loans but J.P. Morgan is the left lead.
A planned $3 billion, five-year A term loan has been increased to $3.75 billion, with pricing
5
set at L+200. Western Digital also plans to draw down a portion of its $1 billion, five-year
revolver at closing.
Issuer ratings have firmed at BB+/Ba1/BB+. The secured debt is rated BBB–/Ba1/BBB–,
with a 2L (lower end of substantial, 80–90%) recovery rating from S&P’s. The unsecured
debt is rated BB+/Ba2/BB+, with a 4L (lower end of average 40–50%) recovery rating.
Irvine, Calif.–based Western Digital makes hard disk drives, solid state drives, and cloud-
network storage solutions, with a client focus on set-top boxes, printers, in-car navigation
devices, and other general consumer electronics. Milpitas, Calif.-based SanDisk makes solid-
state drives and other storage solutions with a client focus on computers, tablets, phones,
and wearables. (March 18, 2016)
You might also want to refer to the attached materials on interest rates and high-yield bonds
in 2016.
(a) Analyze the terms of the Western Digital offering. Here is an extract of the term sheet:
Issuer Western Digital Corporation (WDC)
Ratings BBB–/Ba1/BBB– BB+/Ba2/BB+
Amount
Issue Secured notes (144A-life) Senior notes (144A-life)
Coupon
Price
Yield
Spread UST+
Maturity April 1, 2023 April 1, 2024
Call
Trade March 30, 2016 March 30, 2016
Settle (T+10) April 13, 2016 April 13, 2016
Bookrunners BAML/JPM/CS/RBC/MIZ/MUFG/HSBC/SMBC
• How well has WDC been doing? What is the financing for?
• What exactly is on offer? How do the tranches differ?
• Are the bond callable? If so, when and why?
• What other debt is WDC taking on and how is it structured?
(b) Using the attached information or any other data, whose source you would have to
carefully document, price the debt and complete the above termsheet.
• How is corporate debt priced? Propose a methodology.
• What yields would you propose for the two series? Carefully explain to the lead
banker your reasoning and document your analysis.
• Determine the series’ coupon and price to fill in all the remaining fields above.
(c) Research the issue and try to find out what happened. Did the final offering differ from
the initial announcement and, if so, what happened? How did the pricing vary from
your analysis and why?
6
(d) In order to secure the lead in the deal, your company has agreed to offer liquidity
services up to 12 month. In essence, BAML’s corporate-bond traders stand ready to
make markets in the WDC series, i.e., quote firm bid-ask prices at which they stand
ready to buy or sell typical blocks of $1m to $2m. In order to do so, they have to keep
significant inventory in the notes.
• When traders in corporates have to hold (long) positions for inventory or prop(rietary)-
trading purposes they typically take the offsetting position in maturity-matched US
Treasuries. Why? What is the purpose of this strategy and what is their residual
position?
• What are the risks and benefits of this strategy?
• How would your colleagues at BAML fund the necessary inventory to provide the
promised liquidity services to investors and the issuer and at the same time imple-
ment the long-short strategy? Describe two different implementation and recom-
mend your favorite one.
7. Optional Bonus Problem: Treasury Inflation-Protected Securities. Since 1997, the US 100
Treasury has provided inflation insurance to interested parties through its TIPS program.
TreasuryDirect explains:
“Treasury Inflation-Protected Securities (TIPS) are marketable securities whose principal is
adjusted by changes in the Consumer Price Index. With inflation (a rise in the index), the
principal increases. With a deflation (a drop in the index), the principal decreases. The
relationship between TIPS and the Consumer Price Index affects both the sum you are paid
when your TIPS matures and the amount of interest that a TIPS pays you every six months.
TIPS pay interest at a fixed rate. Because the rate is applied to the adjusted principal,
however, interest payments can vary in amount from one period to the next. If inflation occurs,
the interest payment increases. In the event of deflation, the interest payment decreases. At
the maturity of a TIPS, you receive the adjusted principal or the original principal, whichever
is greater. This provision protects you against deflation…. TIPS are issued in terms of 5
(auction dates: April, *August, *December), 10 (January, *March, *May, July, *September,
*November), and 30 (February, *June, *October) [and, since 2009, 30] years” (* denotes a
reopening, in which the US Treasury sell an additional amount of a previously issued security;
www.treasurydirect.gov/indiv/research/indepth/tips/res tips.htm).
You might also want to refer to the attached material for recent analysis.
(a) What is the rationale to invest in a TIPS? How does it change with economic conditions?
List at least two different reasons and explain.
(b) Consider a normal UST security and and otherwise completely equivalent TIPS. Which
one should carry a higher yield, the TIPS or the nominal UST security? Explain.
(c) Can the yield (to maturity) of a TIPS ever become negative? Why or why not? Explain.
(d) How much have investors apparently been willing to pay for this privilege recently? You
might want to consult recent US Treasury auction results carefully documenting your
information source and data.
7
(e) In 2004, the US Treasury issued the following 10Y TIPS maturing in July 2014:
CUSIP NUMBER 912828CP3
Dated date July 15, 2004
Original issue date July 15, 2004
Additional issue date October 15, 2004
Maturity Date July 15, 2014
Ref CPI on Dated date 188.49677
Suppose that this security were to trade at a bid-ask price of 102-04/05+ (careful: what
does the quote convention mean?) with a coupon rate of 2.0%. Given the reference CPI
data below, what should the index ratio be on Feb 7, 2014? What is the accrued interest
on this security as of Feb 7, 2014? What is its invoice price?
Day Calendar day Ref CPI
02/01/14 1 233.0690
02/02/14 2 233.0683
02/03/14 3 233.0676
02/04/14 4 233.0669
02/05/14 5 233.0661
02/06/14 6 233.0654
02/07/14 7 233.0647
02/08/14 8 233.0640
02/09/14 9 233.0633
02/10/14 10 233.062
