Fixed-Income Securities

Fixed-Income Securities

1.  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.  Term Structure of  Interest Rates. Your investment company’s  trading  system  has be-   100+20

come unstable  after a recent update  so that your superiors  ask you to verify the calculations displayed  on the traders’  screens.

Type Maturity Coupon Price UST Bill 182D   99.9650 UST P-Strip 1Y   99.9000 UST Note 1.5Y 2.30 100.0152 UST Note 2Y 3.80 100.1403    

Spot Yield    Disc Factor     Fwd Rate

(a)  Using current UST security  information  from Bloomberg reproduced  above, you extract the  relevant spot  rates  by  hand  and  fill in  the  remainder   of the  table  to  verify  the computations of your system.  Note that the maturities are exactly  as stated.

You might want to provide  the  requisite  formulae indicating  your exact  calculations  to convince your boss that it is not you who is at fault but rather the IT techs who botched the update.

(b)  Draw  the  corresponding  UST  discount  yield  curve  and  indicate  a  hypothetical  AAA

corporate  term  structure (sketch)  relative  to the US TSIR.

(c)  What  is the  relationship between  the  US sovereign  and  corporate  AAA yield curves?

What  explains  the  difference in yields by maturity and  how do markets  use this  infor- mation?

(d)  The FRB has announced in December 2016 that it will cease to intervene in bond markets and  bring  its policy of quantitative easing to an end.  What  will the  effect of the  Fed’s tapering  announcement on the yield curve be?  Explain

(e)  Optional. Research  the  current yield curve (as of the  date  of the  exam)and compare    20 it to the one at  the beginning  of the year.  What  do you see?  Download the data  (e.g., www.treasury.gov), generate  the requisite  chart,  and explain.

3. Interest-Rate  Risk Management.  As  chief financial  officer (CFO)   of The  California 100
  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 Cash and cash equivalent      10 Equity                                                   11 Annuities,  policies, saving plans      99
Total                                        110 Total                                                   110

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 short-term USD Libor term  structure is as follows:

Maturity (D) Libor 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 boss 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)  Define and calculate  the LIBOR  forward curve.  Why or why not is it a good predictor for future  LIBOR  rates?

(e)  Optional. At expiration, i.e., six months  after  entering  into  the  agreement, the  180D   20

Libor 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.  Funding Positions.  As a junior  trader at  your  investment  bank,  you  quickly  and  cost-    100+20

effectively need to fund overnight a $100m position  in the on-the-run 5Y UST note.  On Feb

17, 2014, this  note,  which  pays  a 3% coupon  and  matures  on 03/21/2019, is quoted  at  a bid-ask of 100 21/32-22/32 (careful:  what  does the quote convention  mean?).

(a)  What  should the invoice price of this note be?  In your computation of accrued  interest, please note that February is an odd month.

(b)  The  general-collateral repo rates  rates  are 1.10%-1.25% (dealer  pays-earns  interest) on

02/17/14.  If the  market  required  a 2% margin,  how much  of the  purchase  price could you have borrowed  in the repo market,  and how much interest would you have paid for a one-day loan?  What  would have your equity  stake  in the position  be?

(c)  At the  expiration of the  1D repo  (next  day),  the  bond  is trading  at  100 22/32-23/32 (careful:  what  does the  quote  convention  mean?).   What  is your  total  profit  or loss if you were to close out your position?

(d)  As an alternative, you consider an overnight loan in the fed funds market.  What  are fed funds rates  and how do they  relate  to repo rates?  Explain.

(e)  Optional. What  are ‘fails’ in the repo market?   Describe two strategies to take  advan-    20

tage of fails and to what  purpose  unscrupulous market  participants would use them.

6.  Swap Valuation.   The  date  is January 3,  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

(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. Your company  has sold a 6Y plain-vanilla  swap on 1Y LIBOR  precisely one   20

year  ago for a swap rate  of 7.15%; as a consequence,  you receive fixed and  pay  float- ing.  What  value should  your accounting  system  attribute to the  swap today  (notional principal:  $40m)?

7. Corporate Bond Issuance and Trading.  As a member  of the  BofA/Merrill Lynch cor- 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: 100
  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 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)

(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



Spread  UST+

Maturity           April 1, 2023                             April 1, 2024


Trade                   March 30, 2016                         March 30, 2016

Settle  (T+10)   April 13, 2016                           April 13, 2016


• 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?

(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.

8.  Treasury  Inflation-Protected  Securities.  Since 1997,  the  US Treasury has  provided    100+20

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)  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 analyst  report  by HIMCO  (May  2014), The

Case for Treasury Inflation-Protected Securities.

(a)  What  is the rationale  to invest in a TIPS?  Does it still hold?

(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.

(e)  Optional. In 2004, the  US Treasury issued the  following 10Y TIPS  maturing in July    20


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 10 233.0626
9.  Optional  Bonus Problem:  Specialness and the Repo Market.  In spring 2008, the Amer- 100
ican (and  world)  financial  system  is rapidly  sliding toward  its biggest  crisis since the  Great  
Depression.  Although  the  banking  industry is in dire straits politician  and  economic-policy  
makers  are in denial  hoping  that monetary policy alone will somehow right  the  ship.  As a  
junior trader on the UST desk of a major Wall-Street house you are checking Bloomberg (see  
Exhibit  1 of the  Midterm  Data ) and  cannot  believe your eyes.  Given your firm’s inventory,  

you might just  have found a license to print money.

(a)  What  are “specials”  in the government-bond and repo market?


(b)  What  could explain both  the pricing of the 3 1 % 02/2018 UST note relative  to the notes

with nearby  maturities and its repo rate?

(c)  What  sort of trade  do the relative  prices suggest,  and how does this trade  relate  to the repo rate?

(d)  Special repo rates  rspec are typically lower than  general ones rgen . The spread  between general and special repo rates  s = rgen ? rspec ? 0 is called the repo dividend.

• In what  type of transactions are special repo rates  used?

• Why  would anybody  accept  a lower rate  on a collateralized  loan which is after  all very similar to a general repo?

• How can a money dealer/trader holding the requisite collateral capture  the repo div- idend? Describe the mechanics of the underlying  strategy and explain the expected profit.

Fixed-Income Securities

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