Define the following yield concepts redemption yield par

Question

Assignment -

Q1. Yields and Bills

(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?

Q2. Term Structure of Interest Rates

Using the below information for BB rated Euro-denominated global corporate debt (ECP is Euro commercial paper) extract the relevant spot rates to generate a BB corporate yield curve. Note that the maturities are exactly as stated and that corporate debt securities issued in the offshore markets, i.e., London or Luxemburg, typically pay interest only once a year.

(a) Corporate yield curve in the global EUR market:

Type	Maturity	Coupon	Price	Yield
ECP	91 days		98.768
ECP	182 days		96.860
Euro-Bond	1 year	8	100.934
Euro-Note	2 years	6	97.760
Euro-Note Strip	3 years		81.401

(b) Draw the corresponding BB yield curve and indicate a hypothetical AAA German Bund term structure, the anchor market for EUR-denominated debt markets, as the relevant sovereign strip yield curve.

(c) What is the relationship between the German sovereign (discount) yield curve and the BB corporate one? Reason by analogy with the US markets and explain.

(d) The Eurozone, i.e., the countries sharing the Euro (EUR) as their common currency, have been in the midst of a long-running debt crisis brought about by sovereign over-borrowing, various banking crises, and lax tax collection and enforcement. As a fixed-income strategist for a major mutual fund, you wonder about the wisdom to invest in Greek bonds and collect the relevant data. What is the current German 10Y yield, the corresponding Greek 10Y yield, and the spread between Greek and German 10Y yields? How would you characterize spread and what does it say about market expectations regarding Greek debt?

Q3. Interest-Rate Risk Management

As chief financial officer (CFO) of TSTR ("Too Small To Rescue") Bank, a small neighborhood bank, one of your primary tasks is the management of its interest rate exposure. You are currently trying to convince your board, composed of neighborhood worthies, to measure and manage your institution's interest rate risk by using mathematical relations between fixed-income prices and yields.

(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 TSTR's investment 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 TSTR Bank's board you propose to change current A&L management practices focusing more on interest-rate risk.

• Formulate an appropriate objective in terms of a measure of interest-rate sensitivity.
• One of your board members, a retired S&L executive, 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 loan portfolio is 3 years whereas the average duration of your various fixed income liabilities (deposits and bonds) is 1.5 years. Propose a strategy to neutralize the effect of interest-rate changes on your balance sheet which is (in million USD) as follows:

TSTR Bank
Assets		Liabilities
Loan portfolio	100	Equity	11
Cash and cash equivalent	10	Deposits, bonds	99
Total	110	Total	110

Q4. Commercial Banking

You are a corporate account officer with TLTF ("Too Large To Fail") Bank. One of your major clients just sold a piece of customized machinery to be delivered in one year's time. The company's CFO inquires about the possibilities of investing USD 10 m in a year from now for one year.

(a) What kind of investment opportunity (contract) would you suggest to them?

(b) Currently, 1-year and 2-year spot rates are 6.50% and 7.25%, respectively. Quote a return for the preceding investment suggestion. Since your customer is of a somewhat suspicious nature you need to indicate the formula used to derive the quote.

(c) What alternative investments could you suggest to your customer?

(d) Define the forward curve. Why or why not is it a good predictor of future interest rates?

Q5. Funding Positions

As a junior trader at your investment bank you quickly and cost- effectively need to fund overnight a $100m position in the on-the-run 5Y UST note. On Monday, March 16, 2009, this note, which pays a 3% coupon and matures on 02/15/13, is quoted at a bid-ask of 100 21/32 - 22/32.

(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 rate is 1.25% on 03/16/09. 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 been your equity stake in the position?

(c) Can general repo rates ever become negative? Why or why not?

(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.

Q6. Swap Valuation

The date is January 3, 2012 and you just returned to work from a 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 (years)	T-Strip Prices 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) 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)?

Q7. Corporate Bond Issuance and Trading

As a member of the BofA/Merrill Lynch corporate 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. Road shows 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+/Bal/BB+. The secured debt is rated BBB-/Bal/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:

• 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 term sheet.

• 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 implement the long-short strategy? Describe two different implementation and recommend your favorite one.

Q8. Corporates, M&A, and Callability

As a member of the BofA/Merrill Lynch corporate bond origination team, you have been working on a transaction on behalf of CVS Health Corp. (NSE: CVS) which had been planning a massive bond offering to fund the acquisition of Aetna Inc (NSE: AET). 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 2018.

In addition to the below recent press coverage of the bond issue, you might want to consult the attached extract from the Offering Circular.

CVS Health completes world's third-largest corporate bond sale: US pharmacy chain raises $40bn to fund purchase of health insurer Aetna

CVS Health completed the third-largest corporate bond sale in history on Tuesday, underlining the market's ability to absorb sizeable debt issuance at the right price, despite a backdrop of rising interest rates and regulatory uncertainty. The pharmacy chain's $40bn sale - to fund its proposed acquisition of health insurer Aetna - attracted $120.7bn of orders, according to four people with knowledge of the sale. Investors said the debt's reasonable pricing supported the record demand, and advance notice from underwriters gave fund managers the chance to set aside cash for the offering.

Bankers and investors said the sale suggested the US bond market was comfortable with two key risks: rising yields on global government debt, and uncertainty about regulators' approach to so-called vertical mergers, or tie-ups between companies that are not direct competitors.

CVS sold nine bonds across seven maturities to fund the deal. Most of the securities face a mandatory redemption if the acquisition is not completed by mid-2019, according to Moody's, which assigned the debt a Baal rating.

Investors submitted more than $110bn of orders for $46bn of bonds issued by Anheuser-Busch InBev to fund its acquisition of SABMiller, and $101bn for the $49bn of bonds issued to fund Verizon's acquisition of Verizon Wireless.

Spreads between yields of the new securities and benchmark government debt were mostly similar or wider than spreads offered in other large bond sales. The new five-year CVS bonds were sold at a yield of 3.899 per cent, a spread of 125 basis points over Treasuries. To compare, five-year spreads were 120 basis points in the Anheuser-Busch InBev deal. CVS's new 10-year bonds were sold at a yield of 4.475 per cent, 160 basis points higher than benchmark Treasuries, giving them the same spread as the Anheuser-Busch deal.

Some commentators have questioned the market's resilience investor Bill Gross, for example, in January predicted the start of a bear market in bonds. Spreads widened for the corporate debt market as a whole in February, according to ICE Bank of America Merrill Lynch indices. "We anticipate an uptick in M&A activity, so the success of today's transaction is important to show the marketplace there is still plenty of liquidity," said Dan Mead, head of the US investment-grade syndicate desk at BofAML.

Some bond tenors were offered with steeper-than-normal price discounts, which investors said was to compensate for the risk that regulators may block the deal. The Justice Department's challenge to the tie-up between AT&T and Time Warner has fuelled uncertainty about the CVS-Aetna deal. However, bullishness about the prospects of the combined company fed demand for the bonds. (FT, March 06, 2016)

(a) Analyze CVS, Aetna, and the terms of the CVS offering.

• How well have CVS and Aetna been doing? What is the financing for?
• What exactly is on offer? How do the tranches differ? Present the terms of the various series in table format.
• What other debt is CVS taking on and how is it structured?

(b) Are the various tranches callable? If so, when and why? How does callability differ in this case from regular corporate callables? What are CVS trying to accomplish and what is unusual about the series' callability?

(c) Using the attached information or any other data, whose source you would have to carefully document, critically review the pricing and terms of the debt.

• How were the bonds rated? How did the deal change CVS' perceived credit risk and how does it influence the pricing of the bonds?
• What yields would you propose for the nine series? How should they vary with the terms of the individual tranches?
• How do price and proceeds diverge?

(d) Research the issue and try to find out what happened. Did the final offering differ from the initial announcement and, if so, why?

Q9. Optional Bonus Problem Treasury Inflation-Protected Securities

Since 1997, the US 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) years" (* denotes a reopening, in which the US Treasury sell an additional amount of a previously issued security;

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) 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.

(c) Decompose the price of a TIPS into its constituent parts. How does it relate to standard US Treasury security of the same maturity?

(d) Based on your decomposition of a TIPS, what would be clear violation of the no-arbitrage condition? How would you take advantage of such a situation?