Midterm Exam Please read the following general information carefully before you begin the exam: • The midterm is an individual take-home exam: it is to be submitted in electronic format by email to me and the course assistants and in identical hardcopy to Faculty Services in KSB 116 by 5h00pm (17h00) on Wednesday, November 20. It is your responsibility to make sure that I receive the completed exam by email before the expiration of the time window: the Outlook time stamp will decide any disputes in this regard. • Submissions consist of your type-written answers and one Excel workbook containing your analyses, both zipped together in the same file; each question or part thereof that requires major calculations is to be presented on a separate worksheet with the bottom tab indicating the precise question number (e.g., 3.a). All file names need to contain 472 Midterm and your last name, e.g., 472midterm hauswald.xxx for the *.zip, *.doc, and *.xls files. Hardcopies should consist of the print-outs of your written answers. Please refrain from printing out entire spreadsheets. • This exam is an individual effort: no cooperation, discussion, joint work, etc. is permitted. Only clarifying questions will be answered. Be reminded that, as part of the honor code, you are not to share the contents or structure of this exam with anyone else, including your classmates not here today or those attending other sections of this course. • By taking the exam early you engage yourself not to communicate any information about its make-up, content, etc. to other students. Since the course grade distribution is fixed and you are graded on a curve, it is in your own best interest to adhere to this policy. • Put your name and ID number on each page of your test. Your answers should be short and to the point, type-written, and may contain pasted excerpts from your analytic spreadsheets together with careful explanations of the analysis and its underlying assumptions. • The midterm comprises 8 questions including some optional parts and one bonus problem with a maximum total number of points of 800 (individual points given in the margin). • Show your work but write to the point: explain each answer as fully and carefully as necessary. Label all diagrams and box intermediate and final results. • Good Luck! 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 Spot Yield Disc Factor Fwd Rate 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 (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 information? (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 2 (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 TSTR (“Too Small 100 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 4. Commercial Banking. You are a corporate account officer with TLTF (“Too Large To 100 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? 3 (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? 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 fixedincome 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? 4 (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 floating. What value should your accounting system attribute to the swap today (notional principal: $40m)? 7. 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 5 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 10 233.0626 8. Corporates, M&A, and Callability. As a member of the BofA/Merrill Lynch corporate 100 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. 6 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 Baa1 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? 7 • 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? 9. Optional Bonus Problem: Pricing Callability. Many bonds come with early repayment 100 options for the issuer (”callables”) or the investor (”putables”). Consider a callable bond with two years to maturity remaining, a 15% annual coupon, and a call schedule indicating call prices (strikes) of K0 = 107.00 and K1 = 106.00 in years t = 0, 1. If the issuer decides to call the bond she has to pay the call price and the coupon on the date the bond is called. Suppose that the evolution of the 1Y spot rate (in %) and the ex-coupon price1 of a 2Y non-callable bond with a 15% annual coupon is described by the lattice below with no further information on the lattice’s type available. Using a standard synthetic replication argument price the callable on an ex-coupon basis. Note that you cannot price the callable directly from the lattice because you do not know what the risk-neutral probabilities are (a safe bet would be the usual q = 1 − q = 1 2 ,though). t = 0 t = 1 t = 2 ruu = 13.01 P (2, 2) = 100 ru = 11.00 Pu (1, 2) = 103.017 r0 = 9.00 P (0, 2) = 109.90 rud = 9.00 P (2, 2) = 100 rd = 7.00 Pd (1, 2) = 107.23 rdd = 4.99 P (2, 2) = 100 (a) First, set up the ex-coupon bond price lattice. (b) On the basis of the preceding ex-coupon price lattice, adjust prices at nodes where the 1Ex-coupon is the price the buyer (original issuer) pays for the bond buying it back; obviously, the seller (investor) will receive the ex-coupon price plus the accrued coupon. 8 bond would have been called in: t = 0 t = 1 t = 2 100.00 Payoff: Action: Pu (1, 2) = 103.017 Payoff: Action: P (0, 2) = 107.00 100.00 Payoff: Action: Pd (1, 2) = 106.00 100.00 (c) In order to value the bond, assume that there is an equivalent noncallable one (NC) and a 1Y zero whose valuations follow from the spot-rate lattice. Use a cash-flow replication argument similar to the one underlying callables arbitrage to value the call option. (d) Less than 30% of bonds are callable these days. Why or why not does it make sense for a company to issue a callable bond? Explain.