help to do the first problem of the assignment, just the first problem !

McGill University - Desautels Faculty of Management Instructor: P. Augustin FINE 448 Financial Derivatives patrick.augustin@mcgill.ca Winter 2016 T.A.: TA: Chao Xiong and Pouya Behmaram chao.xiong@mail.mcgill.ca and pouya.behmaram@mail.mcgill.ca Assignment 1: Forwards and Futures, Interest Rate Derivatives and Swaps Due: Monday, February 15, 2015 All assignments are due on Monday 15th February 2015 by 6:00 p.m. at the latest. Late assignments will not be accepted. This is an individually written open book assignment and you are not allowed to copy from each other. However, you are encouraged to discuss problems and data sources in groups. Please submit a printed (computer or hand-written) and stapled copy of your assignment. You have the choice of submitting your documents in class at the end of the lecture and during the o ce hours, or you can deposit them with Karen Robertson. Mrs. Robertson is located on 5th oor of 1001 Sherbrooke Street West, O ce 517. Any appeal to your grade must be submitted in writing no later than 1 week after the grades have been announced. A request for a re-grade will result in a full second evaluation of all questions. The new outcome may be higher, the same or lower than the initial grade. For clarication questions about the assignment, please consult with Chao Xiong. Alternatively, you can consult with me during o ce hours. Try to have fun and good luck! 1 Hedging with Futures (13p) (a) Table 1 shows historical futures prices for crude oil traded on the NYMEX for the rst Wednesday of each month in 2015. Prices are given for dierent contract maturities ranging from January 2015 to December 2015.1 Prices are quoted in USD per barrel and each contract is for 1000 barrels. Give an intuitive explanation of varying price patterns in the table. (Hint: Given the current dynamics of crude oil prices, what are your expectations about the size of the convenience yield and teh storage costs? On which months is the term structure of futures prices in contango or backwardation? Is this consistent with your initial expectation of the convenience yield?) (b) Suppose that crude oil is currently priced at $37 per barrel and that the crude oil futures price with 4-month delivery is $38.88 per barrel. Assuming a continuously compounded interest rate of 4.5% and a convenience yield of 5.5%, what are the current implied annualized storage costs? (c) Assume, as an exporter of crude oil, that you would like to lock in the price for a large quantity of crude oil which you will produce 18 months from now. You discover 1 Thus, a column corresponds to one contract with prices given on dierent dates. A row corresponds to prices given on a particular date for dierent contract maturities. Date 07-Jan-15 04-Feb-15 04-Mar-15 01-Apr-15 06-May-15 03-Jun-15 01-Jul-15 05-Aug-15 02-Sep-15 07-Oct-15 04-Nov-15 02-Dec-15 Jan *48.77 Feb 48.65 *48.70 Delivery Month Mar Apr May Jun Jul 49.08 49.72 50.48 51.23 51.95 48.45 49.30 50.58 51.89 53.18 *51.60 51.53 53.23 54.55 55.74 *49.55 50.09 51.75 53.06 *60.7 60.93 62.00 *59.61 59.64 *56.87 Aug Sep Oct Nov 52.61 53.25 53.87 54.51 54.38 55.40 56.25 57.03 56.83 57.76 58.46 59.07 53.98 54.74 55.44 56.11 62.56 62.93 63.28 63.66 59.93 60.14 60.31 60.59 56.96 57.37 57.70 58.12 *45.11 45.15 45.55 46.18 *45.11 46.25 46.86 *48.13 47.81 *46.58 Dec 55.15 57.78 59.64 56.74 64.01 60.93 58.55 46.84 47.52 48.40 46.32 *40.10 Table 1: NYMEX Futures prices for crude oil for the rst Wednesday of each month in 2015. A * implies the spot price in the corresponding month. Source: Futures data from U.S. Energy Information Administration that the NYMEX futures crude oil contract for a 18-month delivery currently trades at $45.81 per barrel. Using the same assumptions and calculations made in (b), is there anything you would propose to do in this situation? (d) On Feb 6, 2015, as an airline company, you are concerned about a possible decrease in supply of oil over the next 6 months (i.e., August) due to tensions in the Middle East. Explain how you can use futures contracts to hedge your exposure to oil price risk. Assume the company would like to enter a position that is worth USD $3,500,000. How many contracts do you need to buy/sell? (e) Go to the web site of CME Group2 and nd the historical margin requirements for Light Sweet Crude Oil (WTI) on Feb 6, 2015 for the contract maturity traded in part (d). Assuming the airline company is a hedger, what is the total initial margin required for this position? What is the total maintenance margin? 2 Duration Hedging with Futures (16p) Liability-driven investment policies (LDI) have come to prominence in the UK and the U.S. as a result of recent changes in the regulatory and accounting frameworks. As a result, the O ce of the Superintendent of Financial Institutions of Canada decided to implement LDI policies in its federal pension plan. LDI aims to address the duration mismatch between assets and liabilities, which has become a non-negligible risk to the funding status of pension plans around the world. Assume that the Canada Pension Plan Investment Board (CPPIB) has the balance sheet illustrated in Table 2, in which all numbers are expressed in million $CAD. 2 http://www.cmegroup.com/clearing/risk-management/historical-margins.html 2 Assets Liabilities Liabilities 1,050 Equity Fixed Income 600 400 Total 1,000 Total 1,050 Table 2: Balance Sheet of Canada Pension Plan Investment Board. (a) Is the CPPIB currently under- or overfunded? By how much? (b) What is the total asset duration of CPPIB's investment portfolio, assuming that equity has a duration of zero years, and the xed income portfolio a duration of 5 years? (c) Assume a 10% decrease in global equity markets. How will this aect CPPIB's funding ratio? (d) Assume that the liabilities have a duration of 12 years. Given an independent decrease in interest rates of 100 basis points (i.e., a decrease by one percentage point), how will CPPIB's funding ratio change? Explain duration risk in relation to your ndings. (Hint: By independent, I mean that you should ignore your answer from question (c)). (e) Assume that CPPIB wants to hedge 70% of its liabilities against interest rate uctuations over the following year. It therefore decides to hedge its exposure by investing into bond futures contracts as the LDI solution. If the bond futures is currently priced at 109.4823 percent, and the underlying bond has a duration of 22 years and a par value of $CAD 1 million, how many contracts are needed in order to be fully immunized? You need indicate whether the fund needs to buy or to sell the futures contracts. (f) Once the LDI duration hedging solution is implemented, will the plan remain immunized against changes in interest rates? Why or why not? Explain. 3 Swap Pricing (18p) A Brazilian Software company (KondZilla) plans to expand its business to the U.S. market and requires USD$15 million to fund the expansion. The Brazilian company faces the following borrowing opportunities: obtain a 11.25% Brazilian real (BRL)-denominated loan in Brazil, or a 8.5% USD-denominated loan in the U.S. Meanwhile, a U.S. based minerals extraction company plans to expand its operations to Brazil and requires 60 million BRL to nance its project. The U.S. based company can secure either a 10.75% BRL-denominated loan in Brazil or a 7.5% USD-denominated loan in the U.S. (a) Which company has an absolute borrowing advantage, which company has a comparative borrowing advantage (and in which market)? Why? Which company would you consider to have a higher credit risk? 3 (b) As an alternative option to paying xed rate loans, both companies approach Deutsche Bank, who acts as an intermediary by suggesting to broker a currency swap between the two companies. Essentially, Deutsche Bank engages into a 4-year xed-for-xed currency-swap with both companies: The Brazilian company borrows 60 million BRL at 11.25% and swaps it with Deutsche Bank for a $15 million USD loan at 8.25%. The U.S. based company borrows $15 million USD at 7.5% and swaps it with Deutsche Bank for $60 million BRL at 10.5%. Assuming a at term structure of interest rates in both countries, 4% in the U.S. and 8% in the Brazil and the spot exchange rate of 4 BRL per USD. All interest rates are expressed in continuous compounding. Draw a sketch of the cash ows for the three stages in the transaction: initial cash ow, annual interest cash ow, principal payment at maturity. How much does Deutsche Bank make in USD from the annual exchange of interest cash ows (annual prot)? (c) Calculate the present value of the swap from the perspective of the U.S. based and Brazilian companies in USD. Explain whether entering into the swap contract is benecial to both companies compared to directly borrowing in the nancial markets? (d) Calculate the duration of the swap from the perspective of the Brazilian company. (Use continuous discounting!) (e) How would your answer to (d) change if Deutsche Bank were to use the oating annual rate of 4%+LIBOR instead of the xed rate of 8.25% in its swap with the Brazilian Company? (f) On January 8, 2016, almost 2 years into the swap contract, the ination rate shoots up to 10% in Brazil as Standard & Poor's downgraded Brazil's credit rating to junk earlier in September. Being concerned about the Brazilian company ability to honor the swap contract, Deutsche Bank decides to cancel the Brazilian leg of the swap transaction. How would this aect Deutsche Bank's overall risk prole? Give a qualitative answer. (g) In the above situation, what would happen if the spot exchange rate increases to 4.5 BRL per USD after Deutsche Bank cancels the contract of the Brazilian leg of the swap transaction? Do you think the cancellation of the contract was a good idea? (Hint: think about the credit risk and market risk of Deutsche Bank, and how the remaining cash ows would change with the new exchange rate.) 4 Currencies and Forward Pricing (19p) Table 3 lists the daily spot and forward quotes for the Euro/USD exchange rates in December 2015. The currency is quoted as the number of USD per Euro. 4 (a) December 3 and December 17 represent the two days with the largest price movements in December 2015, measured by the percentage change in spot prices. Go to the website of the European Central Bank (ECB, https://www.ecb.europa.eu/press) and the U.S. Federal Reserve Bank (FED, http://www.federalreserve.gov/monetarypolicy) to see whether there were any major monetary policy changes responsible for the price movements on these days. (b) The spot EUR/USD exchange rate has fallen to around 1.09 by the end of 2015 from 1.20 at the beginning of 2015. What is the intuition behind the exchange rate movement? After the news of an interest rate hike has been released, assuming that no further interest rate hike is expected in the United States, and assuming that uncovered interest rate parity holds, in what direction would you expect the future spot exchange rate to move? (c) Given your ndings in (a), was the subsequent price movement consistent with the change in monetary policy news? Do you think the monetary policy change surprised the market? (d) Describe the currency forward patterns across dierent maturities. Are the forward contracts trading at a premium or a discount? Are the patterns consistent with the theory of covered interest rate parity? (e) Given the spot, 1-month, 3-month, 6-month and 1-year forward rates for the Euro against the USD on December 30, 2015, compute the annualized interest rate dierential implied by each forward contract. (f) Repeat part (e) for December 2 and December 3. Compute and contrast the implied interest rate dierentials before and after the news is released. How are the implied interest rate dierentials related to actual interest rate dierentials? Briey Comment. (g) Go to Bloomberg's website and look up the level of the German stock index (DAX) on December 16, 2015. What is the level of the DAX 30 futures contract with March 2016 delivery on the same day? Hint: Bloomberg's website does not have historical data; but you can read the data from the historical data plot.3 (i) The March 2016 contract of the three-month Euribor futures traded at 100.165 on December 16, 2015. Given the spot and futures prices in (g), what was the annualized implied dividend yield on December 16, 2015? (j) Global markets fell in response to turmoil in the Chinese market on January 4, 2016. The DAX index fell more than 4%. Find the closing level of the DAX on January 4, 2016. Assuming the same interest rate and dividend yield as in (i), what should be the new price of a DAX futures price with March 2016 delivery? 3 You will nd information for the spot price at http://www.bloomberg.com/quote/DAX:IND, and information for the futures price at http://www.bloomberg.com/quote/GX1:IND. 5 01/12/2015 02/12/2015 03/12/2015 04/12/2015 07/12/2015 08/12/2015 09/12/2015 10/12/2015 11/12/2015 14/12/2015 15/12/2015 16/12/2015 17/12/2015 18/12/2015 21/12/2015 22/12/2015 23/12/2015 24/12/2015 25/12/2015 28/12/2015 29/12/2015 30/12/2015 31/12/2015 Source: Datastream. Spot 1.0608 1.0573 1.0852 1.0889 1.0853 1.0871 1.0963 1.0937 1.0997 1.1028 1.0921 1.0944 1.0834 1.0845 1.0918 1.0967 1.0880 1.0959 1.0959 1.0972 1.0906 1.0914 1.0863 1 month 1.0619 1.0584 1.0861 1.0898 1.0863 1.0881 1.0973 1.0948 1.1009 1.1040 1.0934 1.0956 1.0846 1.0856 1.0930 1.0979 1.0890 1.0969 1.0969 1.0982 1.0915 1.0922 1.0871 3 month 1.0636 1.0602 1.0877 1.0914 1.0878 1.0897 1.0988 1.0965 1.1025 1.1056 1.0950 1.0972 1.0862 1.0872 1.0946 1.0995 1.0907 1.0986 1.0986 1.0999 1.0933 1.0939 1.0889 6 month 1.0668 1.0635 1.0908 1.0943 1.0908 1.0927 1.1020 1.0996 1.1056 1.1087 1.0981 1.1004 1.0893 1.0903 1.0977 1.1027 1.0939 1.1018 1.1018 1.1031 1.0965 1.0972 1.0921 1 year 1.0748 1.0716 1.0984 1.1017 1.0985 1.1005 1.1098 1.1074 1.1134 1.1166 1.1060 1.1081 1.0972 1.0982 1.1057 1.1108 1.1018 1.1098 1.1098 1.1113 1.1047 1.1057 1.1004 Table 3: Euro/USD Spot and Forward Rates, December 2015. 6 5 Futures Arbitrage (12p) Anheuser-Busch InBev NV, the Belgium giant for beverages and brewing products, issued a mammoth $46bn bond on January 15, 2016 to fund its acquisition of the UK's SAB-Miller. The company received a record subscription of $110 billion from investors, allowing it to tap the bond market at a fairly low yield, thereby reducing its annual interest costs. This bond issue is the second-largest corporate debt sale on record and proves the strong demand for high-quality corporate bonds in light of the current weak performance in global equity markets. One of the issued bonds has a maturity of 10 years, a yield of 1.6 percentage points above the benchmark U.S. Treasury rate. Hint: you can ignore the accrued interest rate. (a) Suppose the 10-year benchmark Treasury bond yield is 2.07% on January 15, 2016. The bond of AB InBev has a coupon rate of 5%, and the coupon is paid semi-annually. What is the cash price of the AB Inbev bond for a notional value of $10,000? (b) The interest rate curve is upward sloping, with a 6-month USD interest rate of 0.4%, and a 9-month USD interest rate of 0.6%. What is the fair value of a futures contract on AB Inbev's bond with delivery on October 15, 2016, assuming no default risk? Hint: the futures price is quoted with a notional value of 100. (c) If the futures contract on AB Inbev's bond is trading at $109, is there an arbitrage opportunity? If yes, what is the portfolio strategy to exploit this arbitrage opportunity? (d) If one institutional investor faces a at (same rate for all maturities) borrowing cost of 0.8%, and a at lending rate of 0.6%, what is range of futures prices that provide no arbitrage opportunity? 6 Futures Pricing, Hedging and Margin Requirements (22p) Go to the web site of the Montreal Exchange (TMX) (https://www.m-x.ca/accueil en.php) and nd information related to the Five-Year Government of Canada Bond Futures contract, commonly referred to as the \"CGF\" contract. (a) What are the standardized contract terms of the CGF futures contract (Underlying, Contract size, tick size, initial margin ...)? Describe the contract! (b) Table 4 shows daily settlement prices, open interest and volume, for CGF contracts with delivery in March 2016, as well as P&L of an existing margin account that was entered on Dec. 1, 2015. Does the counterparty to the clearing house have a long or a short position in the CGF futures? How many contracts are held by the counterparty? Does the existing margin account belong to a speculator or hedger? What is the percentage of the maintenance margin over the initial margin? Hint: you can nd historical margin requirements for speculators and hedgers from the website of the TMX. 7 (c) Calculate the daily P&L and the value at the end of each day for this margin account from December 1 to December 7. You can assume the initial margin and maintenance margin are constant and given by the requirements on Dec. 1, 2015. How many margin calls are made? (d) Which of the margin requirements for hedgers and speculators is higher? Why? Since margin requirements change on a daily basis, could you think of at least two determinants of margin requirements? (e) Examine the relationship between volume and open interest? What does this tell you about the liquidity in this market? Is it possible that volume is greater than open interest? (f) Go to the website of the TMX (https://www.m-x.caego n jour en.php) and nd the daily settlement price of the CGF contract in December, 2015 (the TMX website only allows for downloading data of 5 days; but you could change the initial date several times to access the whole December data.) At the same time, go the web site of Bank of Canada (www.bankofcanada.ca/rates/interest-rates/lookup-bond-yields/) and nd the benchmark 5-year bond yields (selling at par) in December, 2015. In excel, compute the underlying prices of 5-year Canadian deliverable bonds (you should check the denition of the underlying in CGF's contract specication; for simplicity, you can treat the coupon rate as an annual payment). Calculate the optimal hedge ratio! (Note that for this question, you need to have the Data Analysis ToolPak installed in Excel: open Excel, go to \"Files,\" choose \"Options,\" then choose \"Add-ins,\" click on \"Analysis ToolPak,\" then click on the \"Go\" button next to Manage Excel Add-ins). The Data Analysis icon should now show on your Excel Toolbar. (g) How can you determine the hedge eectiveness? (h) Compare the cash prices and futures prices in (f). Which one is higher? Given that the theoretical futures price is determined by the cash price multiplied by the cost of carry as S0 er c , explain how the shape of yield (interest rate) curve inuences the futures price. (i) Consider the spot and the futures prices on December 15, 2015. If futures prices are determined according to S0 er c , what is the implied nancing rate? (j) Go back to the web site of the Montreal Exchange and browse the available CGF contracts with dierent maturities. Assume you would like to hedge a 5-year Canadian Government bond with nominal amount of $1,000,000, which comes due in August 2016. Which contract maturity would you choose to hedge your exposure? Why? How many contracts would you buy/sell? (k) The delivery standard of CGF contract requires 5-year Government of Canada Bonds which have an outstanding amount of at least C$3.5 billion nominal value. Explain the intuition behind this requirement. 8 Dec-01 Dec-02 Dec-03 Dec-04 Dec-07 Settl. price Open int. Vol. 124.81 4,810 100 124.72 4,571 103 124.20 4,521 259 124.49 4,643 263 124.85 4,634 250 Daily P&L Initial Margin 38040 -3600 Table 4: Margin Account 9 Maitainence Margin 34236