I was wondering if you could explain how they got to the answer in number 3.

Debt and Money Markets Professor Lee Problem Set 5: Forward and Swap Please do all calculations in Excel. Name: Michael Bennett UFID: 14139321 Bid Rate Ask Price in Decimal Bid Price in Decimal sh is ar stu ed d vi y re aC s o ou urc rs e eH w er as o. co m Question 1 Use the data below: STRIPS Maturity Ask Rate 0.5 5.29% 5.33% 97.42315748 97.406076 1 5.44% 5.47% 94.77416756 94.750183 1.5 5.58% 5.61% 92.07620302 92.031877 Remember, customers buy at the ask and sell at the bid; dealers buy at the bid and sell at the ask. a) Using spot transactions at the quoted STRIPS prices and rates, what forward price can an investor (customer) lock in today to buy $100 par of a zero maturing at time 1.5 for settlement at time 1? $97.1779 b) Similarly, what forward price can an investor (customer) lock in today to sell $100 par of a zero maturing at time 1.5 for settlement at time 1? Th $97.1065 c) A firm (customer) is planning to undertake a project at time 1 that will require an investment of $500,000. Funds won't become available until time 1.5. Thus, at time 1, the firm will have to borrow $500,000 for 6 months. The firm uses the spot market to lock in a forward loan from time 1 to time 1.5. How much will the firm have to pay back at time 1.5? $514,898.5929 Locking in the borrowing involves buying $500,000 par of a 1-year zero and selling an equal market value of 1.5-year zeroes. The 1-year zeroes cost $500,000 x d 1,ASK . To raise this money the firm must sell a par value of 1.5-year zeroes of $500,000 x d 1,ASK /d 1.5,BID =$500,000 x 0.94774168/0.9203125=$514,902. This is the https://www.coursehero.com/file/11467827/FIN4243-PROBLEM-SET-5/ amount the firm has to pay back at time 1.5. Question 2 The current price of $1 par of a zero maturing at time 2 is $0.90. In addition, you can contract today to purchase, at time 2, $1 par of a zero maturing at time 3. The forward price to pay at time 2 for this zero maturing at time 3 is $0.94. It costs nothing today to enter into this forward contract. a) What is the forward rate from time 2 to time 3? 6.284% sh is ar stu ed d vi y re aC s o ou urc rs e eH w er as o. co m F 2 3 = (1+f 2 3 /2) -2(3-2) = 0.94 => f 2 3 = 2((1/0.94) 1/2 -1) = 6.284249% b) Describe transactions in the 2-year zero and the forward contract that together synthesize a spot purchase of $1 par of the zero maturing at time 3. (With the spot purchase, you pay for the zero today, rather than in 2 years.) 2-Year Zero Buy Trade Par Forward Contract Buy 0.94 1.00 Enter into the forward contract and buy $0.94 par of the 2-year zero. At time 2, the maturing 2-year provides exactly enough cash to pay the forward price for the zero maturing at time 3. c) Assuming there are no arbitrage opportunities, what is the current spot price (the price to pay today) for $1 par of the zero maturing at time 3? $0.846 Th The synthetic spot purchase involves a cost of 0.90x0.94 = 0.846 today. This must be the no arbitrage price of the 3-year zero. Question 3 At time 0, Investor A enters into a forward contract, at no cost, to buy, at time 2, $100,000 par of a zero maturing at time 3. The forward price this investor locks in to pay at time 2 is $92,000. At time 1, the spot price of $1 par of a zero maturing at time 2 is 0.96 and the spot price of $1 par of a zero maturing at time 3 is 0.93. a) At time 1, what is the forward price an investor could lock in to pay, at time 2, for $100,000 par of a zero maturing at time 3? $96,875.00 https://www.coursehero.com/file/11467827/FIN4243-PROBLEM-SET-5/ b) What is the value, at time 1, of Investor A's position in the forward contract from part (a)? $4,680.00 Question 4 Consider the following information about three fixed income securities: Two coupon-bearing bonds in the table below and a forward contract written on a 1.5-year zero-coupon bond whose face value is The forward price today is $94.78 and the contract will be settled in 1-year time. Coupons are paid semi-annually. Use semi-annual compounding convention to compute the interest. Maturity (years) 1 2 Coupon Rate Price (per $100-par) 12% 103.80 6% 98.13 sh is ar stu ed d vi y re aC s o ou urc rs e eH w er as o. co m Bond # 1 1 t= a) Using the two bonds' prices in the above table, compute 0.5- and 1-year discounting factors. D.5= D1= 0.9654 0.9246 b) Describe the transactions in a zero-coupon bond maturing at 1-year and the given forward contract above that together synthesize a spot purchase of a $100-par zero-coupon bond maturing at 1.5-year. What is the no arbitrage price today of the 1.5-year $100-par zero-coupon bond? Th $87.63 c) Compute the price of the following forward contract: The settlement date of the forward is 0.5-year from today, and its underlying asset is Bond #2 in the above table. The forward contract is settled immediately after Bond #2 pays its coupon at 0.5-year. $98.65 Question 5 The table below lists semi-annual forward rate quotes from LIBOR forward rate agreements on April 7th, 2010. Fill in the table below by calculating the implied LIBOR zero prices and implied LIBOR swap rates from these https://www.coursehero.com/file/11467827/FIN4243-PROBLEM-SET-5/ LIBOR forward rate quotes. 0.5 1 1.5 2 2.5 3 4.00% 3.50% 3.00% 2.50% 2.00% 1.50% 1.00% 0.50% Th 0.00% 0.25% 0.47% 1.06% 1.66% sh is ar stu ed d vi y re aC s o ou urc rs e eH w er as o. co m Maturity t LIBOR Implied Implied Forward rate LIBOR LIBOR Actual swapTreasury f t -0.5t zero price d t swap rate rate par rates 0.37% 0.9982 0.37% 0.88% 0.9938 0.62% 0.58% 1.57% 0.9860 0.94% 2.32% 0.9747 1.28% 1.24% 2.76% 0.9615 1.58% 3.54% 0.9447 1.90% 1.88% https://www.coursehero.com/file/11467827/FIN4243-PROBLEM-SET-5/ LIBOR forward rate Implied LIBOR swap rate Actual LIBOR swap rate Treasury par rates Reference Cells $100.00 Th sh is ar stu ed d vi y re aC s o ou urc rs e eH w er as o. co m Par https://www.coursehero.com/file/11467827/FIN4243-PROBLEM-SET-5/ Par $500,000.00 Th sh is ar stu ed d vi y re aC s o ou urc rs e eH w er as o. co m Reference Cells 2-Year Zero 1-Year Forward Settlement date 0 2 Par $1.00 $1.00 Price $0.90 $0.94 Maturity 2 3 Reference Cells Time 0 1 Year Forward Settlement date 2 Par $100,000.00 Price $0.92 Maturity 3 https://www.coursehero.com/file/11467827/FIN4243-PROBLEM-SET-5/ Time 1 1 Year zero 2 Year Zero Settlement date 2 2 Par $100,000.00 $100,000.00 Price $0.96 $0.93 Maturity 2 3 sh is ar stu ed d vi y re aC s o ou urc rs e eH w er as o. co m bond whose face value is $100. 0 0.5 103.8 2(98.13) -6 3(2) -92.46 -106 103(2) 0 100 Th d1=.9246 1 https://www.coursehero.com/file/11467827/FIN4243-PROBLEM-SET-5/ Powered by TCPDF (www.tcpdf.org)