Finance & Investments assignment

Finance & Investments assignment SHOW YOUR WORK. (10 Questions/100 Total Points) 1. You wish to hedge 90 percent of the current portfolio value with futures. The value of the portfolio is $ 50 million and tracks the S&P 500 index. The index is 1,076.32 ($250 per point) and the portfolio has a beta of 1.2. Calculate the appropriate number of contracts to realize the hedge. 2. What would be the swap fixed rate (SFR) for a plain vanilla, two-year interest rate swap, payments every six months beginning 07/01/0x with the following assumptions/data: • Swap initiation, January 1, 200x • FRA1,0 = 2.221%; FRA1,1 = 2.258%; FRA1,2 = 2.322%; FRA1,3 = 2.388%; FRA1,4 = 2.520%; FRA1,5 = 2.632%; (Read the notation, FRA1,0 as “six-month forward rate from 01/01/0x, FRA1,1 as “six-month forward rate, six-months from 01/01/0x, FRA1,2 as “six-month forward rate, one-year from 01/01/0x, etc.. • LIBOR to remain at 2.18%. 3. The futures contract quote on 5,000 bushels of soybeans traded on the CBOT, Monday, December 31, 2001 was: Open: 423-3/4 ($4.2375/bushel) High: 424 ($4.24/bushel) Low: 419-1/2 ($4.1950/bushel) Settle: 421 ($4.21/bushel) You shorted 3 contracts at $4.22 on December 31, 2001. The settlement for January 2, 2002 was $4.18 (the markets were closed on New Year’s). If you had to post a $1,000 initial margin per contract upon placing the trade, what would be your trade account balance at the close of January 2, 2002? 4. Using the following data, calculate the fixed-rate payer’s first two net quarterly payments/receipts for a hypothetical interest rate swap described below. Notional principal $10 million Fixed rate 7.0% Days in first quarter 91 Days in second quarter 92 Current LIBOR (LIBOR0) 5.0% Expected LIBOR (LIBOR1) 5.3% Expected LIBOR (LIBOR2) 4.8% 5. Calculate the effective duration of a bond to a 100 basis point change in interest rates with a 6-1/4 coupon, 10-years remaining to maturity, and an asking quote of 110.7811 (decimal, not 32nds). 6. Calculate the effective convexity to a 100 basis point change of the bond in Question 5. 7. Calculate the total percentage price change (duration and convexity) to a 65 basis point decrease in interest rates for the bond in Questions 5 and 6. 8. Given the following Treasury spot rate curve, calculate the arbitrage-free value of a 6 percent coupon, 2-year Treasury note. Period Years Spot Rate (%) 1 0.5 3.0000 2 1.0 3.3000 3 1.5 3.5053 4 2.0 3.9164 9. What is the price of a $100,000 Treasury bill with 151 days left to maturity and a discount yield of 3.75 percent? 10. Using put-call parity, what market actions would you take to create a synthetic stock?