Can you help me out with this 3 questions. Any of them will help.

Question 3 S&P 500 Futures Settlements The spot index value = 1,852.21 SP CME S&P 500 FUTURES SETTLEMENT PRICES AS OF 02/09/16 03:20 PM (CST) MTH/ STRIKE MAR16 JUN16 SEP16 DEC16 MAR17 JUN17 SEP17 DEC17 DEC18 DEC19 DEC20 TOTAL TOTAL OPEN 1850.10 ---1815.00 ------------------------- ---- DAILY --HIGH LOW 1862.50 1853.20B 1845.60B 1839.60B 1835.40B 1832.30B 1830.30B 1829.50B 1836.30B ------- 1826.00 1818.20A 1810.60A 1804.60A 1800.40A 1797.30A 1795.30A 1794.50A 1801.30A ------- LAST 1848.50 1836.70A 1829.10A 1823.10A 1818.90A 1815.80A 1813.80A 1813.00A 1819.80A ------- SETT PT CHGE 1848.20 1839.40 1831.80 1825.60 1821.40 1818.30 1816.30 1815.50 1822.30 1845.40 1868.50 -3.80 -3.80 -3.80 -4.00 -4.00 -4.00 -4.00 -4.00 -4.00 -4.00 -4.00 EST.VOL 7514 263 1 EST.VOL 7778 ----SETT 1852.00 1843.20 1835.60 1829.60 1825.40 1822.30 1820.30 1819.50 1826.30 1849.40 1872.50 PRIOR DAY -VOL INT 6264 38 2 VOLUME 6304 126484 2674 198 OPEN INT 129356 (a) Calculate the theoretical price for the S&P500 index futures maturing in December 2016. Assume that the dividend yield on the index is 1.5% per year continuously compounded. Use the above quotes to determine whether there is an arbitrage opportunity. If there is an opportunity, show how the arbitrage would be made, using a payoff table. Assume that the futures contract expires at the end of the month, and use a T-bill rate of 0.45% per year continuously compounded. What are the potential problems with the arbitrage? Question 4 A fund manager has a portfolio worth $50 million with a beta of 0.92. The manager is concerned about the performance of the market over the next 3 months and plans to use 4-month futures contracts on the S&P 500 to hedge the risk. The current level of the index is 1,850, one contract is on 250 times the index, the risk-free rate is 0.30% per annum, and the dividend yield on the index is 1.5% per annum. The current 4-month futures price is 1,840. (a) What position should the fund manager take to eliminate all exposure to the market over the next three months? (b) Calculate the effect of your strategy on the fund manager's returns if the level of the market in three months is 1,700, 1,800, 1,900, and 2,000. Assume that the one-month futures price is 0.20% lower than the index level at this time. Question 5 FIN659 - T. Barkley - Problem Set 1 - Spring 2016 - Page 1/2 A five-year bond with a yield of 11% (continuously compounded) pays an 8% coupon at the end of each year. (a) What is the bond's price? (b) What is the bond's duration? (c) Use the duration to calculate the effect on the bond's price of a 0.2% decrease in its yield. (d) Recalculate the bond's price on the basis of a 10.8% per annum yield and verify that the result is in agreement with your answer to (c). FIN659 - T. Barkley - Problem Set 1 - Spring 2016 - Page 2/2