(a) On April 14, 2008 the 90-day LIBOR was 2.4588%. Did the rates converge?

(b) What was the total profit / loss on April 14, 2008 of a futures contract entered on October 16, 2007?

(c) What would be the total profit / loss on April 14, 2008 of a forward contract entered on October 16, 2007?

(d) Calculate the total profit / loss at each date for the futures contract and forward contract.

(e) How close are profits / losses over time? Plot the values.

Consider the data in Table 3, where pfut(t,T) is the price of a 90-day Eurodollar futures contract expiring on April 14, 2008; f(t,T1, T2) is the time t forward rate for 90-day LIBOR at April 14, 2008; Z(t,T) is the LIBOR discount from t to April 14, 2008; and Z(t, t + dt) is the overnight LIBOR discount (where dt =1 day). Date 16-Oct-07 pfut (t.1) f(t, Ti,T2) 95.6400 4.6877% Zt, T1) Z(t,t + dt) 0.9908 0.9998 17-Oct-07 95.7650 4.6240% 0.9910 0.9998 18-Oct-07 95.8200 0.9912 0.9998 4.5191% 4.3975% 19-Oct-07 95.9350 Table 3 Futures and Forward Rates Z(t, T) Z(t,t + dt) Date pfut, T) ft,T1, T2) 0.9763 0.9998 15-Jan-08 96.8400 3.4128% 0.9766 0.9998 16-Jan-08 96.8200 3.3952% 0.9768 0.9998 17-Jan-08 96.8750 3.4557% 0.9773 0.9998 18-Jan-08 96.9650 3.3795% 0.9780 0.9998 22-Jan-08 97.4000 3.0633% 0.9781 0.9998 23-Jan-08 97.4950 2.7888% 0.9783 0.9998 24-Jan-08 97.2850 2.8347% 0.9787 0.9998 25-Jan-08 97.3150 3.0457% 0.9789 0.9998 28-Jan-08 97.3750 2.8894% 0.9914 0.9998 22-Oct-07 95.9200 0.9922 0.9998 4.2910% 4.3708% 23-Oct-07 0.9931 0.9999 95.9200 96.0250 24-Oct-07 4.2684% 0.9934 0.9999 25-Oct-07 96.0250 4.1984% 0.9933 0.9999 26-Oct-07 95.9850 4.2208% 0.9937 0.9999 29-Oct-07 95.9500 4.2337% 0.9793 0.9998 29-Jan-08 97.3550 2.8914% 0.9938 0.9999 30-Oct-07 95.9300 4.3014% 0.9795 0.9998 30-Jan-08 97.4350 2.9048% 0.9939 0.9999 31-Oct-07 95.8000 4.2978% 0.9795 0.9998 97.4900 2.7524% 0.9941 0.9999 31-Jan-08 1-Feb-08 1-Nov-07 95.9200 4.4467% 0.9795 0.9998 97.4200 2.7229% 0.9999 0.9942 0.9944 2-Nov-07 96.0450 4.2823% 0.9998 4-Feb-08 97.3950 2.8175% 0.9999 0.9798 0.9801 95.9750 4.2683% 0.9998 5-Feb-08 97.4900 2.8289% 0.9944 0.9999 5-Nov-07 6-Nov-07 95.9550 4.3336% 0.9801 0.9998 6-Feb-08 97.5200 2.6975% 0.9946 0.9999 7-Nov-07 96.0050 4.2998% 0.9802 0.9998 7-Feb-08 97.5150 2.6797% 0.9947 0.9999 0.9999 8-Nov-07 96.1450 4.2525% 0.9805 0.9998 8-Feb-08 97.5400 2.7012% 0.9948 96.1800 4.1621% 0.9807 0.9998 11-Feb-08 2.6727% 0.9950 0.9999 97.5450 97.5400 96.1800 4.1147% 0.9812 0.9998 12-Feb-08 2.6667% 0.9951 0.9999 9-Nov-07 12-Nov-07 13-Nov-07 14-Nov-07 96.0500 4.1061% 0.9813 0.9998 13-Feb-08 97.5300 2.6624% 0.9952 0.9999 0.9999 96.0400 4.2176% 0.9813 0.9998 14-Feb-08 97.5150 2.6825% 0.9953 15-Nov-07 96.1950 4.1916% 0.9814 0.9998 97.5100 2.6946% 0.9954 0.9999 16-Nov-07 96.1950 4.1167% 0.9814 0.9998 15-Feb-08 19-Feb-08 20-Feb-08 97.4400 2.7201% 0.9957 0.9999 19-Nov-07 96.0850 4.1807% 0.9816 0.9998 97.4050 2.7613% 0.9958 0.9999 20-Nov-07 96.0800 4.1859% 0.9816 0.9998 21-Feb-08 97.4500 2.8112% 0.9958 0.9999 21-Nov-07 96.2000 4.1664% 0.9998 22-Feb-08 97.4000 2.7526% 0.9959 0.9999 0.9818 0.9820 23-Nov-07 96.2000 4.1445% 0.9998 25-Feb-08 97.3700 2.7999% 0.9961 0.9999 26-Nov-07 96.3450 4.2163% 0.9823 0.9998 26-Feb-08 97.3950 2.8041% 0.9962 0.9999 27-Nov-07 96.2200 4.1268% 0.9824 0.9998 27-Feb-08 2.7692% 0.9963 0.9999 97.4400 97.5000 28-Nov-07 96.1400 4.2386% 0.9824 0.9998 28-Feb-08 2.7251% 0.9964 0.9999 29-NOV-07 96.2350 4.2269% 0.9825 0.9998 97.6300 2.7005% 29-Feb-08 3-Mar-08 0.9966 0.9968 0.9999 0.9999 30-Nov-07 96.2500 4.2295% 0.9826 0.9998 97.6050 2.6394% 3-Dec-07 96.2200 4.1883% 0.9830 0.9998 4-Mar-08 97.5900 2.6463% 0.9969 0.9999 4-Dec-07 96.2150 4.2106% 0.9831 0.9998 5-Mar-08 97.5500 2.6499% 0.9970 0.9999 5-Dec-07 96.2150 4.2254% 0.9832 0.9998 6-Mar-08 97.5850 2.6599% 0.9971 0.9999 6-Dec-07 96.1250 4.2285% 0.9834 0.9998 7-Mar-08 97.7300 2.5730% 0.9972 0.9999 0.9999 7-Dec-07 95.9900 4.2979% 0.9835 0.9998 10-Mar-08 97.7350 2.5766% 0.9975 10-Dec-07 95.9750 4.4052% 0.9838 0.9998 11-Mar-08 2.5463% 0.9976 0.9999 97.6500 97.6950 11-Dec-07 95.9550 4.3895% 0.9839 0.9998 12-Mar-08 2.5598% 0.9977 0.9999 12-Dec-07 96.0600 4.3833% 0.9841 0.9998 13-Mar-08 2.4937% 0.9978 0.9999 97.7400 97.8850 13-Dec-07 95.9850 4.2507% 0.9845 0.9998 14-Mar-08 2.4650% 0.9979 0.9999 14-Dec-07 95.8900 4.3378% 0.9998 17-Mar-08 98.0200 2.2305% 0.9999 0.9846 0.9850 0.9983 0.9984 17-Dec-07 95.9500 4.3672% 0.9998 18-Mar-08 97.8000 2.2285% 0.9999 18-Dec-07 96.0350 4.3408% 0.9852 0.9998 97.8100 2.3206% 0.9984 0.9999 19-Mar-08 20-Mar-08 19-Dec-07 96.0950 4.2711% 0.9854 0.9998 97.7775 0.9985 0.9999 2.3322% 2.4102% 20-Dec-07 96.1200 4.2180% 0.9856 0.9998 25-Mar-08 97.6850 0.9988 0.9999 21-Dec-07 96.0750 4.2125% 0.9858 0.9998 26-Mar-08 97.6750 0.9988 2.4171% 2.4216% 0.9999 0.9999 24-Dec-07 96.0550 4.2241% 0.9862 0.9998 27-Mar-08 97.6775 0.9988 27-Dec-07 96.0550 4.2554% 0.9866 0.9998 28-Mar-08 97.6750 2.4344% 0.9989 0.9999 28-Dec-07 96.1350 4.2421% 0.9870 0.9998 31-Mar-08 97.6900 2.4204% 0.9991 0.9999 31-Dec-07 96.1850 4.1691% 0.9873 0.9998 97.6300 2.4133% 0.9991 2-Jan-08 96.3100 4.1392% 0.9876 0.9998 97.5700 2.4437% 0.9992 0.9999 0.9999 0.9999 3-Jan-08 96.3350 3.9869% 0.9879 0.9998 97.5575 2.4804% 0.9993 4-Jan-08 96.4450 4.0055% 0.9880 0.9998 97.6100 2.4852% 0.9993 0.9999 7-Jan-08 96.4700 3.8896% 0.9886 0.9998 97.5650 2.4620% 0.9995 0.9999 1-Apr-08 2-Apr-08 3-Apr-08 4-Apr-08 7-Apr-08 8-Apr-08 9-Apr-08 10-Apr-08 11-Apr-08 14-Apr-08 8-Jan-08 96.4800 3.8683% 0.9888 0.9998 97.5050 2.4566% 0.9996 0.9999 9-Jan-08 96.5800 3.8023% 0.9891 0.9998 97.5300 2.4582% 0.9996 0.9999 10-Jan-08 96.6500 3.7389% 0.9894 0.9998 97.5300 2.4474% 0.9997 0.9999 11-Jan-08 96.8300 3.6358% 0.9898 0.9998 97.5350 2.4474% 0.9998 0.9999 14-Jan-08 96.8800 3.4026% 0.9906 0.9998 97.5412 2.4588% 1.0000 0.9999 Consider the data in Table 3, where pfut(t,T) is the price of a 90-day Eurodollar futures contract expiring on April 14, 2008; f(t,T1, T2) is the time t forward rate for 90-day LIBOR at April 14, 2008; Z(t,T) is the LIBOR discount from t to April 14, 2008; and Z(t, t + dt) is the overnight LIBOR discount (where dt =1 day). Date 16-Oct-07 pfut (t.1) f(t, Ti,T2) 95.6400 4.6877% Zt, T1) Z(t,t + dt) 0.9908 0.9998 17-Oct-07 95.7650 4.6240% 0.9910 0.9998 18-Oct-07 95.8200 0.9912 0.9998 4.5191% 4.3975% 19-Oct-07 95.9350 Table 3 Futures and Forward Rates Z(t, T) Z(t,t + dt) Date pfut, T) ft,T1, T2) 0.9763 0.9998 15-Jan-08 96.8400 3.4128% 0.9766 0.9998 16-Jan-08 96.8200 3.3952% 0.9768 0.9998 17-Jan-08 96.8750 3.4557% 0.9773 0.9998 18-Jan-08 96.9650 3.3795% 0.9780 0.9998 22-Jan-08 97.4000 3.0633% 0.9781 0.9998 23-Jan-08 97.4950 2.7888% 0.9783 0.9998 24-Jan-08 97.2850 2.8347% 0.9787 0.9998 25-Jan-08 97.3150 3.0457% 0.9789 0.9998 28-Jan-08 97.3750 2.8894% 0.9914 0.9998 22-Oct-07 95.9200 0.9922 0.9998 4.2910% 4.3708% 23-Oct-07 0.9931 0.9999 95.9200 96.0250 24-Oct-07 4.2684% 0.9934 0.9999 25-Oct-07 96.0250 4.1984% 0.9933 0.9999 26-Oct-07 95.9850 4.2208% 0.9937 0.9999 29-Oct-07 95.9500 4.2337% 0.9793 0.9998 29-Jan-08 97.3550 2.8914% 0.9938 0.9999 30-Oct-07 95.9300 4.3014% 0.9795 0.9998 30-Jan-08 97.4350 2.9048% 0.9939 0.9999 31-Oct-07 95.8000 4.2978% 0.9795 0.9998 97.4900 2.7524% 0.9941 0.9999 31-Jan-08 1-Feb-08 1-Nov-07 95.9200 4.4467% 0.9795 0.9998 97.4200 2.7229% 0.9999 0.9942 0.9944 2-Nov-07 96.0450 4.2823% 0.9998 4-Feb-08 97.3950 2.8175% 0.9999 0.9798 0.9801 95.9750 4.2683% 0.9998 5-Feb-08 97.4900 2.8289% 0.9944 0.9999 5-Nov-07 6-Nov-07 95.9550 4.3336% 0.9801 0.9998 6-Feb-08 97.5200 2.6975% 0.9946 0.9999 7-Nov-07 96.0050 4.2998% 0.9802 0.9998 7-Feb-08 97.5150 2.6797% 0.9947 0.9999 0.9999 8-Nov-07 96.1450 4.2525% 0.9805 0.9998 8-Feb-08 97.5400 2.7012% 0.9948 96.1800 4.1621% 0.9807 0.9998 11-Feb-08 2.6727% 0.9950 0.9999 97.5450 97.5400 96.1800 4.1147% 0.9812 0.9998 12-Feb-08 2.6667% 0.9951 0.9999 9-Nov-07 12-Nov-07 13-Nov-07 14-Nov-07 96.0500 4.1061% 0.9813 0.9998 13-Feb-08 97.5300 2.6624% 0.9952 0.9999 0.9999 96.0400 4.2176% 0.9813 0.9998 14-Feb-08 97.5150 2.6825% 0.9953 15-Nov-07 96.1950 4.1916% 0.9814 0.9998 97.5100 2.6946% 0.9954 0.9999 16-Nov-07 96.1950 4.1167% 0.9814 0.9998 15-Feb-08 19-Feb-08 20-Feb-08 97.4400 2.7201% 0.9957 0.9999 19-Nov-07 96.0850 4.1807% 0.9816 0.9998 97.4050 2.7613% 0.9958 0.9999 20-Nov-07 96.0800 4.1859% 0.9816 0.9998 21-Feb-08 97.4500 2.8112% 0.9958 0.9999 21-Nov-07 96.2000 4.1664% 0.9998 22-Feb-08 97.4000 2.7526% 0.9959 0.9999 0.9818 0.9820 23-Nov-07 96.2000 4.1445% 0.9998 25-Feb-08 97.3700 2.7999% 0.9961 0.9999 26-Nov-07 96.3450 4.2163% 0.9823 0.9998 26-Feb-08 97.3950 2.8041% 0.9962 0.9999 27-Nov-07 96.2200 4.1268% 0.9824 0.9998 27-Feb-08 2.7692% 0.9963 0.9999 97.4400 97.5000 28-Nov-07 96.1400 4.2386% 0.9824 0.9998 28-Feb-08 2.7251% 0.9964 0.9999 29-NOV-07 96.2350 4.2269% 0.9825 0.9998 97.6300 2.7005% 29-Feb-08 3-Mar-08 0.9966 0.9968 0.9999 0.9999 30-Nov-07 96.2500 4.2295% 0.9826 0.9998 97.6050 2.6394% 3-Dec-07 96.2200 4.1883% 0.9830 0.9998 4-Mar-08 97.5900 2.6463% 0.9969 0.9999 4-Dec-07 96.2150 4.2106% 0.9831 0.9998 5-Mar-08 97.5500 2.6499% 0.9970 0.9999 5-Dec-07 96.2150 4.2254% 0.9832 0.9998 6-Mar-08 97.5850 2.6599% 0.9971 0.9999 6-Dec-07 96.1250 4.2285% 0.9834 0.9998 7-Mar-08 97.7300 2.5730% 0.9972 0.9999 0.9999 7-Dec-07 95.9900 4.2979% 0.9835 0.9998 10-Mar-08 97.7350 2.5766% 0.9975 10-Dec-07 95.9750 4.4052% 0.9838 0.9998 11-Mar-08 2.5463% 0.9976 0.9999 97.6500 97.6950 11-Dec-07 95.9550 4.3895% 0.9839 0.9998 12-Mar-08 2.5598% 0.9977 0.9999 12-Dec-07 96.0600 4.3833% 0.9841 0.9998 13-Mar-08 2.4937% 0.9978 0.9999 97.7400 97.8850 13-Dec-07 95.9850 4.2507% 0.9845 0.9998 14-Mar-08 2.4650% 0.9979 0.9999 14-Dec-07 95.8900 4.3378% 0.9998 17-Mar-08 98.0200 2.2305% 0.9999 0.9846 0.9850 0.9983 0.9984 17-Dec-07 95.9500 4.3672% 0.9998 18-Mar-08 97.8000 2.2285% 0.9999 18-Dec-07 96.0350 4.3408% 0.9852 0.9998 97.8100 2.3206% 0.9984 0.9999 19-Mar-08 20-Mar-08 19-Dec-07 96.0950 4.2711% 0.9854 0.9998 97.7775 0.9985 0.9999 2.3322% 2.4102% 20-Dec-07 96.1200 4.2180% 0.9856 0.9998 25-Mar-08 97.6850 0.9988 0.9999 21-Dec-07 96.0750 4.2125% 0.9858 0.9998 26-Mar-08 97.6750 0.9988 2.4171% 2.4216% 0.9999 0.9999 24-Dec-07 96.0550 4.2241% 0.9862 0.9998 27-Mar-08 97.6775 0.9988 27-Dec-07 96.0550 4.2554% 0.9866 0.9998 28-Mar-08 97.6750 2.4344% 0.9989 0.9999 28-Dec-07 96.1350 4.2421% 0.9870 0.9998 31-Mar-08 97.6900 2.4204% 0.9991 0.9999 31-Dec-07 96.1850 4.1691% 0.9873 0.9998 97.6300 2.4133% 0.9991 2-Jan-08 96.3100 4.1392% 0.9876 0.9998 97.5700 2.4437% 0.9992 0.9999 0.9999 0.9999 3-Jan-08 96.3350 3.9869% 0.9879 0.9998 97.5575 2.4804% 0.9993 4-Jan-08 96.4450 4.0055% 0.9880 0.9998 97.6100 2.4852% 0.9993 0.9999 7-Jan-08 96.4700 3.8896% 0.9886 0.9998 97.5650 2.4620% 0.9995 0.9999 1-Apr-08 2-Apr-08 3-Apr-08 4-Apr-08 7-Apr-08 8-Apr-08 9-Apr-08 10-Apr-08 11-Apr-08 14-Apr-08 8-Jan-08 96.4800 3.8683% 0.9888 0.9998 97.5050 2.4566% 0.9996 0.9999 9-Jan-08 96.5800 3.8023% 0.9891 0.9998 97.5300 2.4582% 0.9996 0.9999 10-Jan-08 96.6500 3.7389% 0.9894 0.9998 97.5300 2.4474% 0.9997 0.9999 11-Jan-08 96.8300 3.6358% 0.9898 0.9998 97.5350 2.4474% 0.9998 0.9999 14-Jan-08 96.8800 3.4026% 0.9906 0.9998 97.5412 2.4588% 1.0000 0.9999