question 1.2

1. A company enters into a short futures position for 10,000 barrels of oil at a futures price of $74 per barrel. The initial margin is $8 per barrel and the maintenance margin is $5 per barrel. What is (1) the balance in the margin account after marking to market at the end of the first day if the futures price has risen to $76.50 and (ii) the price above which a margin call will be made? a. (i) $55,000 and (ii) $77.00 b. (0) $55,000 and (ii) $78.00 c. () $50,000 and (ii) $77.00 d. (i) $50,000 and (ii) $78.00 e. None of the above. 2. On March 1st a commodity's spot price was $72 and its August futures price was $68. A company entered into futures contracts on March 18 to hedge its purchase of the commodity on July 1st using the August futures contract. It closes out its position on July 1st. What is the effective price (after taking account of hedging) paid by the company if on July 1st (1) the spot price is $75 and the August futures price is $72.30 and (ii) the spot price is $64 and the August futures price is $61.80? a. (1) $70.70 and (ii) $67.80 b. () $72.30 and (it) $67.80 c. (1) $72.30 and (ii) $70.20 d. (0) $70.70 and (ii) $70.20 e. None of the above. 3. A person receives $14,250 in one year in return for an investment of $12,300 now. What is the percentage return per annum (to the nearest 0.01%) with: (1) monthly compounding and (ii) continuous compounding? a. (i) 14.81%; and (ii) 14.67% b. (i) 14.94%; and (ii) 14.67% C. () 14.81%; and (ii) 14.72% d. (i) 14.94%; and (ii) 14.72% e. None of the above. 4. A ninth-month long forward contract on a non-dividend paying stock is entered into when the stock price is 4.36 and the risk-free rate of interest is 4% per annum with continuous compounding. Six months later, the price of the stock is 4.85 and the risk-free rate of interest has fallen to 3% per annum. To the nearest 0.01, what are (i) the forward price when the contract is entered into and (ii) the value of the forward contract six months after it was entered into? a. (i) 4.49 and (ii) 0.48 b. (i) 4.49 and (ii) 0.39 c. (i) 4.63 and (ii) 0.48 d. (i) 4.63 and (ii) 0.39 e. None of the above. 5. An investor has a long position in a well-diversified portfolio of UK stocks. The value of the portfolio is 42 million and the beta of the portfolio is 1.4. The investor plans to use the FTSE 100 stock index futures contract to change the risk associated with this portfolio. The current value of the relevant futures contract is 7400 index points. Each contract delivers 10 per full index point. Calculate the number of contracts (to the nearest full contract) to be bought or sold to (i) fully beta hedge the portfolio and (ii) increase the beta to 1.6. a. () short 795 contract and (ii) long 114 contracts b. (i) long 795 contract and (ii) short 114 contracts c. (i) short 568 contract and (ii) long 341 contracts d. (i) long 568 contract and (ii) short 341 contracts e. None of the above. 6. Which of the following increases basis risk? a. A large difference between the futures price when the hedge is put in place and the futures price when the hedge is closed out b. A large difference between the spot price when the hedge is put in place and the spot price when the hedge is closed out c. Dissimilarity between the underlying asset of the futures contract and the hedger's exposure d. A reduction in the time between the date when the futures contract is closed and its delivery month e. None of the above Table for N(x) When x 0 This table shows values of N(x) for x > 0. The table should be used with interpolation. For example, N(0.6278) = N(0.62) +0.78[N(0.63) - N(0.62)] -0.7324 +0.78 x (0.7357 -0.7324) =0.7350 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4.0 .00 0.5000 0.5398 0.5793 0.6179 0.6554 0.6915 0.7257 0.7580 0.7881 0.8159 0.8413 0.8643 0.8849 0.9032 0.9192 0.9332 0.9452 0.9554 0.9641 0.9713 0.9772 0.9821 0.9861 0.9893 0.9918 0.9938 0.9953 0.9965 0.9974 0.9981 0.9986 0.9990 0.9993 0.9995 0.9997 0.9998 0.9998 0.9999 0.9999 1.0000 1.0000 .01 0.5040 0.5438 0.5832 0.6217 0.6591 0.6950 0.7291 0.7611 0.7910 0.8186 0.8438 0.8665 0.8869 0.9049 0.9207 0.9345 0.9463 0.9564 0.9649 0.9719 0.9778 0.9826 0.9864 0.9896 0.9920 0.9940 0.9955 0.9966 0.9975 0.9982 0.9987 0.9991 0.9993 0.9995 0.9997 0.9998 0.9998 0.9999 0.9999 1.0000 1.0000 .02 0.5080 0.5478 0.5871 0.6255 0.6628 0.6985 0.7324 0.7642 0.7939 0.8212 0.8461 0.8686 0.8888 0.9066 0.9222 0.9357 0.9474 0.9573 0.9656 0.9726 0.9783 0.9830 0.9868 0.9898 0.9922 0.9941 0.9956 0.9967 0.9976 0.9982 0.9987 0.9991 0.9994 0.9995 0.9997 0.9998 0.9999 0.9999 0.9999 1.0000 1.0000 .03 0.5120 0.5517 0.5910 0.6293 0.6664 0.7019 0.7357 0.7673 0.7967 0.8238 0.8485 0.8708 0.8907 0.9082 0.9236 0.9370 0.9484 0.9582 0.9664 0.9732 0.9788 0.9834 0.9871 0.9901 0.9925 0.9943 0.9957 0.9968 0.9977 0.9983 0.9988 0.9991 0.9994 0.9996 0.9997 0.9998 0.9999 0.9999 0.9999 1.0000 1.0000 .04 0.5160 0.5557 0.5948 0.6331 0.6700 0.7054 0.7389 0.7704 0.7995 0.8264 0.8508 0.8729 0.8925 0.9099 0.9251 0.9382 0.9495 0.9591 0.9671 0.9738 0.9793 0.9838 0.9875 0.9904 0.9927 0.9945 0.9959 0.9969 0.9977 0.9984 0.9988 0.9992 0.9994 0.9996 0.9997 0.9998 0.9999 0.9999 0.9999 1.0000 1.0000 .05 0.5199 0.5596 0.5987 0.6368 0.6736 0.7088 0.7422 0.7734 0.8023 0.8289 0.8531 0.8749 0.8944 0.9115 0.9265 0.9394 0.9505 0.9599 0.9678 0.9744 0.9798 0.9842 0.9878 0.9906 0.9929 0.9946 0.9960 0.9970 0.9978 0.9984 0.9989 0.9992 0.9994 0.9996 0.9997 0.9998 0.9999 0.9999 0.9999 1.0000 1.0000 .06 0.5239 0.5636 0.6026 0.6406 0.6772 0.7123 0.7454 0.7764 0.8051 0.8315 0.8554 0.8770 0.8962 0.9131 0.9279 0.9406 0.9515 0.9608 0.9686 0.9750 0.9803 0.9846 0.9881 0.9909 0.9931 0.9948 0.9961 0.9971 0.9979 0.9985 0.9989 0.9992 0.9994 0.9996 0.9997 0.9998 0.9999 0.9999 0.9999 1.0000 1.0000 .07 0.5279 0.5675 0.6064 0.6443 0.6808 0.7157 0.7486 0.7794 0.8078 0.8340 0.8577 0.8790 0.8980 0.9147 0.9292 0.9418 0.9525 0.9616 0.9693 0.9756 0.9808 0.9850 0.9884 0.9911 0.9932 0.9949 0.9962 0.9972 0.9979 0.9985 0.9989 0.9992 0.9995 0.9996 0.9997 0.9998 0.9999 0.9999 0.9999 1.0000 1.0000 .OR 0.5319 0.5714 0.6103 0.6480 0.6844 0.7190 0.7517 0.7823 0.8106 0.8365 0.8599 0.8810 0.8997 0.9162 0.9306 0.9429 0.9535 0.9625 0.9699 0.9761 0.9812 0.9854 0.9887 0.9913 0.9934 0.9951 0.9963 0.9973 0.9980 0.9986 0.9990 0.9993 0.9995 0.9996 0.9997 0.9998 0.9999 0.9999 0.9999 1.0000 1.0000 .09 0.5359 0.5753 0.6141 0.6517 0.6879 0.7224 0.7549 0.7852 0.8133 0.8389 0.8621 0.8830 0.9015 0.9177 0.9319 0.9441 0.9545 0.9633 0.9706 0.9767 0.9817 0.9857 0.9890 0.9916 0.9936 0.9952 0.9964 0.9974 0.9981 0.9986 0.9990 0.9993 0.9995 0.9997 0.9998 0.9998 0.9999 0.9999 0.9999 1.0000 1.0000