Repeat the exercise (i.e., show the analogous Table 4-2) considering now that the agent takes a short position in two gold futures contracts. Use the same sequence of random numbers for the daily variation in the settlement price to generate the tables for the agents with long and with short positions. Given a specific scenario (i.e., for a certain sequence of random numbers for the daily variation in the settlement price), answer the following questions: 1) Is there a symmetry (same values but with different sign) in the cumulative gain column for the long and short positions? Why? 2) Is there a symmetry in the margin call column for the long and short positions? Why?

Consider the operation of margins for a long position in two gold futures contracts as appears in Table 4-2 in your class notes. Day (s) Trade price Settlement price (Ps) Daily gain Cumulative gain Margin account balance Margin call 1,250.00 12,000.00 1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Pi P2 P3 P4 Ps P6 P7 P8 P9 P10 P11 P12 P13 P14 P15 P 16 Assume that the daily settlement price (Ps) is a random variable, and that the daily price movement limits established by the exchange are equal to 2% (i.e; the limit up is 0.02 and the limit down is -0.02 with respect to the price of the previous day). Generate a sequence of random numbers which follow a standard Gaussian distribution (standard normal distribution) for the daily variation in the settlement price and show the analogous Table 4-2 (i.e, settlement price, daily gain, cumulative gain, margin account balance and margin call) for that specific scenario. Additional explanatory information: The futures price when the futures contract is entered into is the one in Table 4-2 (1,250.00) and starting from that price you should generate the sequence of random numbers. Notice that the daily variation should be expressed as a percentage so once the random number X is generated, you have to divide by 100. Thus: P = Pt-1 (1+) = Where -2