why 9.31?

Joanne is thinking about opening a long position in IBM. She plans to buy 133 shares and to ask for a broker loan of $6,407.18. The initial margin is 32.80% and the maintenance margin is 25.46%. The initial price of IBM is $106.51. After doing some research, Joanne realizes that the price of IBM can be either $154.61 with probability 67.60%, or $98.45 with probability 1-67.60%. If she does not invest, she gets to keep a wealth of $11,073.53. If her utility function is U=In(W) where "W" is the wealth. Assume there is no interest on the loan. Ignore margin calls. Compute Joanne's expected utility from the long position. Hint: start by computing the equity if the prices goes up or down. If she enters the position, assume all her wealth is just the equity in the position. 9.31 9.31 margin of error +/- 5% Joanne is thinking about opening a long position in IBM. She plans to buy 133 shares and to ask for a broker loan of $6,407.18. The initial margin is 32.80% and the maintenance margin is 25.46%. The initial price of IBM is $106.51. After doing some research, Joanne realizes that the price of IBM can be either $154.61 with probability 67.60%, or $98.45 with probability 1-67.60%. If she does not invest, she gets to keep a wealth of $11,073.53. If her utility function is U=In(W) where "W" is the wealth. Assume there is no interest on the loan. Ignore margin calls. Compute Joanne's expected utility from the long position. Hint: start by computing the equity if the prices goes up or down. If she enters the position, assume all her wealth is just the equity in the position. 9.31 9.31 margin of error +/- 5%