Joanne is thinking about opening a long position in IBM. She plans to buy 216 shares and to ask for a broker loan of $6,134.20. The initial margin is 39.98% and the maintenance margin is 14.74%. The initial price of IBM is $109.20. After doing some research, Joanne realizes that the price of IBM can be either $150.58 with probability 31.73%, or $98.09 with probability 131.73%. If she does not invest, she gets to keep a wealth of $11,459.15. If her utility function is U=ln(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