1. (20 points) Joseph considers making an investment of $5000 at the beginning of a year. He could use all of the $5000 to buy HSBC stock at the price of $35 per share; or use all of $5000 to buy a mutual fund at $10 per share; or put all of his money in the saving account. Joseph estimates that by the end of the year, the uni share price of HSBC stock will have a 60% chance to rise to $45 and a 40% chance to drop to $30. The share price of the mutual fund is estimated to be either $13 or $8 at the end of the year. It will have an 80% chance to be $13 if HSBC stock price rises, but have only 10% chance to rise to $13 if HSBC stock price drops. If Joseph puts all of his money in the saving account, the annual interest rate is 2%. Draw a decision tree to show how Joseph would make his optimal investment decision if his goal is to maximize his expected return at the end of the year