Paul is a police detective in Glasgow. He solves 70% of his murder cases. This is not a bad achievement considering that he only actively researches 30% of the cases. If he actively researches a case, he has a 90% chance of solving it.

2.1. Assuming that he solves a case, how likely is it that he actively researched it? 2.2. If somebody answers 80% to question 2.1, what type of error is he or she committing? Explain your answer. Ten years later, Paul has set up his own private detective agency. You are curious as to how much salary Paul is earning. You discuss the case with your 12-year old son, who knows absolutely nothing about salaries of private detectives, and he says: I would not be surprised if Paul earns a million dollars per year. Ten minutes later, when you are asked by a colleague how much you think that Paul earns, you reply: Probably a million dollars.'

2.3. Which bias is described in the story above? Given his large success as a private detective, Paul wants to start investing in the stock market. However, he is worried about the occurrence of a new stock market bubble. Therefore, he actively reads up on the Tech/Internet bubble burst that occurred in the year 2000. This bubble was predicted by Alan Greenspan and Robert Shiller well before the year 2000 when they argued that the market could be described by the term irrational exuberance.

2.4. What does the term irrational exuberance mean?

In his job, Paul makes a lot of money from arbitrage. However, one of the problems he has encountered is noise-trader risk. 2.5. Explain the term noise-trader risk. 2.6. Mention and briefly describe two other factors that hamper arbitrage.