Ka-fu Wong & Liang Dai University of Hong Kong 12 March 2007 Is the financial analyst in fact a dummy?* Solving Question 5.97 of Newbold and Carlson and Thorne, 6th edition Ka-fu Wong & Liang Dai University of Hong Kong 12 March 2007 *The ppt is a joint effort: Liang Dai discussed the question with Dr. Ka-fu Wong on 7th March 2007; Ka-fu suggested an interpretation; Liang drafted the ppt; Ka-fu revised it. Use it at your own risks. Comments, if any, should be sent to kafuwong@econ.hku.hk.

The candidate The other day, a young man came into my office, who wanted to work for me as a financial analyst. Using detailed cash flow information, he claimed to be able to spot companies that are likely candidates for bankruptcy. Should I hire him?

Well, let me test him first The analyst was presented with information on the past records of 15 companies and told that, in fact, 5 of these had failed. “Hey, young man, it’s your turn to show your talent! “

Is he worth the salary? To what extent can he work better than an ordinary person, who knows little about financial analysis?

Is he a dummy? Let’s have a glance at a dummy’s performance If a dummy knew nothing about finance and randomly chose 5 from the 15 firms, what is the likelihood that he could have done no worse than the young expert? What is the likelihood that the expert is in fact a dummy?

The likelihood The probability of x successes from 5 firms randomly chosen from the 15 firms follows the hypergeometric distribution. x P(X=x) 0.08392 1 0.34965 2 0.39960 3 0.14985 4 0.01665 5 0.00033 x P(X≥x) 1 0.91608 2 0.56643 3 0.16683 4 0.01698 5 0.00033

The likelihood x P(X≥x) 1 0.91608 2 0.56643 3 0.16683 4 0.01698 5 1 0.91608 2 0.56643 3 0.16683 4 0.01698 5 0.00033 Probability that a dummy can successfully identify at least 3 out of the 5 firms is 0.16683. That is, the probability that the applicant who can successfully identify at least 3 out of the 5 firms but is really a dummy is 0.16683

The conclusion If 0.16683 is considered as small enough, then I should hire the young man.

The question, directly from the text. Using detailed cash flow information, a financial analyst claims to be able to spot companies that are likely candidates for bankruptcy. The analyst is presented with information on the past records of 15 companies and told that, in fact, 5 of these have failed. He selects as candidates for failure 5 companies from the group of 15. In fact, 3 of the 5 companies selected by the analyst were among those that failed. Evaluate the financial analyst’s performance on this test of his ability to detect failed companies.