I teach Real Estate Market Analysis. For many people, the hardest part of this course is acting on the idea that we live in a probabilistic world. It is hard to find examples which illustrate that shift in perspective. Recent events offer two very good examples.
1/ On Testing: The Ontario government notes that 4470 people have been tested for the novel coronavirus and only 74 have shown evidence of the disease (with another 580 pending) (as of today): about 2 percent of people test positive.
Lesson 1: Almost all of the people who display enough symptoms to be tested do not have the disease. In other words, there is lots of uncertainty. Don’t panic.
2/ On the stock market: Lots of people have lost a lot of money during the past two weeks. Even yesterday, when the Toronto Stock Market index fell by the largest point loss in 80 years, it was possible to win.
Numbers add some perspective. Using data from the 200 trading days between May 14, 2019 and Feb. 28, 2020 (when prices were relatively calm), the average change per day was 0.00 percent. The daily (sample) standard deviation was 0.54 percent: i.e. if the daily change is between -0.54 percent and +0.54 percent then, regardless of the exciting media story, nothing special happened. Even a 1 percent change fails the test of being 95 percent confident that it is abnormal (i.e. 1/0.54= 1.85 which is less than the critical level of 1.96 needed to be 95 percent confident that the observed outcome is not due to random variation).
The TSX Index fell by 12.3 percent on Thursday. If you believe that randomness is described by the Normal distribution and in statistical independence over time, which is the basis of most familiar statistical analyses, then Thursday’s drop was equal to 22.8 standard deviations. The best probability table that I use gives up at 4 standard deviations. Excel claims that the probability of observing something even more extreme is about 10 to the power -113 percent (i.e. a 1 in 10000… chance with 115 zeros).
There are about 1600 stocks listed on the Toronto Stock Exchange and, on Thursday, at least 20 stocks worth more than $1 went up.
Lesson 2: A trend is nice but the trend does not apply to everybody. There are opportunities.
Lesson 3: Have a sense of perspective: prices go up and prices go down. That is true of stock prices and of house prices. Recognizing abnormal requires having a sense of normal. The language of probability and statistics was developed for that purpose. Use it.
PA