by Dr. Florin Diacu

o you hope to win the lottery some day? If not, you’re a happy exception. Why happy? Because if you buy a ticket your chances of winning are extremely small. A computation any math sophomore can do shows that the probability of getting all the numbers right at a 6/49 draw is approximately 1 in 14 million. It’s even worse for the 7/49: 1 in 86 million.
     No one can beat the mathematics. The last few 6/49 results tell that it takes about 140 million tickets, sold over several draws, to make 9 or 10 perfect winners. The statistics agree with the laws of probability.
     Your chances of getting killed in a car accident this year are bigger than one in 100,000, which means that you could die a thousand times before winning the lottery. Still, most people gamble and only a few fear driving.
     What about the stock market? Are our chances better there? The common wisdom says they are. We’re told to consult an expert, get a well-balanced portfolio, don’t panic, ignore the fluctuations, invest long term and our future is secure. Or is it? Let’s see what history tells us.
     Between the late 1870s and early 1920s the graph of the average stock price (rescaled to inflation) looks like the profile of a mountain range with a deep valley at the beginning and another at the end, both at about the same height. In other words, money invested in a hypothetical index fund in 1878 won nothing if retrieved in 1921. Then things improved all of a sudden.
     In 1929 stock prices reached an unprecedented high, twice above any previous peak and about 10 times the minimum of the 1920s. Returns were low, but nobody cared. The press of the time shows that investors were exuberant: the market goes only up, nothing can stop its hike; even if something bad happens, those in charge will fix the problem; we are safe.

Diacu (with someone else’s lottery tickets) (Valerie Shore photo)

     But stock prices went down, then up and down; every dip reached below the previous. In 1933 the market fell to an absolute low, lower than 12 years before. The depression loomed large and the level of unemployment made life very difficult. World War II began and led to a global disaster. As a consequence, the economy needed several decades to recover.
     In the late ’50s stock prices finally hiked to the level of 1929. Then they went down and up again. They have been above the 1929 peak only since the mid-’80s. All these historical facts are in sharp contrast with the myth of secure long-term stock-market investments.
     From 1994 to the early 2000 the Dow Jones Industrial Average, which measures the health of the American economy, sky rocketed from 3,600 to 11,700 points. Corporate profits, however, rose less than 60 per cent, and that from a depressed base. During the same period, living standards increased very little. Similar things had happened between 1922 and 1929.
     Since its peak in the year 2000, like in the early 1930s, the market went down. The events of last Sept. 11 seem to have accelerated this trend. Does this decreasing average of most indexes resemble what happened between 1930 and 1933? Are we on the brink of a depression? Not necessarily. In fact, nobody knows. But it doesn’t take an expert to understand that if the market continues to drop, people will lose confidence, sell, and make stock prices plunge even more. In the end, the attitude of investors is what drives the market up or down. It took more than 30 years to rebuild the trust lost after the plunge of the 1930s.
     Whereas the mathematics of lotteries is simple, the mathematics of the stock market is very complicated. Some of the mathematical results obtained in this direction were awarded the Nobel Prize for economics. They help us understand many aspects of the economy but they don’t get too far.
     Though attempts are being made to forecast the market, they’re of no practical use yet. Stock prices show all the characteristics of chaotic dynamic systems, which form an active research area in mathematics. The behaviour of those systems is as unpredictable as the weather.
     If playing the lottery will make us neither rich nor poor, investing pensions or education funds in stocks is a risk based on irrational assumptions. The only reason for such actions lies in a myth unjustified by history and unsupported by any reliable mathematical model.
     Though we know little about the moods of the market, one thing is for sure: a sharp drop in stock prices will affect us all whether we invested in stocks or not. But depending on many factors, including the adopted financial strategy, some will be more touched than others. So let’s hope for the best and be prepared for the worst — an attitude that could save us a lot of grief in the future.


Dr. Florin Diacu is a UVic mathematics professor and the UVic site director of the Pacific Institute for the Mathematical Sciences.