Normal people cringe when they hear the word “statistics” (or they slip into a glassy-eyed stupor). I think it’s a very exciting subject that, for the most part, gets a bad rap. Mark Twain decried, “There are lies, there are damn lies, and then there are statistics!” He was talking about polling data, which can be highly subjective. A pollster can design a poll to say whatever he wants it to say depending on how he phrases a question. But to an investor (or a baseball fan) statistics are a vital component of our analytical toolbox, especially if we’re measuring absolute data, like the daily closing price of an index or the number of hits a player gets in a baseball game. These data points help us to assess past performance and gives us an idea of the possible outcomes the future can hold. This helps wealth managers determine which indices would make good portfolio components and it helps baseball teams determine which players they will offer a lucrative contract.
All you need to know about statistics and investing can be summed up as follows:
The average is the midpoint of all the returns that are measured over a period of time. In other words, half of the results measured will be higher than the average and half of the results will be lower than the average. For example, the annualized return for the Dow Jones Industrial Average (DJIA) since September of 1987 was 8.07% (source: Dow Jones Indexes). This takes into account the crash in October of that year, which was the single largest one month decline of -23%, and our recent performance through March of 2009. As we all know, that doesn’t mean that each year the DJIA plugged along linearly at 8.07% per year. That brings us to our next critical statistical concept, which is standard deviation.
Standard deviation measures the variability of the returns used to compute the average. For the past five calendar years, the DJIA has returned 8.92%, 6.31%, 14.84%, 11.78% and -35.90% in 2008. The standard deviation for the DJIA since September of 1987 through March of 2008 was 15.61% (source: Dow Jones Indexes).
If we have an average rate of return and a standard deviation, we can develop expectations for future performance. If you took the average rate of return for the DJIA (8.07%) and added its standard deviation (15.61%), and then subtracted the standard deviation from the average, this range of possible returns would account for 67% of the likely outcomes for that index. In other words, in two out of three years, the return of that index would be between -7.54% and 23.68% ( 8.07% – 15.61% and 8.07% + 15.61%). If you wanted to account for 95% of the likely outcomes, you could add and subtract two standard deviations to the average, which would give us a possible range of returns between -23.21% and 39.29%. To get 99% certainty for the range of possible outcomes, we would add and subtract three standard deviations above and below the average, which would give us a possible range of returns between-38.82% and 54.90%. This range of outcomes is known as the bell curve or a normal distribution.
I use this concept to design portfolios for my clients. Each asset class has its own risk/return profile. When we blend different asset classes we optimize the likelihood of a favourable long-term result while minimizing volatility over the long-term. Outcomes like what we experienced in 2008 are rare but possible (as we have already figured out). The likelihood of realizing that extreme of an outcome (three standard deviations below the average annual return) two years in a row are, thankfully, highly improbable. I can’t predict what the DJIA is going to do over the next five minutes, but I am highly confident that the probability for good results over the next five years and beyond are quite reasonable.