## Wednesday, June 11, 2008

### Steady Market Rise Lost in the Noise

It’s hard to see the steady rise of the stock market on a day-to-day basis because of the volatility of prices. Whether you focus on the long-term increase in prices or the short-term volatility determines whether you are an investor or a trader.

Let’s suppose that the stock market is expected to rise 10% per year with volatility of 20%. The volatility (or standard deviation) has a precise mathematical meaning, but let’s just say that it creates a return range of 10% plus or minus 20%, or from -10% to +30%. In most years the market return will be in this range.

Because there are about 250 trading days per year, you’d think that we could divide these numbers by 250 to get a range for each day of -0.04% to +0.12%, but volatility doesn’t work this way. From experience we know that daily market movements are very often outside this range.

The problem with this thinking is that volatility partially cancels out over time. A big rise followed by a big drop may leave the stock price unchanged. The stock market’s tendency to rise by 10% per year means that it tends to rise by about 10%/250 = 0.04% per day, but the volatility calculation is a little more complex.

Volatility grows by the square root of the number of days. So, the 20% volatility per year works out to about 1.26% per day. This makes the daily range about -1.22% to +1.30%, which is much closer to what we actually see in the market each day.

A side effect of all this is that the market’s tendency to rise by an average of 0.04% per day is swamped by the volatility that is about 30 times larger. It’s easy to lose sight of the slow, but relentless rise of stock prices with all the ups and downs.

It’s easier to see the market’s tendency to rise by looking at longer periods of time. Over 25 years, the range of returns works out to stock prices increasing by a factor of between 4 and 30. There is no guarantee that all 25-year periods will have returns in this range, but most will.

Long-term investors focus on the 25-year results and let traders fight over the 1.26% swings each day. The long-term investors will spend much less time on investing and will spend less on commissions, spreads, and taxes.