Eddy at Crossing Wall Street put out a call to all nerds for a histogram based on the standard deviation of a database containing logarithms of long-term stock returns. I couldn’t resist.
Here’s a graph of the standard deviation of the logarithm of stock returns since December 31, 1999.
I’ve plotted the actual distribution with the bell curve. There’s not too much of departure. Note that there is an extremely large “fat tail” on the left side of the graph. What that means is, if you take the logarithm of the return for each stock, then calculate the standard deviation of those logarithms, you’ll find that there are a lot more -4 and worse standard deviation moves down than expected. In fact, there are a whole lot more down moves than up moves — about 60/40. That’s what has the distribution shifted to the left. And that’s bad … at least at first glance.
[click to enlarge]
Here’s a graph of the Percent Returns based on a linear scale. Note that it doesn’t look anything like a bell curve. That’s because very few stocks have made small moves. Most stocks are either down big or up big. What’s really amazing is how many have gone up by more than 100% — more than 20% of all stocks have more than doubled. [That’s why the graph is stretched vertically so much. That one data point is so tall, in a normal graph the other data points would be nearly invisible.]
What that means is, even though there have been a lot more down moves than up moves, and even though the down moves are larger when expressed in logarithms, the bottom line is that when expressed in dollars and cents, the average stock (at least according to the dataset provided) is up. And that means, had you invested equal dollars in each stock, you’d be ahead.
I have to tell you, that one shocked me, given the fact that December 31, 1999 was a few weeks away from the all-time peak in NASDAQ. My suspicion is that there is significant survivorship bias. That is, only companies that exist today are in the database. We don’t have the impact of all those companies that went belly up in the dot-com bust or the impact from companies that have been taken over.
Also, I am suspicious of some of the data from back in 1999, as ticker symbols do get recycled. For instance, what was once C in 1998 (Chrysler) is no longer C now (Citigroup), even though both companies are government subsidized basket cases. [That’s one reason why ODDS Online runs off of CUSIP numbers as opposed to ticker symbols.]
But another factor at work is a principle I learned from Peter Lynch back in the 1980s when he described the “ten-bagger”. You buy 10 stocks, putting $1,000 into each. A few years later, two are bankrupt and gone. Two more are down -50%. Three are flat. Two are up 50%. And one is a up 10-fold. Your $10,000 is now worth $17,000, even though the median return was 0%.
Point being, even though the database provided may not be perfect, it does show us something that many people may not realize: If you bought equal dollar amounts of AAPL, GM, C and AIG at the height of the dot-com bubble, your median return would be about -94% because of the three basket cases … and yet your portfolio would still be ahead during a period in which the stock market got slaughtered!
In sum, don’t take this as encouragement to get in or out of the stock market. The bottom line is that statistics sometimes don’t always provide a complete picture. If you’re a novice to the market, be sure you understand the full meaning of the numbers you’re looking at.
