"Here's another way to express the amazing decline in risk as time passes and you hold your stocks. Over a one-year period the standard deviation for stocks is 18 percent. This means that in two out of three years the return on a stock will vary by no more than 18 percentage points from the average—in either direction. Since the average real return is about seven percent, returns should vary two thirds of the time between 25 percent and -11 percent. That's very risky. But over ten-year holding periods the standard deviation drops to five percentage points. Over thirty-year periods it drops to about two percentage points—meaning that two thirds of the time the range is five to nine percent. That's not risky at all. What is truly amazing about these long-term-risk figures is that they are lower than those for Treasury bonds and even Treasury bills, which mature in a year or less. If you keep your money at work for more than twenty years, stocks are actually safer than short-term T-bills rolled over annually. Over a twenty-year period the worst inflation-adjusted return by stocks was an annual average of 1.0 percent. For bonds, however, the worst was -3.1 percent, and for T-bills -3.0 percent. Over one-year periods stocks have outperformed bonds only 61 percent of the time, but stocks beat bonds 92 percent of the time over twenty-year periods and 99 percent of the time over thirty-year periods."

"Volatility" or σ estimates, of and by themselves, beg "I.I.D." conditions https://en.wikipedia.org/wiki/Independent_and_identically_distributed_random_variables which means that the period-to-period correlations, which would severely erode with upside-trend recognition (Box-Jenkins https://en.wikipedia.org/wiki/Box–Jenkins_method being the cure to your Durbin-Watson https://en.wikipedia.org/wiki/Durbin–Watson_statistic ills), go un-recognized. The thing is, statistically speaking, the interesting outcome you cite is just cuz we forget our basic stats. And we do it all the time, too -- 99% of any discussion on markets will assume a distribution/dispersion process unaffected by prior values. (Which is nuts. Butttttt we still do it. Sheeesh. )

https://en.wikipedia.org/wiki/Decomposition_of_time_series ??? In the short term (say, instantaneous) any trend component would not be discernible -- and any effect would be folded into the variance. In the longer term (t=100? 1000? 36,525 days?), the trend's effect on variance is diluted. How can you see this? Compare the variance of your data before/after de-trending. ("Cool!") (BTW, this takes me back 37 years....... and a stat course that I *hated*, but this part jumped out at me and made sense. "Whoaaaaa. Look at that!")

If I understand you, you are raising the concern that the volatility figure itself is unstable. And if the data sample is increased, that the conclusions could change?

He's saying that due to correlation and that the price movement begets price movement, framing the market in terms of normal (random statistical) distributions is not necessarily accurate. In statistical (and mathematical) terms, this is called regression (where the previous output is a subsequent input). This was the basis behind FiveThirtyEight's presidential poll modelling showing 2-3x the chance in prevailing narratives of Trump winning. They explained at length (seemingly daily) that errors within their model were correlated such that under reporting in PA would mirror under reporting in FL....also, Nate Silver is a f'ing genius and a hero of mine. So, to the extent that a stock that performed poorly in the past will continue to perform poorly, and a previously over performing stock would continue, random statistical samplings are not accurate. These are the so-called "fat tail" distributions that form the basis of long OTM option strategies...and likewise, a poor performing stock in a bull market will perform well, as will an over performing stock perform poorly in a bear market. I suspect the majority of profitable option strategies are premised on this. Certainly profitable long strategies (false leverage strategies notwithstanding). As a premium seller, this directly influences my 'soft stops' which are subjective exits earlier than the hard stop on a stock likely to continue its decline (or advance). Another couple other good things to point out, certain prices tend to trade more frequently (150.00 will always show more ticks than 150.47). $0 is a floor price, so the entire tail of the normal curve past there is inaccurate. A "t-Distribution" is another good one to know. Because companies maintain intrinsic value (read some Buffet shareholder letters), you won't have a true normal distribution. An undervalued company will supposedly have more people looking to buy, such that the curve's peak will still be at the current price, but substantially more than half of the area under the curve will be above the current price.

Doesn't this apply to real prices and not so much to %? Wouldn't it be more correct to say that on longer term there's a (more) normal distribution with the top at the 7% level?

It depends, some distributions skew more in percentages, some skew less. Some only skew more on the up side. But it can be really tough to tell because of the iterative nature of them. To accurately state, you need to control for the output that goes back in, but it can't be separated out. Even among sample methods, there's disagreements about which most accurately models something reliably...and even applicability to different situations (a normal curve works great in chemistry, but Nate Silver argues a t-Distribution is more accurate for political poll modeling...) Honestly, if I had a good answer, I'd make a lot more money trading options...or someone else would.

Yes, financial market data is unstable and vulnerable to outliers. However, some conclusions can be drawn from long samples (and IIRC the data I posted originally is from the US from 1933 to 2000), especially when the data repeats similarly on multiple countries. Maybe the US will go down a bad path and history will present a false picture of what the future will bring, however, a much higher degree of stability can be achieved by stock investors by buying, not a US focused stock ETF but a global basket of stocks from all the major parts of the world, either through a global stock ETF or by buying several continent ETFs. The latter will likely to be a lot more stable given that country risk is diversified. In a way, the US provides a proxy for what a global ETF experience would be like. To me, what is interesting is that, for very long-term capital, stocks not only beat bonds on returns (which is nothing new and everybody is aware of) but it also beats on volatility (in terms of having less return variablity over long periods of time).

I decided to try to replicate the author's findings to see if there is some data mining going on (especially given the suspicious 1933 start date). Turns out that they are mostly right, using Damodaran's return database (1928-2016) with inflation adjusted figures I found: The Neg SD is the standard deviation from negative returns only (so, only losing 10/20/30 year periods are considered) The Div/0 issue is due to the fact that there are no negative returns on those periods (that's right, there was not a losing 20 or 30 year period for stock investors, even if they bought in 1929! Meanwhile bonds and bills had many losing 20/30 year periods) They overhyped the fact that the standard deviation of stocks was lower than bonds, it wasn't, except for the 30y holding period. And T-bills SD was lower than bonds and stocks (unlike what they claimed). But their broader point was completely right, US stocks historically are less risky than bonds over long periods of time. This is captured both by the Neg SD and the worst return (like Jack Schwager says, no one really cares about upside volatility). When people say that stocks are riskier than bonds, they are right, in the short-term, over the longer term, not only stocks tend to return more (as expected) but also they tend to have less risk The US has been a stable country, so this is a proxy for a stable dataset. Today, in order to replicate that stability and achieve similar returns, focusing on the US only is probably flawled, maybe the US has been lucky. But I believe similar results can be achieved through a global ETF of stocks with exposure to countries in all 5 continents. Like Buffett said back in 2008 "Today people who hold cash equivalents feel comfortable. They shouldn’t. They have opted for a terrible long-term asset, one that pays virtually nothing and is certain to depreciate in value." The stability of cash and bonds is an illusion!