Whenever I've done extensive comparative backtesting of a whole range of stop-loss methods (which admittedly isn't "hundreds of times", because it's terribly time-consuming, albeit very interesting, too), SD-based stops have never been among the relative high-performers. Over the years, I've certainly built up enough of a general impression of this subject to agree with you (and Taleb) that the answer's "no".
Are Standard Deviation based stops, one of the best stops? I don't think so and I don't think logic based predominantly on statistics produces the best results.
I have no idea what you posted. But yeah, you're missing something. If you can't recognize the SPY, here's the SPX index -- on your time period. And if you think that's at all special, here's PBR -- as in "Brazil." Same story told: great equivalency between ATR and σ. Period. No qualifiers; no maybes. Gotta go.
Not so fast Tom, there are in fact a couple of qualifiers. I see now why we have been reaching different conclusions … I have been comparing ATR with Standard Deviation. You have been comparing ATR with “Historical Volatility”. … that’s why we have been posting different charts. The reason I posted a simple SD measure is because that what the OP’s post was asking about. I’m sure you’re aware that Standard Deviation and Historical Volatility are not the same. And even HV can be calculated in a range of ways, but it looks like your chart is coming from Interactive Brokers and given that it so closely matches ATR, I would suggest to you that they are using a 30 day EWMA of volatility employing the Garman-Klass model which incorporates the daily high and low prices. So without wanting to enter into an ongoing shit-fight over this, I’m standing by my original statement that SD and ATR do not always align. But then you are quite correct that ATR and IB’s definition of Historical Volatility will always align as they both take into account the daily range, whereas SD only uses the closing price.
There is nothing either esoteric or limiting about IB's calculation of historic volatility. Volatility *is* a single standard deviation. What is commonly conflated is that volatility is stock price movement computed in percentage-change terms, instead of price-change terms. But this is only the difference between a Normal distribution, and a logNormal distribution. In the context of setting stop-loss orders, this is immaterial. For an indication of this, I'd suggest putting up a graph of volatility and ATR. Oh wait. Been done.
I can only give my own experience/results, from my own backtesting and live trading, and of course can't promise that they're going to be the same as anyone else's findings (but I do more or less believe in the fractal nature of financial instrument charts, so I suppose there might be some overlap ... for what it's worth, my observations are based on relatively fast-moving intraday trades - but not scalping! - with their entries based only on price-action parameters, primarily now/recently on trading futures from constant-volume bars and before that from having originally traded spot forex from M5 - M15 charts) ... 1. Trailing a stop-loss manually just above/below the most recently formed swing-high/low (probably my best method, overall, but understandably hardest to back-test in bulk because of the near-impossibility of automation) 2. Trailing a stop-loss manually just above/below the level of a Kijun Sen line (from the Ichimoku indicator-set) three or four bars/candles/periods before the current bar/candle/period (probably my next-best) ("Kijun Sen" is just the Japanese name for something known to Western TA as a "Donchian channel midline", though they don't tell you that in any of the books!) 3. Closing trades on the occurrence of certain bar-patterns ("crescendo", "diminuendo", "congestion", "exhaustion", etc.) (I still do all of these, in conjunction with "1" above) 4. Trailing a stop-loss manually at the level of an "x"-period Hull moving average of the typical price [(H+L+C)/3] right-displaced by "y" periods (different variables for different instruments) 5. Using an ATR multiple as a stop-loss (this works significantly better than SD-based stop-losses when trading futures with constant-volume bars) All "just my own experience" and "your mileage may vary", but SD-based stop-losses are more or less "nowhere" on my list. Nor are automated trailing-stops (though I suppose it's possible that one or two of the suggestions above could actually be automated by an experienced programmer, so I should perhaps say "nor are fixed-distance automated trailing-stops" - very frankly, I think these are straw-clutching nonsense).
I use #5. It works very well for me and I trade stocks only. But I place stops a multiple of ATR below/above recent low/high and not from recent price or entry price. If a trend line or channel low is $20 for example and ATR is $0.15 then movement down to $19.85 is not unexpected and would be considered within the ATR. Its when price goes BELOW that ATR that now your low is really being violated. How much that ATR has to be violated and what time period to use for ATR is something you have to figure out for yourself based on your trading. So in this example I would place a stop somewhere $19.84 or lower. The farther I place it below that the more movement is allowed and less likely I will get stopped out. The higher I place it the more shares I can buy since the difference between my stop and entry price determines the number of shares I trade. So when ATR is lower like in areas of consolidation I can place tighter stops (ATR is low) than in areas where price has already started to move in my intended direction (ATR is USUALLY higher as price moves) and the day's range is higher.
If its based on assumption that price is normally distributed then yes you should be correct. Btw have you made any simulation on history. I would also like to calculate daily standard deviation for past 3-4 years and place some random trades with 2 sigma, 3 sigma stops to see how it works. But would it give you an edge?