Volatility, Standard Deviation, and "Risk"

[Karen]

A number of OT comments moved here from the "Many funds seem overbought" thread

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Mar 6, 2024 5:27:11 GMT FD1000 said:

...It's more than that, a stock like NVDA, has a huge volatility and trying to use T/A indicators can be very tricky.

Not sure what you are basing your opinion on, but NVDA does NOT have "huge volatility."

marketchameleon.com/Overview/NVDA/IV/

Excerpt:

NVDA implied volatility (IV) is 48.2, which is in the 73% percentile rank. This means that 73% of the time the IV was lower in the last year than the current level. The current IV (48.2) is -8.4% below its 20 day moving average (52.6) indicating implied volatility is trending lower.

Conversely, SMCI DOES have what someone might describe as "huge volatility."

marketchameleon.com/Overview/SMCI/IV/

Excerpt:

SMCI implied volatility (IV) is 117.7, which is in the 100% percentile rank. This means that 100% of the time the IV was lower in the last year than the current level. The current IV (117.7) is 23.3% above its 20 day moving average (95.5) indicating implied volatility is trending higher.

We trust you will disagree with this, but these are, you know, FACTs, and if you disagree with them, you will be wrong.

We find that it is generally best to limit one's posting to what we know or what we have a question about. 

[Chahta]

RSI is confusing. If it is about price movement, then CBLDX being overbought for months doesn’t make sense. So making too much in interest must add to the overbought position.

[mnfish]

Since FD is always posting about low SD perhaps this makes sense of his earlier post -

"Standard Deviation is used as a proxy for risk, as it measures the range of an investment's performance. The greater the standard deviation, the greater the investment's volatility."

[liftlock]

Years ago there was a tool called "Risk Grades" which attempted to measure the risk of securities based on the standard deviation / variability of their price action. Many of the high flying stocks and funds leading up to the dot.com bubble bursting had received very favorable risk grades suggesting low risk because their price action trended up with relative low volatility.  It wasn't until after the dot.com bubble burst the true risk in these securities became known. 

Measuring standard deviation or the relative strength of short term price action seems more useful in identifying market sentiment than in measuring risk.

[yogibearbull]

liftlock , I remember Risk-Grades and used it a lot. It was bought by MSCI and is now offered as a professional product. Haven't we heard this story elsewhere? Think M* that has been turning lots of free stuff into professional stuff.

Anyway, my replacement for Risk-Grades functionality has been via Portfolio Visualizer (PV) and Stock Rover (SR). This is critical for my portfolio system where volatility assessment comes first, and I don't much care where the performance falls.

[FD1000]

Mar 6, 2024 12:21:47 GMT Karen said:

Mar 6, 2024 5:27:11 GMT FD1000 said:

...It's more than that, a stock like NVDA, has a huge volatility and trying to use T/A indicators can be very tricky.

Not sure what you are basing your opinion on, but NVDA does NOT have "huge volatility."

marketchameleon.com/Overview/NVDA/IV/

Excerpt:

NVDA implied volatility (IV) is 48.2, which is in the 73% percentile rank. This means that 73% of the time the IV was lower in the last year than the current level. The current IV (48.2) is -8.4% below its 20 day moving average (52.6) indicating implied volatility is trending lower.

Conversely, SMCI DOES have what someone might describe as "huge volatility."

marketchameleon.com/Overview/SMCI/IV/

Excerpt:

SMCI implied volatility (IV) is 117.7, which is in the 100% percentile rank. This means that 100% of the time the IV was lower in the last year than the current level. The current IV (117.7) is 23.3% above its 20 day moving average (95.5) indicating implied volatility is trending higher.

We trust you will disagree with this, but these are, you know, FACTs, and if you disagree with them, you will be wrong.

We find that it is generally best to limit one's posting to what we know or what we have a question about. 

In the last 3 years, NVDA volatility=SD was 58 while SPY is under 18...and why NVDA volatility is huge.

[chang]

SD by itself is a meaningless number without reference to the mean. Hasn’t this been discussed to death? SD is a measure of variation about the mean. An SD of 10 around a mean of 10 is a lot of volatility. An SD of 10 around a mean of 100 is very little volatility.

The “variance” of a data sample is the average of the squares of the differences between the data points and their mean. This measures “spread” about the mean. The SD is the square root of the variance, which has the same units as the data.

No offense, but if this isn’t crystal clear, then one needs to read some basic statistics. No one should compare standard deviations between data sets with different means. (In this case, the data set is the stock’s price in $ measured on N different days.)

[FD1000]

I was discussing NVDA SD in general which is the market=SPY. Based on that NVDA showed in the past that it's SD was much higher than SPY.
What about the future? Nothing is guaranteed but there is a good chance NVDA volatility will continue to be much higher.

[chang]

Mar 7, 2024 10:45:36 GMT FD1000 said:

I was discussing NVDA SD in general which is the market=SPY. Based on that NVDA showed in the past that it's SD was much higher than SPY.
What about the future? Nothing is guaranteed but there is a good chance NVDA volatility will continue to be much higher.

Sorry, but SD of NVDA versus SPY is a meaningless comparison. The two data sets have different means. You can compare ratios of SD/Mean, but not SD alone.

BRK-A has a much higher SD than BRK-B.

I don’t know how else to explain it.

Are you actually quoting SD/Mean ratio? Or SD as a % of the mean?

[Karen]

Mar 7, 2024 12:41:11 GMT Karen said:

So, we're not sure why FD crossed this discussion over to SD. Volatility is measured by IV, or Implied Volatility as discussed in our previous post.
(EDIT: See yogibearbull post below that provides excellent color to the history/current state!)

seekingalpha.com/article/4501215-implied-volatility

Excerpt:
What Is Implied Volatility?
Implied volatility is a statistical measure of the expected amount of price movements in a given stock or other financial asset over a set future time frame. Traders use IV for several reasons which can include:

As a measurement of risk for a given trading instrument.
To calibrate models such as value at risk (VAR) and to establish position sizing and limits.
To calculate fair prices for options contracts using models such as the Black–Scholes method.
To tell whether an asset is currently at a high or low level of volatility compared to its history.
Determining if the market as a whole is currently at a high or low level of sentiment.

Which of course calls to mind the VIX, or overall market Volatility Index, that currently sits at 14.42.
The CBOE Volatility Index, or VIX, is a real-time market index representing the market’s expectations for volatility over the coming 30 days. Investors use the VIX to measure the level of risk, fear, or stress in the market when making investment decisions.

From what FD is posting, we're getting the impression that he may not even know that the IV measurement (for underlying stocks, ETFs) exists and instead is concentrating on their respective SDs, a measurement that he is aware of and attaches to volatility. (Being a self-described prolific trader, that seems more than a little odd to us.)

Here are IVs for the SPY, Mag 7 and SMCI. Yes, NVDA's IV, like TSLA's, is much higher than the S&P, but they pale in comparison to SMCI.

So one can accurately say that NVDA's IV (or volatility) is high compared to SPY, but SMCI's would be the one somebody might call "huge," if they were inclined to use such a word.

My husband would conversely call SMCI's IV "extremely high," while NVDA's and TSLA's would be called "high."

IV
SPY 12.1
MSFT  21.1
AAPL 22.1
AMZN 25.0
GOOGL 26.0
META 28.9
TSLA  47.9
NVDA 49.8
SMCI 114.3

NOTE: Our previous post provides links to NVDA's and SMCI's IV.

[yogibearbull]

chang , spoke like a true mathematician or statistician. BTW, SD as % of mean (or average) is like inverse Sharpe Ratio.

Yes, I know the difference between average and mean, but in business, they seem to be used interchangeably.

People in business do things a they please. SD, VAR, etc have been separated from means (or averages) for a long time. Business people who struggled with grades in math in college (i.e. those who even took it), cooked up bond ratings/grades such as AAA, etc, where even BB or below became bad grade. In college grading, A+ is as far as it got but many still have A as the top grade, and B is a perfectly fine grade.

Implied volatility (IV) is an estimate based on Black-Scholes formula (old way) or options pricing (current way). There is also realized/historical volatility. The two differ a lot, but still the latter cannot be had now, so we are stuck with the former.

So long as we are musing about things....

[chang]

yogibearbull: “average” and “mean” are same. For a data set of N numbers, it’s just the sum of the numbers divided by N. (In other words, “arithmetic” mean as opposed to “geometric” mean.)

Both words mean the same thing.

[yogibearbull]

chang , as you know, one definition of mean is the point when half the data points are above, and the rest below. Then, Mean = Average for normal (or symmetric) distributions.

But using mean for average is also common.

BB posters who just got up are probably rubbing their eyes & going for a coffee refill .

[chang]

yogibearbull - that’s the median, not the mean!

[racqueteer]

Quite a few of us aren't using terminology correctly. Certainly, I am guilty of that, as I tend to think in terms of actions rather than definitions, and don't have a background in statistics. Chang gave a nice, concise definition of 'variance': "This measures “spread” about the mean". I rather suspect that most of us think of this as volatility. Something routinely making large % moves, up or down, would be 'volatile'. What's needed is a term for the strength of a trend; something like 'persistence' perhaps. Then a high-volatility asset might be relatively 'safe' temporarily because its persistence value is positive and also high. Do we have term like that?

[uncleharley]

Mar 7, 2024 14:27:38 GMT racqueteer said:

Quite a few of us aren't using terminology correctly. Certainly, I am guilty of that, as I tend to think in terms of actions rather than definitions, and don't have a background in statistics. Chang gave a nice, concise definition of 'variance': "This measures “spread” about the mean". I rather suspect that most of us think of this as volatility. Something routinely making large % moves, up or down, would be 'volatile'. What's needed is a term for the strength of a trend; something like 'persistence' perhaps. Then a high-volatility asset might be relatively 'safe' temporarily because its persistence value is positive and also high. Do we have term like that?

Velocity should work in the literal sense but it is rarely used in finance.  Chart readers frequently refer to the slope of a trend.  I have begun to use the LAR technique [Looks About Right] to cover that and other aspects of T/A.

[racqueteer]

Mar 7, 2024 16:01:03 GMT uncleharley said:

Mar 7, 2024 14:27:38 GMT racqueteer said:

Quite a few of us aren't using terminology correctly. Certainly, I am guilty of that, as I tend to think in terms of actions rather than definitions, and don't have a background in statistics. Chang gave a nice, concise definition of 'variance': "This measures “spread” about the mean". I rather suspect that most of us think of this as volatility. Something routinely making large % moves, up or down, would be 'volatile'. What's needed is a term for the strength of a trend; something like 'persistence' perhaps. Then a high-volatility asset might be relatively 'safe' temporarily because its persistence value is positive and also high. Do we have term like that?

Velocity should work in the literal sense but it is rarely used in finance.  Chart readers frequently refer to the slope of a trend.  I have begun to use the LAR technique [Looks About Right] to cover that and other aspects of T/A.

Rate of change of change; second derivative?  That seems like it would be a very short-term indicator?  I'm thinking of something more attuned to direction than to magnitude.  On second thought, maybe you're just talking about slope of the price curve; first derivative?

[retiredat48]

Chahta ,steelpony10 ,FD1000 ,Mustang ,rhythmmethod ,yakers ,retiredat48 ,yogibearbull ,fishingrod ,chang ,Karen ,mnfish ,liftlock ,uncleharley ,anitya ,oldskeet ,bruce ,racqueteer ,

Practical guidance for readers...

--If comparing two things, put them on a compare chart. The one fluctuating more in percentage in its up/down cycles is the more volatile one.

--Trends tend to remain in motion until price crosses a Moving Average line, up or down. A 200 day MA provides a good high percentage measurement of this. The SLOPE of the MA is also important. An MA "skiing downhill" is in a downtrend!

--Most of the time, higher volatility comes with the strongest movers/gainers...best performers.

--401.K investing is dollar cost averaging. SEEK volatility, as you can get a bonus return of up to 2% CAGR versus less volatile investments.

R48

[yogibearbull]

Thanks chang for straightening out mean vs median. I will leave the posts as they are as to edit them would be more messy.

I also thought more about the idea of pairing mean and SD. I noted already that SD as % of mean is really the inverse Sharpe Ratio.

But I have kept thinking about this all morning, and the fact that business & finance has moved to looking at SD only.

Finally, it struck me.

Add an arbitrary constant C to a data series Xi with mean Xbar and SD. The new mean is Xbar + C, but SD is unchanged.

So long as C is arbitrary, why not set it to produce a mean of 0? Some may call it normalization.

Or, why not consider a data series of X - Xbar? Then mean then is 0, SD is unchanged.

I think that is why the business & finance started looking into SD in isolation.

For most, this may be arcane, but I use Relative SD, or SD/SDbenchmark, as a critical criterion, and named it effective-equity, so I had to resolve the issue for myself.

[anitya]

Employees in big business are into buzz words and oversimplified concepts. For them Accuracy is never a priority and is always subsumed by speed. I think Chang is trying to convey that this forum should strive to do better than buzz words and oversimplified concepts and I agree with him.

[FD1000]

I was never a mathematician and not intend to be one.
The basics I stated are enough for most to understand what I meant.
But, the most important is how do you use them and if it worked.
If you don't think SD has any meaning ignore it, all I know is by the time I watched SD, SHARP Ratio, and charts of 2+ funds/ETFs, I get a good feel for their characteristics and which one I want to own.
l use SD and Sharp to find funds and charts to see real time volatility.
BTW, I also have been comparing different categories using the above and that help me with risk-adjusted performance.
Examples: PIMIX beat SPY for 3 years 2010-3.
PRWCX is known for it.
YTD: VGIT vs RSIIX.

[richardsok]

Mar 7, 2024 17:51:36 GMT retiredat48 said:

Chahta ,steelpony10 ,FD1000 ,Mustang ,rhythmmethod ,yakers ,retiredat48 ,yogibearbull ,fishingrod ,chang ,Karen ,mnfish ,liftlock ,uncleharley ,anitya ,oldskeet ,bruce ,racqueteer ,

Practical guidance for readers...

--If comparing two things, put them on a compare chart. The one fluctuating more in percentage in its up/down cycles is the more volatile one.

--Trends tend to remain in motion until price crosses a Moving Average line, up or down. A 200 day MA provides a good high percentage measurement of this. The SLOPE of the MA is also important. An MA "skiing downhill" is in a downtrend!

--Most of the time, higher volatility comes with the strongest movers/gainers...best performers.

--401.K investing is dollar cost averaging. SEEK volatility, as you can get a bonus return of up to 2% CAGR versus less volatile investments.

R48

1.    Agree.   Do whatever you must to improve yr clarity of thought.   Be a doodler.
2.    Ehhhh.... kinda.  There's helluva lotta gelt to made made (and lost!) long before you ever reach 200DMA.
3.    In 2022-24, sure.....maybe even generally.   But you wouldn't have written this in 2008 or 2021.      The yr 2-year SPY chart: much more volatile on the way down than in rally.
4.    Interesting perspective.   Very true, I'd say especially for younger workers with many years of savings ahead of them.


And how come I'm not on yr recipients list?   Gonna disinvite me from yr Kwanzaa party too?

[yogibearbull]

richardsok, the way "All" tag works at PB is that it includes all posters on THAT Page. So, after you have posted on this Page 2, next "All" tag WILL include you. This isn't any special recipient list.

[liftlock]

Mar 7, 2024 11:28:27 GMT chang said:

Mar 7, 2024 10:45:36 GMT FD1000 said:

I was discussing NVDA SD in general which is the market=SPY. Based on that NVDA showed in the past that it's SD was much higher than SPY.
What about the future? Nothing is guaranteed but there is a good chance NVDA volatility will continue to be much higher.

Sorry, but SD of NVDA versus SPY is a meaningless comparison. The two data sets have different means. You can compare ratios of SD/Mean, but not SD alone.

BRK-A has a much higher SD than BRK-B.

I don’t know how else to explain it.

Are you actually quoting SD/Mean ratio? Or SD as a % of the mean?

I believe FD is referring to the Morningstar definition of SD (Standard Deviation) which is expressed in percentage terms.  The Morningstar SD appears on many investing websites and I believe FD uses it in his search for less volatile funds .

www.morningstar.ca/ca/news/187689/the-morningstar-dictionary-standard-deviation.aspx

"The Morningstar Dictionary: Standard Deviation

This popular measure gives investors a sense of how volatile a fund's performance has been.

No concepts are more fundamental to investing than risk and return. And when it comes to risk, the most widely used measure to determine the investment risk level of mutual funds and ETFs is standard deviation.



So what is it? Well, in technical terms, standard deviation measures the dispersion or spread of a fund's returns around its average return over a certain period of time.



At Morningstar, standard deviation is computed using trailing monthly total returns for the appropriate time period, 3, 5 or 10 years. All of the monthly standard deviations are then annualized and it's expressed as a percentage.

[retiredat48]

Mar 7, 2024 22:41:11 GMT yogibearbull said:

richardsok , the way "All" tag works at PB is that it includes all posters on THAT Page. So, after you have posted on this Page 2, next "All" tag WILL include you. This isn't any special recipient list.

richardsok,...richardsok,...richardsok,......Yogi is right; didn't realize your name was not on list for "all."  After all, you are on most lists in these parts!

R48

[chang]

liftlock - What a terrible page. It’s amazing how little information Morningstar can pack into so many sentences and paragraphs. Not even one actual definition of SD! Just a page full of blather.

The only way SD has meaning when comparing different data sets (or “random variables” for any mathematicians out there) is as a proportion of the mean. If SD is given as a % then hopefully (!) it is actually SD/Mean x 100 % that they are giving.

[Mustang]

Mar 8, 2024 3:16:13 GMT liftlock said:

I believe FD is referring to the Morningstar definition of SD (Standard Deviation) which is expressed in percentage terms.  The Morningstar SD appears on many investing websites and I believe FD uses it in his search for for less volatile funds .

www.morningstar.ca/ca/news/187689/the-morningstar-dictionary-standard-deviation.aspx

"The Morningstar Dictionary: Standard Deviation

This popular measure gives investors a sense of how volatile a fund's performance has been.

No concepts are more fundamental to investing than risk and return. And when it comes to risk, the most widely used measure to determine the investment risk level of mutual funds and ETFs is standard deviation.



So what is it? Well, in technical terms, standard deviation measures the dispersion or spread of a fund's returns around its average return over a certain period of time.



At Morningstar, standard deviation is computed using trailing monthly total returns for the appropriate time period, 3, 5 or 10 years. All of the monthly standard deviations are then annualized and it's expressed as a percentage.

Also from Morningstar:  community.morningstar.com/s/article/Standard-Deviation-Std-Dev

In this article Morningstar is describing a normal distribution where 68% of the data falls within one standard deviation and 95% fall within two.  This definition is taught in all basic statistics classes.  It has been a very long time since I've studied statistics but your link Morningstar is talking about a 3-year standard deviation of 6.33%.  This appears to be the range around the mean.

Calculating a percent change in percentages can get confusing.  For example if the average return is 5% and the actual return is 6% there is a 1 percentage point difference or a 20% difference (1 divided by 5).  By range around the mean I'm talking about percentage points not percent difference.

Using a normal distribution 68% of the data falls within one standard deviation, 34% above the mean and 34% below.  If using this to forecast the future than there is a 68% confidence level that a future data point will fall withing that range.  If 6.33 is the standard deviation then 3.165 was above the mean and 3.165 (Percentage sign was removed to prevent confusion).  If the average return is 5 then with a 68% confidence level the return would be between  -1.94% and 17.66%.

Since they didn't actually say that, this is pure speculation.

[johntaylor]

Risk and volatility are sometimes used interchangeably, but are different

[chang]

Mustang That article is perfectly correct, and this is the correct definition of SD; whereas, I think others are probably using a % of the mean.

Note that stock or fund returns are not quite normally distributed (i.e., Gaussian) and so the 68-97 rule does not necessarily apply. But it’s probably not far off.

[liftlock]

Mar 8, 2024 7:32:06 GMT chang said:

liftlock - What a terrible page. It’s amazing how little information Morningstar can pack into so many sentences and paragraphs. Not even one actual definition of SD! Just a page full of blather.

The only way SD has meaning when comparing different data sets (or “random variables” for any mathematicians out there) is as a proportion of the mean. If SD is given as a % then hopefully (!) it is actually SD/Mean x 100 % that they are giving.

I don't' doubt that you could write a better description for Morningstar.

I remember first learning about SD - Standard Deviation when taking a course in college statistics.  I don't think I began to understand what information SD was trying to convey until years later as I tried to learn more about it's use in investing.

The AAII has often described SD as comparative tool for measuring the risk of different investments in terms of the variability of their returns. I believe they use the Morningstar definition as they source the SD data from them.

As I started to learn more about investing, I had to relearn statistics in an effort to make any sense of why SD might be useful in measuring the relative variability of investment returns.  I remember it taking a while before it finally dawned on me that SD was a only raw number measuring the deviation of a data set around it's mean.  As you state it doesn't have much comparative value unless the SD is expressed a % (proportion) of the mean.  The same holds true for the slope of the line which is a raw number.  It doesn't have much comparative value in investing unless is it expressed as percentage change over time.  Unfortunately, the Morningstar SD if often published without a % label indicating what it represents.  That simply adds to the confusion / lack of clarity about what the SD actually represents.  

When evaluating investments I always try to use statistical values which are expressed in percentage terms.  One of my pet peeves is when the daily financial news informs me that a financial index gained or lost some absolute number without providing the percentage gain / loss.  This same challenge exits when interpreting other statistics.   One has to understand what the numbers they are looking at actually represent.