90% data set within +/- 1 standard deviation

[sathishrosario]

Thanks for the detailed analysis.

I am investigating investment return, whether it can be simulated by SPC tools.

But the results are different (95% values in between +/- 1 sigma).

 

[Semoi]

So, you should check if transformations or the usage of other distributions provide a better results. However, I would not expect that this is the case. After all, the selection process of investments should not constitute a random process -- at least if the investor does it correctly.

PS: In my previous post I stated that the grey area is a 95% CI. This is easy to misunderstand. They are "point-wise confidence bands for the normality test", see Aldor-Noiman, S. et al. (2013). The Power to See: A New Graphical Test of Normality. The American Statistician. 67:4.

 

[Bev D]

What “SPC Tools” do you mean? If it’s control charts you need to remember that control charts work perfectly without the data having a Normal distribution. (So there is no need to perform any Normality tests or transforming the data…in fact transformations do more harm than good)

If you are trying to use other statistical tools it really is important for us to understand exactly what you are trying to do. Blind application of statistical tools will not help. You should also answer the two questions I asked regarding how the risk/reward is CALCULATED as this will have a direct effect on what statistical tools (and what control chart) will work.

Frankly I am not sure what you are trying to do or where the data come from. Without that this is an exercise in futility…

 

[sathishrosario]

With all due respect,

I have already answered your questions. Risk is what I may loose. Reward is what I may gain in trading.

SPC tool means: histogram with sigma level.

I just want to know how my risk reward is forming normal distribution curve and what is the sigma.

Thank you.

 

[Bev D]

With all due respect you have not answered my questions. HOW ARE YOU CALCULATING WHAT YOU MAY GAIN OR LOSE? This is essential to understanding and making the right calculations.

Once we know this I am all but certain that your data will not be Normally distributed. Not all data are and that is perfectly OK.

There is no way to calculate sigma levels without specification limits

With all due respect I still don’t understand what you are trying to accomplish and I’m not sure you do either.

 

[Bev D]

For those who may be reading this thread: the problem with this particular data set is that it is a dimensionless ratio of two estimates or in layman’s terms - ‘guesses’. This is what Donald Wheeler termed “numerical jabberwocky”. In other words the ‘data’ are not really real and any mathematical calculations will not be real either.

In addition, the OP has stated that they want to know if they can simulate return using “SPC tools”. (Which I interpret as being any statistical approach.). See post #21 above.

Of course you can run ‘simulations’ of investment return with one requirement and one caveat. The requirement is that you must have data that includes potential causal factors and actual results (in this case, actual money spent and returned). Then you can run correlation modeling. The OPs data set has none of this; it only has the a priori ‘risk/benefit ratio’ which tells you nothing about how much money is spent & how much money is gained or lost. It is completely lacking in any factors that effect the outcome. A histogram of this data will only tell you teh variation in the risk/benefit ratio, which again is a guesstimate devoid of results.

The caveat is that finding the causal relationships of ‘trading’ is tenuous at best and fleeting at worst. Dr. Deming stated years ago that SPC wouldn’t work for the stock market because it is not driven by real factors but by irrational emotions. There are a few papers on Control Charts and stock market prediction (basically modeling the market on results only) and a few that try to discuss full modeling (input factors and results). A search for Stock market and control charts will yield a few hits. One such paper is here. The siren song of being able to statistically predict the market has seduced many people in the past, but hen again so did the idea that we might be able to turn lead into gold…

 

[Steve Prevette]

Yes, ratios can cause really wonky problems. Especially in investing. At 50 percent loss followed by a 50 percent gain does not imply you are back at your original investment, you have still lost 25%. A more reasonable use of SPC (as in a control chart) is to plot the risks over time, and the rewards over time as two separate rates. Or consider a cusum SPC chart or plotting the change in value of the investments by time interval (which would avoid the ratio problem). I agree with Bev, a histogram with standard deviation lines, collapsing the time series data into one set without maintaining a time series is NOT Statistical Process Control, at least as defined by Drs. Shewhart, Deming and Wheeler.

BTW currently on Diamond Princess off the coast of Japan.

 

[Steve Prevette]

Yes, ratios can cause really wonky problems. Especially in investing. At 50 percent loss followed by a 50 percent gain does not imply you are back at your original investment, you have still lost 25%. A more reasonable use of SPC (as in a control chart) is to plot the risks over time, and the rewards over time as two separate rates. Or consider a cusum SPC chart or plotting the change in value of the investments by time interval (which would avoid the ratio problem). I agree with Bev, a histogram with standard deviation lines, collapsing the time series data into one set without maintaining a time series is NOT Statistical Process Control, at least as defined by Drs. Shewhart, Deming and Wheeler.

BTW currently on Diamond Princess off the coast of Japan.

An additional thought - This is a very lop-sided distribution, terminated at -100% (you can only lose your total value) yet you can make unlimited (or at least several hundreds of percent) gain. That is why the normal distribution curve looks the way it does - the right tail goes much "fatter" (farther) than the left tail.

 

[Bev D]

BTW currently on Diamond Princess off the coast of Japan.

Practicing retirement or actually retired?

 

[Steve Prevette]

Practicing retirement or actually retired?

OFF TOPIC. Both. My "day job" employer put me on leave of absence back two years ago at the end of a contract they had with a facility I was supporting. I chose to retire from that job rather than hang around "awaiting assignment". I had been teaching a course at Southern Illinois University at Carbondale, and they agreed to up me to a 3/4 time (three courses) employee, which gives me State of Illinois employee health benefits. I can teach the class remotely from most cruise locations on cruise ships due to the Star Link and other systems Princess (and others) are using. I am off for the summer, but could have kept up with teaching even here in Japan (yes, I've logged into the school while here).

Mostly living off two small pensions, SIUC pay, and (primarily) IRA until hitting Medicare and then full Social Security age. The teaching does help give me something to do (or so my wife says), and I can work at home (my office hours are in the "train room") or the cruise ships. Pay is minimal (compared to the old day job) but the insurance is worth it. And I can pass on knowledge - the students for the most part like Dr. Deming (and Shewhart and Wheeler's) work, or at least better than their old "traditional" STATS 101 course. A lot say they are using the Red Bead Experiment lessons on the job. So still "stirring things up".