I think method like "Completely Randomised Design" of 'Design of experiment' can be useful. AVOVA can also be tried

The companies will all move some, even if this is just random variation, so translating your description into statisticalese it sounds like you are asking is this variation over time greater than chance (or is there marked heteroskedasticity). Is this what you mean? Given the variation will be correlated across time periods it is worth looking at books on longitudinal data analysis and time series. My favorite is the one linked to below.

http://gseacademic.harvard.edu/alda/

If I got it right, you have m=10 years data (say Y) on n=100 companies. You could possibly try fitting a linear model 

Y(ij) = mu + C(i) + e(ij)     i=1,...100    j=1,...,10                         (1)

mu = general mean, C(i) = effect of company i, e(ij) = residual. Note that the residual e(ij) are likely to be auto-correlated. You could therefore fit model (1) to account for this autocorrelation (say AR1 or whatever is more appropriate) using ReML. You could treat C(i) as a fixed effect. The estimates of C(i) directly provides the information on how individual companies may differ from the mean of all companies (which is mu).  

Thank you all very much for those very helpful answers.

z Score

"A z-score (aka, a standard score) indicates how many standard deviations an element is from the mean. A z-score can be calculated from the following formula.

z = (X - μ) / σ

where z is the z-score, X is the value of the element, μ is the population mean, and σ is the standard deviation.

Here is how to interpret z-scores.

A z-score less than 0 represents an element less than the mean.

A z-score greater than 0 represents an element greater than the mean.

A z-score equal to 0 represents an element equal to the mean.

A z-score equal to 1 represents an element that is 1 standard deviation greater than the mean; a z-score equal to 2, 2 standard deviations greater than the mean; etc.

A z-score equal to -1 represents an element that is 1 standard deviation less than the mean; a z-score equal to -2, 2 standard deviations less than the mean; etc.

If the number of elements in the set is large, about 68% of the elements have a z-score between -1 and 1; about 95% have a z-score between -2 and 2; and about 99% have a z-score between -3 and 3."

standard deviation

" A measure of the dispersion of a set of data from its mean. The more spread apart the data, the higher the deviation. Standard deviation is calculated as the square root of variance."

Source: Investopedia

Because your data is not independent across years for the same company, all ratios could be considered as continuous outcome, you may assume they are normal distributed, (examine residuals after modeling to check if they are normal or not and if they have the same variance), For repeated measurement you should perform a repeated measures ANOVA, or MANOVA rather than ANOVA. However you only have one record for one company, using company as a class predictor for MANOVA, you use a full model, hence it doesn’t work for your either.

Hence I suggest you use a linear regression model, the outcome is the ratio, and the predictor is the year.(value of 0,1,2,3,.. to 9.

1.  Do overall analysis, generate a id number for each company and each year, say company 1, the id is 0-9, company 2, is 10-19,

Get residuals from the simple reg model in 1. Compare the residuals, find the a certain number of extremes, say 10,  the smallest and the largest to see which companies are identified by the id number.

2.  Perform the analysis in 1, by 100 companies separately,

Get the 100 interceptions and 100 slopes (the regression coefficient for year), compare the slopes, to see which company has the largest slope or smallest slope,

Compare the interception, which is for the first year, you can compare any year you like. By using predict value for a given year, or reset year value.

The following is a makeup example for 4 years data and 8 company, you can change to 10 years and 100 company using SAS as your reference.

DATA old;

  INPUT sub company dv1 dv2 dv3 dv4;

CARDS;

1 1  3  4  7  3

2 1  6  8 12  9

3 1  7 13 11 11

4 1  0  3  6  6

5 2  5  6 11  7

6 2 10 12 18 15

7 2 10 15 15 14

8 2  5  7 11  9

;

RUN;

PROCPRINTDATA=old ;

RUN;

  DATA new ;

  SET old;

  dv = dv1; year = 1; sub1=10+sub;OUTPUT;

  dv = dv2; year = 2;  sub1=20+sub;OUTPUT;

  dv = dv3; year = 3;  sub1=30+sub;OUTPUT;

  dv = dv4; year = 4; sub1=40+sub; OUTPUT;

  DROP dv1 - dv4 ;

RUN;

procregdata=new;

model dv=year ;

id sub1;

outputout=resid p=p r =resi;

run;

procunivariatedata=resid plot;

var resi;

run;

procsortdata=new; by sub;

procregdata=new OUTEST=para; by sub;

model dv=year ;

procprintdata=para;

run;

procunivariatedata=para plot;

var intercept year;

run;

When I copy the SAS code in, the space between proc reg, etc, dispeared, I think you can figure out. Because you have 100 companys you dhould use do loop otherwise you you will need 100 statements: for  OUTPUT; or you can just type the data in.Here, I just a little "lazy" to type the data 32 times.

In order to compare the global means on time with the individual behavior of any company there are a lot of techniques can be used, one of those techniques that give good numerical and graphical information are the control charts like CUSUM, X-R or X-S control charts, and if the information for any company is a multivariate data I use T-Hotelling Control Chart (This type of control chart are used with variables data – data that is taken along a continuum time)

THanks for those answers too - very helpful indeed!

It's important know the objecctive of your research, but thinking in a very simple way :

I see 2 approaches: transversal (each year) and longitudinal (tendency along the period).

#1: Transversal:

Define a Confidence Level, calculate the average each year,  separate companies outside the Confidence Interval, rank them for each year and you will get the volatiles. Who where significantly out of average.

#2: Longitudinal:

You can use the companies from #1 and define a threshold for companies that are frequently present in this group, discarding the companies that are mostly inside the confidence interval, I mean, the "accidentals".

Analyse tendencies using, for example, Control Chart . You can see tendencies, out of control and a lot of other behaviors, just seeing them.

There is conjunctural influencies that affects some sectors the same, if this happen to distorce the behaviour, think about some compensation process to mitigate the influence.

I agree with suggestions given above.