Mathematical and Statistical Methods for Actuarial Sciences and Finance

Checking financial markets via Benford’s law: the S&P 500 case 101

5 Conclusions

To the best of our knowledge, several aspects concerning the use of Benford’s law-
based analyses in financial markets have not yet been investigated. Among the various
ones, we consider the following:

• Given the few studies on this topic, the actual capability of this kind of approach
  to detect anomalous behaviours in financial markets has to be carefully checked
  and measured. To this end, the systematic applications of these approaches to a
  large number of different financial markets is needed;


• From a methodological point of view, we guess that restricting the analysis we
  performed in this paper to the different sectors compounding the financial market
  could be useful for detecting, in the case of anomalous behaviours of the market
  as a whole, which sectors are the most reliable;


• We guess also that, in order to make this analysis more careful, we should at
  least take into account the probability distribution of the second significant digit
  (see [6]), i.e.,

Pr(second significant digit=d)=log 10

∑^9

k= 1

(

1 +

1

10 k+d

)

, d= 0 ,..., 9 ;^6

• Finally, the results we presented in this paper areex post. Currently, we are be-
  ginning to develop and apply a new Benford’s law-based approach in order to
  check some predictive capabilities. The first very preliminary results seem to be
  encouraging.

References

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(^6) We remark that zero is significant as a second digit.