Converting exposure values with log for weighted average method

cercig

New Member
Hello,

I have a couple of transaction types with different risk scores in a scale between 0 to 10 [0-10]:
Code:
Trans_type_1_risk = 8 and Number_of_trans_type_1 = 1.000.000 (~0.04% of Total_nbr_of_transactions)
Trans_type_2_risk = 4 and Number_of_trans_type_2 = 1.000.000.000 (~40%  of Total_nbr_of_transactions)
Trans_type_3_risk = 9 and Number_of_trans_type_3 = 2.000.000 (~0.08% of Total_nbr_of_transactions)
Trans_type_4_risk = 5 and Number_of_trans_type_4 = 1.500.000.000 (~60%  of Total_nbr_of_transactions)
I want to calculate an overall risk score by using some "weighted_average" method or something like that.
Code:
Overall_risk = (Trans_type_1_risk * Nbr_of_trans_type_1 + Trans_type_2_risk * Nbr_of_trans_type_2 + Trans_type_3_risk * Nbr_of_trans_type_3 + Trans_type_1_risk * Nbr_of_trans_type_4) / Total_nbr_of_trans
However, when I use the number of transactions as weight, then the weights of the most risky transactions types (type_1 and type_3) become insignificantly low (~0.04% and ~0.08% respectively).

I don't want to underestimate the most risky transactions types 1 and 3, so I came up with the idea of using the log functions for the number of transactions. Thus:
Code:
log(Nbr_of_trans_type_1) = log(1.000.000) = 6 which is ~19.7% of (6+9+6.3+9.2) so the new Weight_1 becomes 19.7%
log(Nbr_of_trans_type_2) = log(1.000.000.000) = 9 which is ~29.4% of (6+9+6.3+9.2) so the new Weight_2 becomes 29.4%
log(Nbr_of_trans_type_3) = log(2.000.000) = 6.3 which is ~20.7% of (6+9+6.3+9.2) so the new Weight_3 becomes 20.7%
log(Nbr_of_trans_type_4) = log(1.500.000.000) = 9.2 which is ~30.2% of (6+9+6.3+9.2) so the new Weight_4 becomes 30.2%
With this log-conversion and new weights, the risky trans_types 1 and 3 can contribute to the result significantly (19.7% and 20.7%) and still the trans_types 2 and 4 contributes to the results the most (29.4% and 30.2%) due to their number of transactions. So everything looks perfect with this method.

Code:
Overall_risk = (8 * 19.7% + 4 * 29.4% + 9 * 20.7% + 5 * 30.2%) / 30.5 = 6.125
However, I have difficulty to motivate "How I could use the log-conversion for the weighted-average calculation" according to the statistical principles. Does my method make any sense statistically?

Last edited:

katxt

Active Member
What do you intend to do with the calculated overall risk?
Are there penalties associated with each type of risk?

cercig

New Member
What do you intend to do with the calculated overall risk?
Are there penalties associated with each type of risk?
Hello @katxt ,
The main point here is that I want to calculate an overall risk score which represents all transactions risks fairly. Like I mentioned previously, weighted average method seems fair at first sight. But with this calculation, the impact of the high risk transactions types 1 and 3 is almost zero due to their very small volume compared to the other transaction types. That's why I used log-function to have better distributed weights. My question is, if this new weight distribution makes any sense statistically?

katxt

Active Member
does this new weight distribution makes any sense statistically?
It seems too artificial to me, I'm afraid. A statistical justification needs more information, like a combination of risk, frequency and cost, and a purpose for the weighted risks.
when I use the number of transactions as weight, then the weights of the most risky transactions types (type_1 and type_3) become insignificantly low (~0.04% and ~0.08% respectively).
Probably they are insignificantly low, unless they have very severe consequances.