Kreps Ratios TVARs

On page 54 of Kreps Ratios, he says,

Management decides to adopt the rule “We want our surplus to be 11/2 times the average negative income in the cases where it is below the 2% level.” That row is in italic, and this rule means that the 9,000,000 surplus is sufficient.

I am not understanding this. According to my interpretation of the table, the VaR at 2% threshold is (4,732,795). The TVaR is (6,159,564). So the average negative income in cases where it is below the 2% level would be (6,159,564), no? And 1.5 times (6,159,564) is (9,239,345.49), so 9,000,000 is not sufficient.

Unless I am misinterpreting (entirely possible), 4,732,795 is the value at the 2% threshold, not the average value below the 2% threshold. 6,159,564 would be the average value below the 2% threshold.

I think you are reading it correctly, and $9M is only sufficient to cover 1.46*Tvar(98%). Maybe management looked at that and said “close enough”.

Someone asked this same question a couple years ago.

I remember finding an earlier version of the Kreps DFA excel file online where the TVAR 99.8 was a little less than 6M, so multiplying by 1.5 was a little less than the 9M of current surplus and it tied out.

I think something may have changed in the excel file that’s referenced now, but it’s still “close enough” to 9M that it wasn’t worth going back and updating the paper, etc. Unfortunately, I don’t remember where I found that excel file.

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I had considered that maybe my spreadsheet had recalculated and that my simulation results were a little different due to randomness, but the 6,159,564 TVAR98 figure comes directly from the text of the pdf itself, so I wouldn’t think this was due to differences in excel attachments.

I had also considered that 9.2M is “close enough” to 9M, but I thought it’d be crazy to construct in an illustrative example with a threshold that was technically insufficient, then deem it to be sufficient with no further commentary.