Q13a - Excess Category B/C Capital Deduction

warn9795warn9795
in PRACTICE EXAM

Hi,

The way I'm reading the solution to this question, it seems to me that the category C capital still exceeds 7% of Total Capital less AOCI after making the adjustment: (6000 - 1625)/((69500 - 1625) - 7000) = 7.19%. Is this intended, or an oversight of the method being used?

When I did this problem, I ended up solving for X such that: (6000 - X)/(62500 - X) = 7%, which gives us:
X = (6000 - 62500*7%)/(1-0.07) = 1747.31

Hence Deducted Capital Available = 69500 - 1747.31 = 67,752.69.

This is different than the solution, which assumes the denominator remains unchanged when we reduce Cat. C capital. Have I overlooked a detail of the reading that prescribes such an approach?

Thanks!

Comments

  • grahamgraham
    edited October 2019

    I see what you're doing and it's very reasonable. I would call that a "mathematician's" approach. After you calculate the deduction, you substitute it back into the formulas to see if the limits are now satisfied. If not, then iterate until the Category C capital is indeed within the acceptable limit. (Or just set up an equation and solve for X directly.)

    But I don't think OSFI intends for it to be done like this. I believe they intend for this to be a very straightforward, non-iterative procedure. Even though the excess capital is technically from Category C, the deduction of 1,625 isn't specifically taken from Category C. Rather, this 1,625 is deducted from general capital available.

    Of course, I'm reading between the lines here because they don't really say, but I think at least for the exam, you only need to apply this "limit" test one time exactly as they describe in the reading.

  • warn9795warn9795

    Thanks Graham. I don't think I was suggesting this to be an iterative method, but rather the first and only solution used would solve for X recognizing that X is also in the denominator, not only in the numerator of the ratio. It's actually a very subtle difference from the answer in the practice exam:

    Method A: Solve for X such that (6000 - X)/(62500 - X) = 7%, and if X>0 then we need a deduction for excessive category C capital. Gives X =1747.31

    Method B: Solve for X such that (6000 - X)/(62500) = 7%, and if X>0 then we need a deduction for excessive category C capital. Gives X = 1625

    Method B above corresponds to the answer key, but in general should always give an outcome slightly greater than 7% of capital available after deduction since the denominator in reality will be smaller than assumed in the calibrated answer.

    Anyway, a minor enough detail that I wouldn't be surprised if both approaches are accepted on the exam. It seems to be ambiguous enough in the source guidelines that an argument could be made either way.

    Thank you.

  • grahamgraham

    Ok, agreed. Good luck on the exam.

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