Has anyone figured out how to make the numbers in Table 3 (PDF p. 10) in the stress test results add up? I understand what all the lines mean individually, but the presentation seems incomplete. Looking at Citi for example, I know that they expect 104.7 in losses on existing assets, but they expect Citi to make 49.0, for a net loss of 55.7. Common capital on 12/31/08 was 22.9, and 22.9 – 55.7 = -32.8, so absent recapitalization that would leave Citi at -32.8 on 12/31/10. The “SCAP buffer” (which seems like the opposite of a buffer, but whatever) is 92.6, so with the buffer Citi would have 59.8 on 12/31/10. But 59.8 is well over 4% of Citi’s risk-weighted assets of 996.2.

Maybe the model has Citi’s assets climbing up to $1.5 trillion? Or maybe the losses and “resources to absorb losses” do not have a dollar-for-dollar effect on common capital?

Anyway, it seems like at least one number is missing. If you can explain this, or link to someone who can, I will . . . be grateful.

Update: The most common theory is that 59.8 is 6% of 996.2. But I don’t think that is the explanation, for the reasons I cite in this comment reply and that Nemo also flagged. Also, Erich Riesenberg points out that the fact that this works out to 6% for Citi is a pure coincidence, if you look at the same calculation for other banks.

By James Kwak

55 responses to “Help

  1. “maybe the losses and “resources to absorb losses” do not have a dollar-for-dollar effect on common capital?”
    That’s the point of risk-weighting your assets. Everyone was so surprised that COF graded out so high given its CC ABS portfolio, but CC ABS has always been at 100% risk-weighting. On the other hand, primary mortgages are only at 20% risk-weighting.

  2. This seems a better explanation than any posted after it, but I am still a little lost…

    Could you elaborate on the math a bit? Maybe work an example step-by-step with made up numbers?

    I thought “common capital” was essentially assets (not risk-weighted assets) minus liabilities. And the projected losses are certainly not risk-weighted. So shouldn’t the losses deduct dollar-for-dollar from both common capital and total Tier 1 capital?

    (I also noticed that 59.8 divided by 996.2 is 6%, but (a) Prof. Kwak’s numbers are for common capital, which is supposed to be 4%, not 6%, of assets; and (b) a similar calculation for the other columns in the table give widely varying results.)

  3. James Tanner

    Page 15 of the report:

    Specifically, the SCAP capital buffer for each BHC is sized to achieve a Tier 1 risk-based ratio of at least 6 percent and a Tier 1 Common capital ratio of at least 4 percent at the end of 2010 under the more advrse macroeconomic scenario.
    By focusing on Tier 1 Common capital as well as Tier 1 capital, the SCAP emphasized both the amount of a BHC’s capital and the composition of its capital structure. Once the SCAP upfront buffer is established, the normal supervisory process will continue to be used to determine whether a firm’s current capital ratios are consistent wih regulatory guidance.

  4. James Kwak

    (I fixed your formatting for you – since I’m an admin, I can edit comments later. I didn’t change any of the content.)

  5. James Tanner

    OK, cut n paste didn’t work…odd, sorry about that.

    Basically, they want Tier I overall capital to be at least 6% with common capital at least 4%. 59.8 is about 6% of 996. See page 15/38 of the PDF.

  6. James Tanner

    Presumably, that’s why they’re calling it a buffer. Require a higher percentage than the minimum to make sure they’ve got enough capital if things turn out worse than the adverse-case scenario. To their credit, it amounts to a recognition that (a) the minimum standards are kinda threadbare and (b) the adverse scenario isn’t so adverse anymore.

  7. James Kwak

    I think the fact that 59.8 is 6% of 996.2 is an accident, for two reasons that Nemo also pointed out above:

    1. According to the parenthesis on Table 3, the buffer is calculated in terms of “Tier 1 common/contingent common,” not all Tier 1 capital. So the threshold should be 4%.

    2. I started my calculation with 22.9, which is the “Tier 1 common capital” number. If we’re going to use the 6% figure, then we have to start with the Tier 1 capital number, which is 118.8. Then we would get a final number of about 155.9 instead of 59.8, and 155.9 is about 16% of 996.2.

  8. James, pardon my french but just RTFM.

    page 3 of The Supervisory Capital Assessment Program: Overview of Results

    “….9 of the 19 firms already have capital buffers sufficient to get through the adverse scenario in excess of 6 percent Tier 1 capital AND 4 percent Tier 1 Common capital.“

    Nemo has commented on my blog: “… 6% is supposed to apply to COMMON Capital, not total Tier 1.”
    False, period.

  9. James Tanner

    Heh, well, I tried…a little out of my depth here, I guess. I see what you’re saying and I have no answer.

    By the way, whence transparency? If Geithner et al. don’t want this to look like pure smoke-and-mirrors, shouldn’t their basic math be at least digestible? For the pros, at least?


  10. gabistan1234

    well this is one of the most frightening things ive ever read… we’re doomed.

  11. The ratio under the scenario detailed in the table is 6 not 4%.

  12. riverdaughter

    Getting the right answer is so uncreative and authoritarian. Why don’t you just shoot for an estimate or invent a completely new way of dividing by zero?
    By the way, you are asking your readers to adopt the “sage on the stage” attitude. We prefer “guide on the side”.
    Keep at it! We know you can do it!

  13. James Tanner

    One item of note regarding Citi:

    The Fed credits Citi with 87.1 billion of capital actions and transactions in Q1 2009, mostly offsetting the 92.6 billion dollar hole they’d otherwise be in. 58.1 billion of that 87.1 billion is basically an accounting chimera – exchanging preferred stock (liability) for common stock (equity).

    And how did Citi announce today that they’re plugging the remaining 5.5 billion gap? By expanding the preferred-for-common exchange with the Fed by 5.5 billion. Voila, problem solved. Citi is now officially on the up-and-up with the Fed. And the American people are left to hope that these numbers aren’t cooked, and that 63.6 billion of Citi stock will still be worth that much over the coming years. Such a joy.

  14. James Tanner

    And there’s nothing in the report that answers the real question: how do we know that Citi’s “risk-weighted” assets are worth 996 billion? That’s the number that every ratio they use relies upon, and there’s no meaningful exposition on the subject in the report.

    As per 17/38 of the PDF, looks like the 996 billion number is simply Citi’s reported assets from 4Q 2008 plus any assets since brought onto the balance sheet in accordance with FAS 140 (that is, the standard transfer of assets rules, before FASB tinkered with the mark-to-market rules in April).

    But didn’t we audit those assets? Check a sample of the loan tapes and whatnot, to make sure the 4Q number was realistic? If not, what the hell took so long to do the report?

  15. James Tanner

    Sorry, quick correction…FAS 140 is the rule from last year preventing banks from moving securities off the balance sheet by transferring them to qualified special purpose entities. So as far as the 2009 revisions go, the’re including security sent to a QSPE in the current assets/liabilities columns. Not sure if that matters much, but there you go.

  16. James Twiner

    psha! It took so long to do the report because all the best “creative” accountants were retained by Citi and BoA with those inducement bonuses, so the Fed had to make do with second rate talent.

  17. James Tanner


  18. I am not a shareholder of any of these 19 BHCs but if I were I would not be able to reach any real conclusions from reading “The Supervisory Capital Assessment Program: Overview of Results” dated May 7, 2009.

    The main reason for that is that everything in the study refers to “risk-weighted assets” and these figure can, first, mean nothing at all if, as could be the case, those risk-weights bear little relation to the real world; and second, make any comparisons between BHCs impossible since the differences between the risk-weighted assets could be larger than between apples and oranges.

    In this respect we must also consider how the risk-weighted assets will move not only according to incurred losses but also in accordance to changes in for instance the credit ratings.

    Finally, I do not really get what we want coming out from this report. Do we want to strengthen the weaker so that many survive or do we want to show who are weak so that we strengthen the stronger to make sure that some survive?

    I do believe in transparency but sometimes, especially when the King might be walking around in the nude, ignorance might be real bliss.

  19. Erich Riesenberg

    I took the projected capital (common capital – losses + earnings), added the SCAP to sum the equity the entities are required to hold.

    Divided that by risk weighted assets and got answers from 2 % to 10 %.

    So, the rquired ratio of common to assets varies quite a bit, it appears to me.

    Will be fun to look back and see how far off they are on losses.

  20. James K; you got all numbers and formulas right. except for focusing on 4% of tier_1 capital, as opposed to tje 6% of tier_1 capital (as James T pointed out). The 4% rate applies to RWAs to tangible common equity, which will required C to expand its preferred exchage offer to come to make up for the $5.5 bn shortfall

  21. K. Williams

    “Will be fun to look back and see how far off they are on losses.”

    The stress test’s estimates on losses and capital needs are very similar to the IMF’s estimates, so unless you think the IMF is lowballing, which seems pretty unlikely, there’s no reason to think the Fed is.

  22. James Kwak

    Similar, as in same order of magnitude, but still not that close, I think. The IMF said U.S. bank capital requirements would be $275-500 billion; the government is saying $185 billion, and only in the “more adverse” scenario (which, we all know, is now the likely scenario). Now, that’s only for 19 banks, but they are a majority of the system, and probably in worse shape than most of the small banks. Given how little money is left in TARP, $100 billion can make a big difference, politically at least.

  23. didn’t IMF say capital requirements were $275-$500B through 2011 and the stress tests say $185B through 2010?

  24. well then it’s probably just a matter of different assumptions and different information. for instance how did the imf count the $308B in citi assets currently under govt guarantee? (does imf know what they are?) in any case these are all just guesses and are motivated partially by institutional agendas.

    in any case we are looking at estimates. and you will notice that obama has not removed the $250b request for additional bank aid from the budget.

    the other thing is that if losses are reasonably bounded it should be easy enough to raise new capital in the market. a healthy bank of america probably would be worth around $250b and so if at the end of 2010 they need to raise $50b to be completely healthy they should have no problem doing it. similar story for wells.

    i’d guess that the only serious problem is citigroup at this point. if the economy gets much worse or we get deflation that is another story.

  25. James Tanner

    Both are also saying that most of the lossess will take place by the end of FY 2010. It’s a substantial gap.

  26. Hi James,

    I would like to suggest that it would be interesting to sort out what it was about those banks that passed the test without a necessity for additional capital. Asset mix, asset quality, non-credit operating profits, liability mix, etc. What do the winners have that the others lack? A related question, perhaps impossible to answer, is what would BAC and WFC have scored had they not absorbed failing institutions? Lastly, can anyone foresee combinations of banks whose merger would mean no need to raise capital? To me it is more important to try to see what the Supervisors will infer from these results than to quibble over their assumptions or their math. This level of insight into the regulatory perspective is very rare. You would be hard pressed to get a Supervisor to agree that there is anything wrong with the figures or the assumptions. If this was your view of the state of the nation’s banks, what would you be thinking to yourself and preparing for (as opposed to what you might say in public just at this moment).

  27. I’m getting numbers that seem roughly correct with the following procedure:

    4% of risk weighted assets = 40
    Add expected losses: 104.7 + 40 = 144.7 to get capital buffer needed.
    Subtract expected income: 144.7 – 49 = 95.7
    Which is close enough to 92.6 for me to think this may approximate their procedure.

  28. in addition to SFAS 140, I would say that they’re probably estimating that Citi will have a higher allowance for loan losses in YE 2010 compared to 2008. That requires more capital to fund.

  29. I think there’s a problem with “risk-weighted assets”. On 12/31/08 Citi reported 377,635 + 256,020 + 694,216 = 1,307,871 in trading account assets, investments, and loans, respectively, and 1,938,470 total assets.

    Tier 1 Common of 22.9 is also hard to reconcile with anything reported for Stockholder’s Equity, which shows 19.2 of common stock, -9.6 of Treasury stock, and -25.2 of unrealized losses.

    Bank of America is similarly hard to reconcile. Maybe the SCAP numbers are stated according to POOBA basis (pulled out of ben’s *ss).

  30. Posted that one without thinking it through. Of course the method above assumes Citi doesn’t have any Tier 1 common capital.

    Not a good sign if that’s the assumption you need to make for the numbers to match.

  31. Given egc’s post, perhaps they are treating Citi’s capital as naught — but aren’t willing to write it out clearly on paper.

  32. I think they are shooting for 6 percent
    If so the numbers are right on

  33. to clarify the above see page 3 para 4
    6 pct of tier 1 or 4 pct of tier 1 common
    6 pct of 996 is 59.8

  34. Isn’t this just a nice way of saying that Citi has a lot of garbage in off-balance sheet SPVs that are going to get pulled onto the balance sheet before 12/31/10? They can’t quantify it now – since they are ostensibly using the 12/31/08 marks, based on prevailing GAAP, and don’t want to point to the glaring extent of today’s capital deficiency – but they want to get to a place where it can be admitted down the road.

    Wonder if all the banks can pull a Goldman and shift reporting periods to give themselves an off-the-record month to do their housekeeping.

    Footnote 11:
    …supervisors evaluated the potential impact of proposed changes to FAS 140 and FIN 46(R) which are expected to be finalized in May 2009 and implemented in January 2010. The agencies’ accounting specialists discussed the amendments with FASB members and staff and other experts to assess the reasonableness of firm estimates of assets likely to be brought on to the balance sheet starting in 2010 as a result of the amendments. The on‐boarding of assets were also factored into our assessment of risk‐weighted assets and the associated ALLL needs.

  35. Interesting. If this explanation is correct, then the authors of the report obviously had this information in their own spreadsheet but chose to omit it from the published table.

    And if this is the only source of the discrepancy, then we have enough information to reconstruct what they omitted; i.e., to see how much off-balance-sheet exposure each firm is expected to bring on-balance-sheet. Could be an amusing exercise.

  36. The challenge is that while it seems to work for C and BAC (who would be pulling $498bn and $163bn onto the balance sheet, respectively, which at least directionally fits my conception of each firm), Fifth Third does not seem to have a capital deficiency and yet requires additional money.

    Perhaps we are seeing three things:

    (1) Off-balance-sheet items coming on-balance sheet;
    (2) Regulator’s unquantified concerns about some firms;
    (3) C and BAC’s negotiating power.

    Nemo’s exercise was amusing until it made my head hurt and my dwindling faith in the test dwindle further. How difficult would it have been to give a clear set of numbers that add down? You know, like a financial statement…

  37. it wouldn’t be the only source of discrepancy. the size of the risk weighted asset pool is going to change due to new lending and defaults between now and then. so it is a projection as well.

  38. James Kwak

    That’s a good theory. If something is causing the denominator (risk-weighted assets) to shift between 12/31/08 and 12/31/10, that could fill the gap.

  39. .04 is applied to Tier 1 Common (22.9), .06 to Tier 1 (118.8), so

    Target SCAP: (0.06*996) – 22.92118.8 + 104.7 – 49.0 = -3.3, so they have enough Tier 1 according to SCAP.

    “Risk-weighted assets” of 996 may be net of government guarantees of 300, adjusted for BofA in note (5) of table 3, but not for Citi.

    996 + 300 = 1296 is closer to the risk assets shown on Citi’s balance sheet.

  40. the citi gov guaranteed assets are risk-weighted at 20%

  41. Quite clear, and also quite wrong.

    Several commenters have presented the same “DUH IT’S 6%” analysis already. Prof. Kwak has already replied giving two reasons why it does not hold water.

    Perhaps you could read others’ comments, or at least those from the author, before posting your own? Just a thought. :-)

  42. Erich Riesenberg

    Yes, clear if you only consider Citi and for some reason assume the targe is 6% instead of 4% as stated in the paper.

    Could you explain why Fifth Third is at 3.5% or PNC at 1.9%? That would be so helpful. Thanks!

  43. Erich Riesenberg

    I hadn’t accounted for the purchase accounting adjustments. If that is added back PNC comes at 4.3%.

    Of the companies with a “SCAP buffer” Citi comes in highest at 6%. The others are below 5%.

  44. the paper says: “…capital buffers sufficient to get through the adverse scenario in excess of 6 percent Tier 1 capital and 4 percent Tier 1 Common capital.”

  45. RWA increases to 1,495 as off b/s credit card receivables and other assorted goodies are brought back on b/s. You can back out the implied change in RWA with the info that’s provided. Add the buffer of 5.5 to initial common equity of 22.9 and you get 28.4, then subtract losses of 104.7 add earnings of 49 as well as true ups of 87.1 and you get 59.8 of required common equity. Divide by 4% and you get ending RWA of 1,495.

  46. then it fails the 0.06 tier 1 test.

  47. C doesn’t fail 6% tier 1 if you add back 87.1B of “Capital Actions and Effects of Q1 2009 Results.” When you do that C has a $60.5B tier 1 surplus but a $5.5B common equity deficit.

  48. the 87.1 is already in “tier 1”, that’s why the whole exercise is pointless if the bank can’t raise common equity, then preferreds included in “tier 1” convert to common equity to boost “tier 1 common equity” while leaving “tier 1” unchanged.
    In any case, releasing the anticipated RWAs for end-2010 would have made life easier for all and since banks were required to provide the numbers for the stress test, I am left wondering why they are not included in the results.

  49. note that citi is unique.
    it loses all its common capital and it is the only one to do this
    22.9 – 104.7 +49 is negative – ie all the common is gone and some of the preferred also.
    if you assume that the transfusion goes into preferred then the original capital is gone
    there are two rules – one that allows lending with a reserve ratio of 4 pct and one that allows at 6 pct.

    bofa on the other hand does not lose all its common
    74.5-136.6-74.5 is positive.

    perhaps all the other banks are on some form of proration between 4 and 6 – I will try to work it out.

  50. Erich Riesenberg

    Here is a spreadsheet as best I can understand. The rows in blue are calculated based on the data.

    When capital is required in the row “SCAP Required” it appears additional capital is being required. Looking at the row “Net Capital as % of RWA” it shows a range of percentages for companies required to raise capital.

  51. Pingback: Alea | Updated Citi Stress Maths

  52. It seems pretty clear that in the case of Citi the authors used 6 percent to calculate the SCAP Buffer for 12/31/2008

    Citi 12/31/2008 Scap = 6% of assets + loss adjusted for resources – original capital

    92.6 = 0.06*996.2 + (104.7 – 49) – 22.9

    It is also clear that they used a different scheme for the other banks.

    Citi is unique in that the common interest is pro forma wiped out in the exercise while this does not happen to the other banks.

    Ie 22.9 – 104.7 + 49 < 0 !! wipe out

    This apparently simplifies their calculation since it otherwise has 2 rules – one involving 4 pct and the other involving 6 pct.

    I’m trying to back into the rules used elsewhere – no luck so far.

  53. “Has anyone figured out how to make the numbers in the stress test results add up? ”

    In the Baseline Scenario blog, James Kwak says Table 3 of stress test results implies Citi TCE ratio of 6% on 12/31/10 (well over 4%). Too high.

    Either risk weighted assets have to grow from 996.2 to 1.5 trillion – unlikely. Or, earnings:capital impact not 1:1.

    My own answer is that the SCAP assumptions do indeed include growth in assets to 1.5 trillion, upon implementation in 2010 of the revised FAS 140 accounting for off-balance assets. Citi could easily get to that level of assets given 1.1 trillion off balance sheet assets.

    Tim Mamin
    SVP Audit /Model Validation
    Bank of America