These comments on the LBMA Liquidity Survey come from FOFOA's blog. I've assembled them here for my future reference convenience and are probably of interest to about four people. See also
this post for earlier comments on the survey.
To the extent that the clearing banks have the same mix of clients there would probably never be any sustained/ongoing movement of physical from one to another as over time a bank's flows would net.
However if the mix of clients is not even (eg one bank predominantly has mining/selling clients and another has jewellers/buying clients) then there would be ongoing movement of physical from one clearer to another.
This was a debate I was having with FOFOA around the LBMA survey imbalance as if the mix of clients between banks is not symmetric then you will have an imbalance in the trading reported (yes, I have not forgotten, it is still on my to-do FOFOA). FOFOA doesn't think so, I do, but maybe I need more time to get to where he is. Fwiw, that survey was actual reported volume (divided by two in the table so as not to double count). Any additional banks reporting would only have added to the total. Even if the rest did the smaller volume, that would not have reduced those totals given. So that is why it can be taken as a minimum.
That's right MF, but the question FOFOA (and I) had was whether LBMA in aggregate sold more unallocated ('gold') than they purchased. The net difference between purchases and sales was some 7500t over the surveyed quarter, and this is too much to be hedged in non-LBMA 'gold' instruments such as COMEX, TOCOM etc.
So if they indeed sold more than they bought, this would indicate that they are not flat 'gold', but that they rather delta-hedge their net exposure to 'gold' using correlated instruments, say AUDUSD, CADUSD etc.
The question that got us there was the question of why the 'gold' price goes up after a GLD puke. The puke is just a small amount of physical, say about 13 tonnes, which is a lot less than the 2700 tonnes of paper that are traded every day. So how can that little puke move the price over the subsequence 2-6 weeks?
If LBMA in aggregate does delta-hedging, this might be the explanation: after the puke they shift their hedge from 'gold' correlated instruments to proper 'gold', thereby running up the 'gold' price. (They would lose a bit due to friction if they do this, but, hey, you are the market maker and if you fleece everyone by a fraction of a percentage point, you should still come out even).
If Bron is right, and LBMA in aggregate is flat 'gold', then the GLD puke indicator still awaits an explanation.
Bron Suchecki December 3, 2012 9:43 PM My suggestion as to why the GLD puke indicator may work is that in the fact of net selling the APs and others will use all and every means to arbitrage GLD to spot except redeeming (as that has a slight cost). They would build up "stock" of GLD shares in the hope they can resell it later (and avoid redemption and subsequent creation costs).
If the selling continues they build up too much GLD shares (long) and too much leased unallocated (short) so at some breakeven point it is less costly to redeem GLD and collapse the hedge. These capitulations by the APs signal their assessment that the selling is "real" (ie not temporary).
On a sentiment basis this represents a low point, from which on probabilities, the price has more of a chance of rising. Just a theory.
I'm glad to see that you brought this up again, because I was just explaining my take on our debate to Joe Yasinski and Dan Flynn of GBI the other day. Did you happen to see that they mentioned the discrepancy in the LBMA survey in their latest post?
The way I explained it is basically this. We have three proposed explanations for the 7,575 tonne (aka $337B) discrepancy between purchases and sales in the 1Q11 LBMA member survey. As you correctly pointed out, it is likely a combination of these explanations, because as I recall you finally conceded that the discrepancy is far too large to be solely explained by the survey methodology. But even still, that "halving of interbank transactions" is our first of three explanations.
The second explanation is yours, which we called "asymmetric reporting". And the third is mine which is basically that demand shocks are being contained/absorbed by expanding or contracting paper supply rather than by price. Three competing/complementary explanations for the reported discrepancy:
1. Statistical methodology
2. Asymmetric reporting
3. More paper gold sold than bought
As Victor just mentioned, we have an explanation for the hedging requirement of the price exposure implied by my explanation which is similar to what they do for FOREX exposure. So having given this brief synopsis of our debate, here's an excerpt from one of my emails to Joe the other day:
Bron's explanation is that there is a difference in clients between the LBMA members who chose to report on the survey and those who chose not to report, and that this difference informed their decision of to report or not to report. In order for Bron's explanation to explain the entire discrepancy, there needs to be a flow of physical gold twice the size of the discrepancy, or 15,150 tonnes (7,575 X 2) from the non-reporting members to the reporting members and then on to their (the reporting members') clients. It must be double because of the halving of the interbank transactions in the survey. This is simply a ridiculous notion given of the sheer size of physical gold flow (15K tonnes of physical in one quarter) required to explain the entire discrepancy between purchases and sales given the methodology of the survey.
But Bron may have a point that, on some level, certain types of LBMA members might have been more prone to report than others. His theory is that the BBs selling to Giants and industrial users are reporting, and the mints and refineries buying from mines and scrap dealers are the non-reporting members. Something like that anyway. So that phenomenon might contribute to someof the discrepancy. So how much?
As you point out in your post, new mining supply in one quarter is only about 625 tonnes. Add some reasonable number for scrap supply and then halve the total, and that's the very most that Bron's explanation could account for in the discrepancy. So let's say (generously) that 500 tonnes could be accounted for by asymmetric reporting.
So now we have three explanations for the discrepancy, and we can assign reasonable numbers to two of them. Statistical methodology could possiblyaccount for around 750 tonnes of the 7,575 tonne discrepancy. And asymmetric reporting could maybe account for another 500 tonnes of the discrepancy. So…
7,575 – 750 – 500 = 6,325 tonnes discrepancy unaccounted for
And that leaves my explanation as the winner for the remainder, IMHO.
(Note: The 750 tonnes potentially attributable to the "halving methodology" is just my guess as an amateur statistician. But I think it's a generous and close guess. It could be a little more, but not more than twice that number, and it's probably less. I mentioned p-valuein one of the comments before our debate moved to email. It is a way of distinguishing what is statistically insignificant from what is significant. In this case, up to the limit of statistical insignificance is possibly attributable to the "halving of interbank transactions without all banks reporting", in my amateur opinion of course. ;) I saw his article, but this comment:
"Based on the survey, we deduce that in 1Q11 excess demand for gold was 243,560,000 ounces which translates into approximately 7,575 metric tons. In a typical year, quarterly physical production (new mining supply) is approximately 625 tons. One would imagine that with a traditional commodity, physical demand outstripping new supply in a given quarter by a factor of 10 would cause a significant increase in price!!"
Is really not a correct way to look at it, because the 7575t is not all physical demand and 625t is not the only physical supply in that quarter.
I disagree with this statement:
"...there needs to be a flow of physical gold twice the size of the discrepancy, or 15,150 tonnes (7,575 X 2) from the non-reporting members to the reporting members and then on to their (the reporting members') clients."
The survey was of bullion bank trades/turnover, which would not relate to flow of physical gold.
The reason I'm not so keen to jump to a conclusion is I have an idea of how trades (paper and physical) are recorded in trading systems and the errors that are likely to inflect the data based on how the database was interrogated.
For example, head of precious metals passes on LBAM request to IS guy who has a lot on their plate, they run a query which they think is OK, but they haven't thought about whether the two legs of a swap should be treated as two trades or one, or if they have excluded reversing (error) trades out etc etc.
Then assuming no errors I need to think through typical transctions and how those may be reported once summarised into the LBMA requested data and whether they will result in the correct result, which is what I'm trying to do with my spreadsheet.
And I think you are underplaying the importance of a correct/representative sample size in determining statistical significance. That sort of stuff relies on normal distribution and representative samples. If a certain group bullion banks of the same type have not reported for strategic reasons then you can't rely on statistical assessments but need to go back to understanding the underlying data.
If asymmetric reporting is to account for the discrepancy, then "there needs to be a flow of gold twice the size of the discrepancy, or 15,150 tonnes (7,575 X 2) from the non-reporting members to the reporting members and then on to their (the reporting members') clients."
I removed the word physical. Do you still disagree with the statement given this change?
"I removed the word physical. Do you still disagree with the statement given this change?"
Taking physical out helps.
"there needs to be a flow of gold twice the size of the discrepancy, or 15,150 tonnes (7,575 X 2) from the non-reporting members to the reporting members"
Don't agree. From my model of the 56 banks, random spread of trades between them all, this is how one of the random runs plays out:
Reporting Banks Buys 5780t
Reporting Banks Sells 5627t
Reporting Banks Discrepancy 153t long
This is a 2.71% compared to 4.35% in the actual LBMA survey. Good enough for an example, I don't have time to run through all iterations to find a 4% discrepancy. For those "reported" figures above, the model shows:
Non-Reporting Banks Buys 3096t
Non-Reporting Banks Sells 3232t
Non-Reporting Banks Discrepancy 136t short
All Banks Buys 8876t
All Banks Sells 8859t
All Banks Discrepancy 17t long
So from a simple model of 56 banks summed buys and summed sells with each other bank (a total 3136 bank-to-bank data point relationships) with random data we get a overall 56 bank universe trading position of 17t over 17734t of turnover.
However, that minimal net position of 17t "appears" when we look only at the reporting banks to be a 153t position over 11407 of turnover. The key point is the non-reporting banks are net short 136t.
The mathematics don't work out as you think.
The very idea of your asymmetric reporting explanation for the discrepancy (as you are standing it in opposition to my explanation) represents a net flow from LBMA members more heavily weighted in one kind of client (selling clients) to BBs more heavily weighted in a different kind of client (buying clients).
We are both operating on the premise that the banks are not exposing themselves to a large net-position. Your explanation opposes mine in that the banks' "net-neutrality" comes from the non-reporting members as opposed to derivative hedges in other markets as described above by Victor. This neutrality would obviously be reflected in a net-neutral position, aka an "All Banks Discrepancy" that is zero or much smaller just as your model puts forth.
So I think that in your example above you are conflating statistical insignificance and the asymmetric reporting explanations. Let's stick, for the moment, to the question of my statement about the flow required for your asymmetric explanation to fully suffice.
Here's your model, except I reversed the buys and sells to make it directionally the same as the real LBMA survey (easier to discuss that way IMO):
Reporting Banks Sells 5780t
Reporting Banks Buys 5627t
Reporting Banks Discrepancy 153t short
Non-Reporting Banks Sells 3096t
Non-Reporting Banks Buys 3232t
Non-Reporting Banks Discrepancy 136t long
All Banks Sells 8876t
All Banks Buys 8859t
All Banks Discrepancy 17t short
In your model here, the top portion (reporting banks) represents all that we can see in the LBMA survey (magnitude doesn't matter in this discussion because we are discussing the flow issue related to the asymmetric reporting explanation at any magnitude). So this is our "toy LBMA survey":
Reporting Banks Sells 5780t
Reporting Banks Buys 5627t
Reporting Banks Discrepancy 153t short
My statement would therefore be adjusted to read: "there needs to be a flow of gold twice the size of the discrepancy, or 306 tonnes (153 X 2) from the non-reporting members to the reporting members"
We are both assuming that the individual banks (as well as in aggregate) have no (or little) net position/exposure. So what we are seeing in this toy LBMA survey is that the reporting banks are short vis-à-vis their clients but long vis-à-vis the non-reporting banks in nearly equal amounts so as to be net-neutral. And the non-reporting banks (because they are more heavily weighted with selling clients like mines and the Perth Mint) are long vis-à-vis their clients and short vis-à-vis the reporting banks (which have more buying clients). All in all, the banks themselves are net-neutral (or at least close to that; your model shows them with a real net position almost an order of magnitude smaller than the reported discrepancy).
The point is that your reporting members in aggregate hold the same (or similar) net position in magnitude, but opposite in direction, vis-à-vis their clients and vis-à-vis the non-reporting members as the non-reporting members hold in aggregate. This is the asymmetric reporting explanation!
So if the banks are essentially net-neutral, why are we seeing any discrepancy at all? We are seeing it because only the interbank transactions were halved, not the client transactions. So the reporting members are net short vis-à-vis their clients and net long vis-à-vis other banks in equal/similar amounts, yet because we halved only the trades with other banks, we see a discrepancy of 153t. So the discrepancy is the product of the halving the directional net flow, therefore the magnitude of directional net flow must be twice the discrepancy.
This applies in all of your models, from your simplest to your most complex, if we assume asymmetric reporting.
So let's adjust my statement one more time and see if you still disagree with it…
"For whatever portion of the discrepancy asymmetric reporting is to account for, there must be a flow of gold twice the size of that portion of the discrepancy from the non-reporting members to the reporting members and then on to their (the reporting members') clients."
Do you still disagree with the statement given these changes?
Bron, your model is describing asymmetric reporting, intentional or not, so you really should consider this flow issue and whether it makes any sense at larger magnitudes like we saw in the actual survey. In your model we can peek at the non-reporting banks and thereby know the "all banks discrepancy" which your model is keeping low through asymmetric reporting. But asymmetric reporting requires this flow, and if you can get your model to spit out a 4.35% discrepancy like the real survey while still keeping your "all banks discrepancy" low then it requires that much larger (and therefore that much less likely) of a net-flow from one group to the other.
If, on the other hand, you allow the "all banks discrepancy" to rise (perhaps offset by derivatives in other correlated markets), you eliminate the asymmetric reporting and the need for this unlikely net-flow of gold, be it paper or physical. So whatever the actual net-flow from non-reporting members in aggregate to reporting members in aggregate is in reality, half of that number is the portion of the 7,575 tonne discrepancy which can be accounted for. If it's not the whole thing (i.e. 15K tonnes in one quarter), then that forces your "All Banks Discrepancy" up which is a net-position they must be hedging elsewhere.
You wrote: "However, that minimal net position of 17t "appears" when we look only at the reporting banks to be a 153t position over 11407 of turnover. The key point is the non-reporting banks are net short 136t.
The mathematics don't work out as you think."
Your statement backs my point. You need the non-reporting banks to be net in the opposite direction which requires a net flow of twice the discrepancy. My math is fine. I think the true net position is higher, close to the reported discrepancy, and that the non-reporting banks are probably not as different from the reporting banks as to be exactly opposite as your model requires to keep the "net position" low without the need for derivative hedges.
Bron Suchecki December 4, 2012 9:59 PM "Do you still disagree with the statement given these changes?"
Yes, because I'm running various iterations of my toy model and it doesn't produce such a flow. I can produce a situation where net overall the buying and selling of clients is net and banks are net, but still result in a reporting banks discrepancy with no x2 flow between reporting and non-reporting.
Note also that just because overall BBs are net doesn't mean that all individual BBs are net.
My model isn't perfect and I want to refine it, but I think the interaction of 56 banks trading with each other is more complex than you realise.
I think the idea the BBs are naked short massive amounts is unrealistic, but I think "offset by derivatives in other correlated markets" is pretty close to unrealistic as well.
I'm going to have to leave this here and maybe I'll get time over Christmas to look at my toy model and come to understand the dynamics of 56 banks better and get back to you.
I the meantime, letting Joe think this is a 100% resolved issue, and then him misapplying it to say there is 10 times more physical demand than physical supply is not right. I can see an incorrect meme starting from that.
I think you are missing the point. I understand you are short on time, but perhaps you could provide a sample iteration of this, in the same format as the one above:
"Yes, because I'm running various iterations of my toy model and it doesn't produce such a flow. I can produce a situation where net overall the buying and selling of clients is net and banks are net, but still result in a reporting banks discrepancy with no x2 flow between reporting and non-reporting."
Also, I never claimed that the LBMA survey was showing "10 times more physical demand than physical supply". First of all it's not physical demand, it's paper "foreign exchange" demand for gold held and traded as a currency, and in the case of the survey it was only one quarter. I'm guessing that the next quarter demand was probably flat and the quarter after that a lot of that paper was probably unwound/sold. So it's not constant demand. It's that demand *shocks* in both directions are being absorbed more so by paper expansion/contraction than by simply letting the price take care of it. Like a shock absorber.
I don't think you are accounting for this "FOREX currency use" of unallocated gold which could easily overwhelm the gold market at current prices without such a shock absorber.
BTW, Bron, I just let GBIJoe know about this thread so that he can come read it and see for himself that this issue is not resolved between you and me. I told him that in my earlier email anyway, but at least this will reassure him that we are still not in agreement! ;D
Regarding complexity, you wrote: "I think the interaction of 56 banks trading with each other is more complex than you realise."
The LBMA asked for reporting down to the individual trade, and the survey even reported the total number of trades (385,852) broken out into purchases (184,140) and sales (201,713). The daily average number of trades was 6,125 over 63 trading days among 36 reporting members. So each member reported, on average, 170 gold trades per day, averaging 81 purchases and 89 sales per day.
We can even calculate the average size of each transaction, although it will be off a little due to the interbank halving. The average individual sales trade was $38.4M+. And the average purchase trade was $40.3M+, or a little less than one tonne per trade.
This is the kind of complexity that I'm taking into account that I don't think your model is. Remember what I wrote in one of our emails last July?…
"The key difference between your random iterations and mine is that you are keeping the magnitude of complexity the same with each iteration. I was comparing different magnitudes of complexity. Whether we randomize the individual transactions or the choice of reporting banks doesn’t make a big difference because the point of my exercise was that the more complex the model, the lower the discrepancy.
You picked a specific level of complexity – 3,136 transactions – and then you reiterated that model and found that the average discrepancy (for your model) was .11% and the maximum was 2.96%.
What I did was to simply run 1 iteration on 3 different models of gradually increasing complexity. The fact that I randomized the reporting banks and you randomized the size of the individual trades is inconsequential. It’s also inconsequential whether we had 75% reporting or 64% reporting.
Your original model had 9 trades, so my three levels of increasing complexity were 63 trades, 126 trades and 252 trades. What we saw from a single iteration of each level of magnitude was this:
9 trades – 10%
63 trades – 5.6%
126 trades – 2.7%
252 trades – 1.69%
I’m calculating the percent a little different than you. I’m saying there X% more sales than purchases, and you’re saying there are X% less purchases than sales. That’s why you came up with 4.35% on the LBMA survey and I came up with 4.5%. But that’s not a big deal.
So your new model has a complexity of 3,136 trades as compared to my most complex model with 252 trades. What we find is that we’d expect a single iteration to yield less than 1%, or maybe around 1%. So it looks like this:
9 trades – 10%
63 trades – 5.6%
126 trades – 2.7%
252 trades – 1.69%
3,136 trades – 1%
The LBMA survey reported a total of 385,852 trades.
If you want to try skewing the reporting banks toward sales, that’s fine. But you need to run comparisons of increasing magnitude, not just iterations of the same magnitude. I’ll bet if you keep it realistic we’ll see the same results… it’ll still trend toward zero too quickly."
Perhaps you could expand on how you are taking into account more complexity than I realize.
Bron Suchecki December 5, 2012 5:02 PM "So your new model has a complexity of 3,136 trades ... The LBMA survey reported a total of 385,852 trades."
That statement tells me you do not understand how the LBMA survey was constructed. If every bank reported the LBMA could only have got a maximum of 3,136 data points. The LBMA was not given 385,852 individual trades.
If a bank had sold 1oz to 100 clients and covered that with 10oz purchase from 10 BBs it would have reported this to the LBMA:
Sell to Clients - 100oz
Buy from Clients - 0oz
Sell to BBs - 0oz
Buy from BBs - 100oz
It doesn't matter how many trades or clients it did, it will only report 4 data points to the LBMA.
BTW, I had not thought about this "So each member reported, on average, 170 gold trades per day, averaging 81 purchases and 89 sales per day."
170 trades per day is impossible, that makes no sense to me when I look at how many individual trades we do with bullion banks per day.
Those "trade" numbers must, at a minimum, be net settlement with a counterparty. For example, if a BB bought 5 times from client A and sold 6 times to client A on one day, that was reported as 1 sale trade.
On average each BB having net settlements with 170 of its clients/other BBs each day makes more sense.
I am going to have to write to the LBMA about that survey.
Of course the banks didn't report each trade to the LBMA. The banks essentially performed their own internal survey and then reported the aggregate numbers to the LBMA.
"That statement tells me you do not understand how the LBMA survey was constructed."
Um, okay. If you say so. Your statements likewise tell me that you do not understand the points I'm making. So there! ;D
The point is that 385,852 is how many trades (or net daily settlements with individual counterparties as you pointed out) are reflected in those aggregate numbers we see on the survey. Each trade (or net settlement) is presumably the result of some counterparty's independent decision(s) and subsequent action(s). So the coordination of actions essentially rests at the (resolution) level of the trade (net daily settlement per counterparty), which was, on average, around $40 million.
The point of running iterations at increasing levels of complexity (increasing numbers of presumably random trades/daily counterparties) was to show you that the more presumably random trades you aggregate, the lower the expected discrepancy (deviation) between purchases and sales after applying the statistical methodology of the survey.
As I showed, at 9 random trades, we found a 10% discrepancy between purchases and sales. But as we increase the number of random trades, we quickly drop toward zero. Even at 3,136 trades we were close to 1% discrepancy on average. In fact the largest discrepancy/deviation your model produced after 100 iterations was 2.96% and the standard deviation was 1.21%. This is compared to 4.35% in the actual survey.
Can you see a trend forming here?
9 trades – 10%
63 trades – 5.6%
126 trades – 2.7%
252 trades – 1.69%
3,136 trades – 1.21%
Does this next one fit the trend or stand out?
385,852 trades – 4.35%
There's a point here which you don't seem to understand.
The point of looking at it this way is to help us determine if the 4.35% discrepancy/deviation found in the actual survey is statistically significant or insignificant. Clearly it is significant, and therefore it requires an explanation beyond the "halving methodology" under which the survey was published. We are well past this point, but you don't seem to understand that, because you keep coming back to your model trying to tweak it, make it more complex, or reiterate it enough times to get an outcome so rare that it is more than three standard deviations, a 4.35% discrepancy. You'll probably have to run more than 1,000 iterations to get just one of those in your simple model with only 3,136 random trades.
As I say, each reporting LBMA member essentially conducted its own internal survey of, on average, apparently, 170 "trades" per day. If those trades were "random" (as in not coordinated/one-directional) then, looking at my "trend" above, we could probably expect random discrepancy/deviation between purchases and sales from each reporting member after applying the "halving methodology" of the survey on the order of about 2% in any given day. When we (as a BB conducting our own internal "survey") aggregate 63 presumably random days, we now have an aggregate of 10,710 data points. So, after applying the final survey methodology, we'd expect to see, on average, a deviation of below 1.21% between purchase and sales.
And then, as the LBMA aggregating these numbers from 36 separate reporting members, we would expect (presuming randomness/insignificance) a discrepancy of 1% or less given the aggregate number contains data points from 395,852 presumably random "trades" *after applying the "halving methodology"*.
If it's not 1% or less (which it wasn't), then there must be another explanation."
As I said, Bron, I thought we were well past this point and yet you keep coming back to your model to show how we can get to such a large discrepancy as we saw in the actual survey. Fine, you keep playing with your toy model and I'll keep pointing out that in every iteration where you show a high discrepancy between purchases and sales, there must be one of three explanations:
1. There must be a net flow of twice the magnitude of the discrepancybetween reporting and non-reporting members…
or
2. There must be a net-change in the volume of paper gold equal to or greater than the magnitude of the discrepancy during the reporting period…
or
3. A combination of the two.
You seem to be saying, "no, no, there must be another explanation. You just don't understand how complex these bullion banks are. I do, because I'm a bullion professional who has direct dealings with them, and believe me, they are complex!"
Fine. Let's see your alternative explanation. The only one I can infer so far from your comments is perhaps:
4. A reckless abandon when reporting numbers (i.e., bogus numbers) which would render the entire survey meaningless.
I suppose that is valid alternative explanation, but I thought we were working on the assumption that this is not the case. If so, I eagerly await your new, alternative explanation (as well as that sample iteration that doesn't produce a flow).
Bron Suchecki December 5, 2012 8:34 PM We've been over this in our previous email exchange.
I am not modelling 3,136 trades, which is the point you do not get. You cannot go any further in terms of data points. The "trend forming" was about getting more accurate models that reflects the survey, not about modelling more underlying trades.
It does not matter if we could construct a model with 300,000 underlying trades or 900,000 trades, they only aggregate up to a maximum of 3136 data points upon which the LBMA methodology is applied and that is as far as you can model.
What I am trying to do is to model various scenarios with those 3136 data points - eg
1) totally random, which my model is currently doing
2) asymmetric BBs, which I haven't even started to create scenarios for in my model
3) volume of client trading to BB trading, ie how much speculative trade do they do off client flow?
4) for the above, either zero net position, or some long or short position, for each BB
It is only by exploring these scenarios that we can determine how much the LBMA methodology may distort the underlying buy-sell difference reality.
Before I want to come to any conclusions about the results of the LBMA survey I want to understand how the methodology works. You don't to understand that we are not “well past this point” and I think we are talking at cross purposes.
“each reporting LBMA member essentially conducted its own internal survey” – just to check, when saying “survey” do you mean “sampled”?
“There must be a net flow of twice the magnitude of the discrepancy between reporting and non-reporting members” – I don’t think the maths of Client A to Non-Reporting to Reporting to Client B work out as simply as this when you are talking about 3136 interrelationships between 56 banks
BTW, I had far too little client volume vs BB-to-BB volume. Tweaking the model gives an average discrepancy of -0.15% with a standard deviation of 5.14% over 1000 iterations. While that could explain away the LBMA result, I will not accept it and continue to refine my understanding. You'll just have to wait for me to do that.
Sounds good, Bron! I think I've made my case for any prying eyes to decide for themselves and, like I said, I (we) eagerly await your studied conclusions and your Occam's-worthy explanation for the discrepancy between purchases and sales!