Manipulation of Balance Sheets may have its advantages if uncovered. Credit Rating Agencies use Balance Sheets to come up with their ratings (‘come up’ and not compute as ratings, according to CRAs are opinions) which means that cooked books can get you a better rating. Public companies manipulate their Balance Sheets to look good on the market and raise more cash. Private companies do it obtain better credit conditions from their banks. Sometimes, it is simply to hide theft.

The possibility of being able to uncover Balance Sheet manipulation is mouth-watering to say the least. The problem is that there is no single scientific way of producing a balance statement. Apart from the fact that a Balance Sheet should always balance, i.e assets must equal liabilities, we’re not talking of science here. This highly discretionary nature of the exercise is precisely what leaves the door open to fraud.

A solution exists. The way we do this is according to the following logic:

1. A given business (or business model) is based on a series of processes that possess structure (i.e the way information flows in the system).

2. This structure is reflected in its Balance Sheet (and in Cash Flow, Income Statement, Ratios, etc.) which too, has its own structure. Essentially, one structure is (implicitly) mapped onto another. The creation of Balance Sheets is done according to sets of rules, such as the International Accounting Standards (IAS).

3. The said Balance Sheet structure is reflected in our Complexity Maps which show the interdependencies between its entries. This is computed using a proprietary ‘generalized correlation’ algorithm.

4. When the underlying business model of a company changes, so do the processes as well as the topology of its Complexity Map. The same happens, however, if the Balance Sheet is manipulated with fraudulent intent.

5. Balance Sheet manipulation is typically an exercise of arithmetic and the fact that this manipulation alters the underlying correlation structure is often overlooked. Typically we’re looking at loss of structure due to ‘de-correlation’ between the entries of the Balance Sheet. If the person committing fraud changes the arithmetic but does not alter the structure of the underlying Complexity Map accordingly, then this will show up immediately and raise a red flag.

6. We use complexity of a Balance Sheet to infer if it falls into one of two classes: 1 – potentially genuine, 2 – potentially manipulated. We require the last 12 quarterly balance statements for the purpose.

Let us examine two very simple examples. The first Complexity Maps is that of a genuine Balance Sheet. Note the value of complexity (27.2 cbits) and a high resilience rating (4 stars)

The second one is of the same company but has been (severely) manipulated. Complexity now is 2.1 cbits. The density of the Balance Sheet Complexity Maps is now 26% (down from 69%). This means that there are significantly less interdependencies in the data. This points to the mentioned data ‘de-correlation’. What this means is that from an arithmetic point of view the Balance Sheet may still look good but manipulation has introduced disorder into the data. In fact, we had 810 rules, or interdependencies in the genuine balance statement, now there are only 165.

We now introduce the Balance Sheet Credibility Index, or BCI. The BCI is a function of the C/N ratio where C is the Balance Sheet complexity (measured in *complexity bits*, or cbits) and N is the number of entries in the Balance Sheet. In the case above N is 49. For the two cases in question, we have:

Genuine Balance Sheet: C/N=27.2/49=0.55, BCI=67%

Manipulated Balance Sheet: C/N=2.1/49=0.042; BCI=0.1%

The function BCI=*f*(C/N) is proprietary.

Even though the BCI is expressed in percentage terms on a scale from 0 to 100%, we feel it is sensible to split all cases in only two classes: potentially genuine (the BCI is high) and potentially manipulated Balance Sheets (the BCI is low), i.e. a green or red light. In addition, a further indication of manipulation may be given by a sudden and large decrease of the BCI.

What completes our BCI analysis is an indication of where the Balance Sheet has been potentially tweaked. In the case above we don’t go into the details but, examining the two Complexity Maps, this should be pretty evident.

This brings us again to the question of ratings. We compute (yes, compute) the so-called Resistance to Shock (RtS) Ratings, which too are based on Balance Sheets. Imagine the following four (extreme) cases:

- BCI is high, the RtS Rating is high – good
- BCI is high, the RtS Rating is low – this is bad
- BCI is low, the RtS Rating is high – this too is bad
- BCI is low, the RtS Rating is low – this is really bad

The picture below illustrates the above.

Basically you should stay away from the lower left hand-side quadrant.

Since both the BCI and the RtS Rating are expressed on a scale from 0 to 100%, they can be multiplied, producing an augmented RtS rating. This means that, for example an RtS rating of 90% and a BCI of 90%, yields an augmented RtS Rating of 81%.

Below are two examples of Complexity maps and BCIs of two banks. The first is a Chinese bank, the second one is from the EU.

The BCI in this case is 51%. Note how little structure there is in the map. This means that either many Balance Sheet entries haven’t been reported or that they vary so chaotically that they appear as independent. In the next case the situation changes substantially.

Here the BCI is 82%, a full 30% more.

The effects of Balance Sheet *manipulation-induced de-correlation* may also be appreciated by examining the *entropy-correlation landscape*, which illustrates in a 2D scatter plot all the possible Balance Sheet entry combinations and the corresponding entropy and generalized correlation. Those combinations which do not produce an interdependency are shown in purple, those that do are orange. The entropy-correlation landscape contains a wealth of information, the description of which is beyond the scope of this short blog. However, its shape is of great importance and reveals interesting properties of systems. An example of three landscapes is shown below.

The system on the left is one in which the Complexity Map is very sparse as the ratio of orange dots to the total number of dots (interdependencies) is very low. The situation changes in the case of the second landscape, where this ratio is close to 1/2. In the case on the right the situation is similar but the corresponding Complexity Map has certainly less variables than the one in the middle. It is easy to imagine why entropy-correlation landscapes can be very useful in performing Balance Sheet forensics.

Let’s also be clear on one thing. Messing with a Balance Sheet *can* give rise to new interdependencies in the map. However, unless manipulation is going on for many quarters, this is unlikely. More soon.

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