Bank Funding and Spread: The Margin and the Base It Sits On

This calculator takes two published interest lines, a set of balance sheet lines, and a base for each limb, and returns the difference between the two rates as a percentage of that base. The base is the whole exercise. The same Rs 7,440 crore left over reads 5.17, 3.65 or 3.10 per cent for the year depending on whether the divisor is advances, earning assets or total assets, and nothing but the divisor moved.

Every rupee amount divided below comes off one invented statement covering one stated year, and every percentage is worked from two of those amounts. Suvarna Commercial Bank Limited and Rukmini Finance Limited, both invented lenders, each carry one year on record, and one year is one observation rather than a direction of travel. The requirement rows further down carry the Reserve Bank of India as the authority that writes each of them, and each one moves.

Set as it arrives, the instrument reproduces the published year of Suvarna Commercial Bank Limited. Both sides of its sheet add to Rs 2,40,000 crore, so they agree, and on the funding side deposits are 80.00 per cent of the total, borrowings and other liabilities 10.00 per cent and own funds 10.00 per cent, three printed shares that come to 100.00. Both limbs sit on earning assets of Rs 2,04,000 crore: Rs 18,600 crore of interest earned is 9.12 per cent of that base for the year, Rs 11,160 crore of interest expended is 5.47 per cent of the same base, and 5.47 plus 3.65 comes back to 9.12, so the two printed parts add to the printed whole. The difference is 3.65 per cent of earning assets for the stated year, and that is the reading worked through by hand below.

Three moves take it away from there. Change the base under the cost limb to deposits and the panel says the subtraction has stopped being a spread: it prints 3.31 per cent against the correct 3.65 per cent of earning assets, and names the 0.34 point gap. Push interest expended up to Rs 18,600 crore and the difference goes to nil. Push it past that and it goes below nil, and the panel prints the shortfall with the word minus in front of it rather than a stray sign.

One sentence carries the whole subject, and it has nothing to do with banking. A rate is an amount divided by a base. Two rates can only be subtracted from one another when they were divided by the same base. Everything the calculator above does follows from that one line, and every wrong answer it can produce breaks it.

The rule is already believed in daily life. A household spends Rs 6,000/- on food in a month. Against a household income of Rs 30,000/- that is a fifth of everything coming in; against Rs 50,000/- it is twelve per cent. Only the thing the rupees were held up against moved, and a listener given one answer without the other has been told close to nothing. Put that same reader in front of a bank statement, where four large numbers sit a short distance from each other and nothing says which belongs underneath which.

A spread is a subtraction between two rates, so it is only a spread at all when both rates were struck on one named base. Say which base it sits on in the same breath as the number, or the calculation is not finished.

What does this calculator work out?

The calculator divides and subtracts, and it stops there. The calculator takes one published amount away from another, divides the result by a named base, and shows that same subtraction again as two rates struck on that base, so the difference can be seen rather than taken on trust. The arithmetic computes, and it assesses nothing. A division cannot supply a judgement and a subtraction cannot supply a comparison, so the answer carries neither.

Say it in the order the arithmetic happens. Interest comes in over a year and interest goes out over the same year. The difference is net interest incomeWhat is left when the interest paid out is taken away from the interest taken in, over one stated period. Net interest income is a rupee amount rather than a rate, so a base has to be chosen before it can be quoted as a percentage., a rupee amount for that year and not a rate at all. Turning it into a rate means dividing it by something, and the divisor is a decision the tool forces into the open.

What has to be entered, and where is each number found?

Four things the arithmetic needs, and the note against each says only where to look, never what it means. The instrument above asks for the balance sheet lines as well, and builds each candidate base from them rather than asking for a total.

The period is a field rather than a detail, because a rate with no period against it is not a rate. Three and a half per cent of what, over how long? A figure answering the first question and not the second can be quietly compared against a monthly figure by the next person who picks it up. The two interest lines and the period travel together off the same statement, so nobody has to reconcile two documents to fill this in.

Some things are not fields. There is nothing for what kind of lending produced the interest, nothing for the rate paid on any one class of funding, and nothing for the year before. The record carries one year for one institution and no split inside either interest line, so the tool asks only for what is printed.

Why is the base a field rather than a setting?

Because an ordinary bank balance sheet offers more than one candidate, all of them are used, and they are not degrees of accuracy about one question. Three sit on the asset side: advances of Rs 1,44,000 crore; advances plus investments, Rs 2,04,000 crore, the part that actually earns interest; and total assets of Rs 2,40,000 crore, the whole institution including the cash, the central bank balance and the premises, none of which earn a rupee. The funding side offers three of its own, and the instrument above lists all six.

The six bases are not refinements of one another. Each is a different question with its own correct answer. Dividing by advances asks how much is earned on what is lent. Dividing by everything that earns asks how much is earned on everything that earns. Dividing by total assets asks how much is earned on everything held, idle parts included. A reader who wanted the third and got the first did not get a rough answer, but the answer to a question they did not ask.

A base chosen by the tool would answer whichever question its builder had in mind and leave the reader no way of telling which of the six had been answered. So the base is named instead. Naming it makes the question explicit, and the printed answer carries its divisor beside it for the same reason.

What does one published statement look like when the base is moved three times?

Work it once, slowly, on Suvarna Commercial Bank Limited, dividing everything yourself rather than quoting a number somebody else divided. The bank reports interest earned of Rs 18,600 crore for the stated year and interest expended of Rs 11,160 crore for the same year, so Rs 7,440 crore is left. Its balance sheet shows advances of Rs 1,44,000 crore, investments of Rs 60,000 crore and total assets of Rs 2,40,000 crore, so the part that earns interest is Rs 2,04,000 crore.

Three readings, one numerator, and more than two percentage pointsThe unit for the distance between two percentages. Moving from 3.10 per cent to 3.65 per cent is a move of 0.55 percentage points, and calling it a move of 0.55 per cent means something else entirely. between the highest and the lowest, every one correct and every one answering a different question. Step 5 therefore does not read 3.65 per cent but 3.65 per cent of earning assets.

Now put both limbs on one base, the check that the tool is doing what it claims. Rs 18,600 crore over Rs 2,04,000 crore is 9.117647 per cent for the year, printing as 9.12, and Rs 11,160 crore over the same Rs 2,04,000 crore is 5.470588 per cent, printing as 5.47. One from the other leaves 3.647059 per cent, printing as 3.65 and matching step 5 to the last place. The subtraction lands exactly on the answer the division gave.

Where the record stops, and what can still be said

One thing this statement does not show, and it matters for what follows. The Rs 11,160 crore of interest expended is a single line, not split between what went to depositors and what went to anybody else. Worked down the funding side, there is somebody else: Rs 2,40,000 crore of total assets, less Rs 1,92,000 crore of deposits, less net worthThe shareholders' remainder once every claim on an institution has been settled against it. At a lender, it is the slice of the book paid for out of its own pocket instead of with borrowed money. of Rs 24,000 crore, leaves Rs 24,000 crore the record does not name. Nothing published names that Rs 24,000 crore of funding or says what it costs.

So the cost of deposits alone is not knowable from what is published here, and the honest form of the answer is a limit rather than a figure. Charging the entire Rs 11,160 crore to deposits gives 5.8125 per cent for the year, printing as 5.81. The 5.81 per cent is a ceiling, not a cost. Every rupee of that bill that went to the unnamed Rs 24,000 crore of funding is a rupee that was not paid to depositors, so the true deposit rate can only be lower. Nothing published says whether that funding pays interest at all, so how much lower is unknowable.

One end of a payment is half a payment, so turn the two lines around. The Rs 11,160 crore that left the bank arrived, to the rupee, with the people and the markets that funded it, and the Rs 18,600 crore that came in came, to the rupee, from the borrowers and the issuers who paid it. Both net to zero across the two parties, and neither party is at fault for the size of the number.

What comes out, and how is the bar read?

Two limbs stacked into one bar, the difference showing as the remainder on top: the dark part is the slice handed straight back to whoever supplied the funding, the bright part is what stayed. The bar sits on a scale fixed from 0 to 14 per cent that does not rescale itself, and that decision is the difference between a picture that teaches and a picture that lies politely. A bar drawn to its own maximum is always full, so each reading produces an identical bar and the reader concludes the base did not matter. With the scale nailed down, 5.17, 3.65 and 3.10 per cent sit visibly apart. The instrument above holds its scale still the same way, and says so on its face where an entered reading would run off it.

What goes wrong when the two limbs sit on different bases?

Mixed bases are the one wrong answer the tool can produce, and it is built to make that answer visible rather than hide it. Take the earned limb over one base and the cost limb over another, subtract, and what falls out belongs to neither. The figure that falls out is not an approximation. The figure is a quantity with no denominator at all.

Run it on the instrument above. The earned limb stays on earning assets at 9.117647 per cent. Strike the cost limb on deposits instead: Rs 11,160 crore over Rs 1,92,000 crore is 5.8125 per cent for the year, printing as 5.81. Subtract that from 9.117647 and 3.305147 per cent falls out, printing as 3.31. Beside the correct 3.647059 per cent of earning assets, the two are 0.341912 percentage points apart, printing as 0.34. In a quantity that ordinary movement shifts by hundredths, a third of a point is a long way.

The size of that error is not noise. The error is an exact quantity that can be computed in advance: the cost rate multiplied by the gap between the two bases, divided by the base that was kept. Earning assets exceed deposits by Rs 12,000 crore. Taking 5.8125 per cent of that Rs 12,000 crore and dividing by Rs 2,04,000 crore gives 0.341912 points with nothing left over. The same worked on the printed 5.81 gives 0.341765, and that also prints as 0.34 without being the same number. The identity holds on the unrounded 5.8125 per cent and only on it.

An error that can be worked out in advance is expensive rather than merely wrong. An error that wandered about would eventually stick out. The mixed base error is a fixed function of two balance sheet lines that barely move from one year to the next, so it returns next year at very nearly the same size, and a run of figures built this way looks consistent while being consistently wrong by a third of a point.

Does the same thing happen at a lender that takes no deposits?

The same failure appears in a different shape where there are no deposits at all, so the defect belongs to the arithmetic rather than to banking. Rukmini Finance Limited takes no deposits and borrows in the market instead. The finance company reports a yield of 14.50 per cent for the stated year on its Rs 18,000 crore book of assets under managementThe size of the book a lender or a manager is running, stated as one rupee total. Here it is what the finance company has lent out and holds., with a cost of 8.50 per cent for the same year on Rs 14,400 crore of borrowings.

Subtract the second from the first and 6.00 points fall out. Almost everybody stops there, and 6.00 points is not a margin on anything: it is a yield struck on Rs 18,000 crore set against a cost struck on Rs 14,400 crore, two bases Rs 3,600 crore apart. Put both limbs on the one base and the answer changes by well over a point. The Rs 1,224 crore the finance company actually paid, over that same Rs 18,000 crore book, is 6.80 per cent for the year, and 14.50 less 6.80 leaves 7.70 per cent of assets under management, or Rs 1,386 crore over Rs 18,000 crore.

The correction is the same subtraction in both institutions, and its size is what the lender funds with its own money rather than with somebody else's. The difference between 8.50 and 6.80 is 1.70 points, and that is exactly 8.50 per cent of the Rs 3,600 crore of net worth over the same Rs 18,000 crore. Every figure there is exact rather than a printed rounding, so the identity closes with nothing left over. The naive gap charged a market cost against every rupee of the book, including the rupees nobody lent it.

One more absence, and it changes what may be said. The record carries a single total for that Rs 18,000 crore book and no split inside it, so there is no second base here and the choice the bank faced cannot be posed. The 14.50 per cent yield is a floor rather than a fact about the earning part: if any of that book earns nothing, whatever does earn must yield more than 14.50 per cent for the year. How much more is not knowable from the record.

Who actually does this arithmetic, and when?

What does the output not show?

A great deal. The output does not show whether a spread is a good one. Judging a spread takes other lenders and other periods to set it against, and a single statement supplies neither.

The output does not show where a spread came from. A wide reading might come from lending to riskier borrowers, from funding cheaply, from holding a large book of securities, or from all three, and the two lines feeding it cannot tell them apart. A guess at the split would be inventing the most interesting part of the answer.

The output does not show what next year holds. One year is one observation. A path needs an earlier year and a later one, and one statement has only the year it covers. A figure computed correctly on a named base is a fact about one published statement, and every question beyond that needs something this tool does not have.

Who decides what a bank must publish?

Not the arithmetic above. Five requirements sit behind everything worked through so far, and every one belongs to the Reserve Bank of India: which lines a bank publishes, in what form and how often; the reserve and liquidity it maintains against its deposits; the capital and the buffers above it; how a loan rate must be benchmarkedTied to a reference rate published outside the lender, so the loan rate moves when the reference moves rather than when the lender decides it should.; and what it discloses about the rates it pays and charges.

Every one of those moves, so each row below carries the authority that sets it rather than a value. A value written in from memory keeps reading as complete for years after the requirement behind it moved. A row carrying an address instead is a form that can be completed from the authority itself on the morning the answer is needed.