Bank Margin and Deposit Mix: Work the Number Yourself

A bank's deposit mix decides what it pays for the money it takes in, and what margin is left over. At Suvarna Commercial Bank Limited, an invented lender, Rs 1,92,000 crore of deposits sits 42.0 per cent in current and savings accounts, and the margin for the year reads 3.65 per cent struck on Rs 2,04,000 crore of earning assets. Moving that share while holding both deposit rates still redraws the interest bill, the net interest income and the margin.

What does a bank's own deposit mix cost it?

The fields open on Suvarna Commercial Bank Limited's stated year, so a complete worked example is running before anything is changed. Deposits of Rs 1,92,000 crore sit 42.0 per cent in current and savings accounts. The split is Rs 80,640 crore of cheap balances and Rs 1,11,360 crore of term deposits. At 4.00 per cent a year the cheap pool costs Rs 3,225.60 crore and at 7.125 per cent a year the term pool costs Rs 7,934.40 crore, and the two add to Rs 11,160 crore, the interest expended the bank reported. On the earning side, advances of Rs 1,44,000 crore at 9.50 per cent a year earn Rs 13,680 crore and investments of Rs 60,000 crore at 8.20 per cent a year earn Rs 4,920 crore, and those two add to the Rs 18,600 crore of interest earned the bank reported. Both sides close on a total the bank published. Closing on those two totals is the one thing the opening state had to do. Net interest income is Rs 7,440 crore, the margin is 3.65 per cent on earning assets of Rs 2,04,000 crore, and the yield on those same earning assets is 9.12 per cent.

Not one of those four rates was read off anything. Each was solved backwards so that its own side would add to the single total the bank published, and the instrument will do that solving again on whatever figures it is given. Solving the two rates backwards once shows what a reported bill does and does not pin down. Drop the rate on cheap balances to 2.00 per cent and solve again: the term rate becomes 8.573276 per cent a year, the bill is still Rs 11,160 crore, and the margin is still 3.65 per cent. The reported year has not moved at all. The story the rates tell has moved. At the opening pair, a point of deposit mix was worth Rs 60 crore for the year; at this pair it is worth Rs 126.21 crore, more than double, on figures that reconcile exactly as well. The reported bill pins the pair down together, never either rate on its own, and any pair that adds up is as defensible as the pair this calculator opens with.

The last button does the same to the other assumption, the one about who paid the bill. Cost Rs 10,000 crore of the funding outside deposits at 6.00 per cent a year and Rs 600 crore of the bill goes there, so the deposit base is left carrying Rs 10,560 crore, the term rate solves to 6.586207 per cent, and the implied cost of the deposit base falls from 5.8125 per cent to 5.50 per cent. Reattributing a bill between funding lines changes who is said to have paid it and never how much was paid, so the margin does not move by a hundredth. Suvarna's record shows no such funding line. The field therefore opens at zero, and the button asks what would follow rather than claiming anything is there. Moving the bill between funding lines is also the quickest way to see that the computed cost of the deposit base is a ceiling and not a measurement.

What does this calculator compute?

Here is what makes that possible. Interest expendedThe reported line for everything a bank paid on the money it took in over the period, added together as one figure. is not one rate applied to one pool of money. Interest expended is the sum of what each kind of deposit costs multiplied by how much of that kind there is. Change the proportions without touching either rate and the total still moves. Weights are the whole idea, and the arithmetic below works them on Suvarna Commercial Bank Limited, whose reported year the computation reproduces exactly.

Think of a tea stall that buys milk from two suppliers, one at a lower price for the bulk it collects itself and one at a higher price for what gets delivered. Neither supplier changes its price all year. The stall still ends the year with a different milk bill depending on how much it collected and how much it had delivered. A bank's interest bill works the same way, and the two suppliers are the two kinds of deposit account.

The calculator computes four figures in a chain, all of them for the same stated year, all of them from Suvarna Commercial Bank Limited's own reported numbers plus two declared assumptions. The chain runs: split the deposits into two pools by the share held in current and savings accounts, cost each pool at its own rate to get the interest bill, subtract that bill from interest earned to get net interest income, then divide by earning assetsA bank's advances plus its investments, the assets that actually produce interest, as against total assets which include buildings, cash and everything else. to get the margin. Every step is a single line of arithmetic a reader could do on paper, and the whole point of running it is to see which step the deposit mix is actually touching.

The answer to that last question is one step and one step only. The deposit mix touches the interest bill. The mix does not touch interest earned, it does not touch earning assets, and it does not touch either rate. Everything that moves here moves because one number underneath it moved.

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

Five inputs, and four of them have an address. Total deposits sit on the liabilities side of the balance sheet. The share of those deposits held in current and savings accounts sits in the bank's own reported deposit composition. AdvancesThe banking word for the loans a bank has made and still holds on its books, shown on the assets side of its balance sheet. and investments both sit on the assets side, and adding them gives the base this computation strikes its margin on. Interest earned for the year sits in the income statement, one line above the bill. A field note says where a number is found and nothing about what it means, and the discipline matters because a reader who knows where to look can repeat this on any bank's reported figures without being taught anything further.

The fifth input has no address at all. To split the interest bill between the two kinds of account, this computation needs what the bank paid on each kind separately, and a bank reports one interest expended figure for the period. There is no line to look up.

Where do the two deposit rates come from, if a bank does not report them?

Both rates come from this computation, and both are labelled as assumptions everywhere they appear. The two rates are 4.00 per cent a year on current and savings balances and 7.125 per cent a year on term depositsMoney placed for a fixed number of days or years at a rate agreed when it goes in, as against balances the depositor can draw on any working day.. Neither rate was read off anything: both were solved backwards so that the two pools, costed separately and added, come to exactly the Rs 11,160 crore of interest expended Suvarna Commercial Bank Limited reported for the year.

The odd precision of 7.125 is the tell, and it is worth sitting with. Rates a bank actually quotes land on halves and quarters. A rate carried to three decimal places is almost always a rate that was solved rather than quoted. Here it is exactly that: fix the cheap rate at 4.00 per cent, cost the cheap pool, take the answer away from the reported bill, divide what is left by the term pool, and 7.125 per cent a year is what falls out. Only the combination of the two rates is pinned down by the one figure the bank actually published, so changing the cheap rate would move the term rate to compensate.

How does the deposit mix reach the interest bill?

Start from the deposit base at Suvarna Commercial Bank Limited, Rs 1,92,000 crore for the stated year. At the reported share of 42.0 per cent, current and savings balances are Rs 80,640 crore and term deposits are Rs 1,11,360 crore. At the assumed 4.00 per cent a year the cheap pool costs Rs 3,225.60 crore. At the assumed 7.125 per cent a year the term pool costs Rs 7,934.40 crore. The two pool costs add to Rs 11,160 crore, the interest expended the bank reported for the year, to the rupee. Interest earned of Rs 18,600 crore less Rs 11,160 crore leaves net interest income of Rs 7,440 crore, and that is a margin of 3.65 per cent for the year struck on Rs 2,04,000 crore of earning assets.

Now run the same four steps at two other mixes and nothing else changes. Lift the cheap share to 60.0 per cent and the bill for the year falls to Rs 10,080 crore, net interest income rises to Rs 8,520 crore, and 4.18 per cent is the margin, on the Rs 2,04,000 crore earning base, in that same year. Drop the cheap share to 30.0 per cent and the bill rises to Rs 11,880 crore, net interest income falls to Rs 6,720 crore, and and 3.29 per cent is what the margin prints, on that same base and in that same year. Thirty points of deposit mix moved net interest income by Rs 1,800 crore. On earning assets of Rs 2,04,000 crore that is 0.88 percentage pointsThe difference between two percentages. A move from 42.0 per cent to 43.0 per cent is one percentage point, which is a different thing from a one per cent increase. of margin, and not one rate anywhere in the bank changed to do it. The rupee difference is divided rather than subtracting the two rounded margins. Each printed margin is rounded to a hundredth, and subtracting the two would give 0.89.

A smaller version of that arithmetic is worth carrying away, and it is the one a reader can do in their head. One percentage point of the deposit base is Rs 1,920 crore. Shifting that Rs 1,920 crore from the term pool to the cheap pool saves the difference between the two assumed rates, 3.125 percentage points. Rs 1,920 crore multiplied by 3.125 per cent is Rs 60 crore off the interest bill for the year. Set Rs 60 crore against the Rs 2,04,000 crore earning base and it is a shade under 3 basis pointsOne hundredth of a percentage point. Rates and margins move in small enough steps that a whole percentage point is often too blunt a unit to talk in. of margin. So the reader now has a rule of thumb for this bank at these assumed rates: a point of mix is worth Rs 60 crore and about 2.94 basis points for the year.

What does the output actually show?

Two pictures move together, and the second one is the one to watch. The share is the input, and the deposit bar re-proportions between the cheap block and the term block as that share moves. The income bar holds interest earned at Rs 18,600 crore for the year as a fixed height, with the interest bill eating into it from below, and what survives at the top is net interest income. The top edge of the income bar never moves. Everything the reader sees happening to the margin is happening on the funding side and nowhere else.

Plot the margin against the mix and the shape is a straight line. The straightness is worth knowing, and it says something about the model rather than about banking. The line is straight because both rates are held fixed and only the weights move, so the bill is a weighted average of two constants. Between a cheap share of 30.0 per cent and one of 60.0 per cent the margin on earning assets runs from 3.29 per cent to 4.18 per cent for the year, and it passes through exactly 4.00 per cent at a cheap share of 54.0 per cent.

What does this calculator assume that a real disclosure would not?

Three assumptions, and each one is doing real work. First, the Rs 18,600 crore earned is nailed down for the whole year. Nailing it down assumes a bank can change what it pays for its funding without touching what it lends at or how much it lends. In an actual year those move together and often in the same direction. Second, both rates are held fixed while the mix moves, when in practice a bank chasing more current and savings balances is usually paying for them somehow. Third, the whole interest bill is loaded onto the deposit base.

The third assumption is the one a reader is least likely to notice, so it deserves a sentence of its own. The whole of Suvarna Commercial Bank Limited comes to Rs 2,40,000 crore of assets. Set the deposit base of Rs 1,92,000 crore beside net worth of Rs 24,000 crore and the pair still falls short of that total, so there is funding on the balance sheet which is neither of them. The record for this bank does not break that funding down and does not split interest expended across it. Part of the bill this computation divides by deposits was not paid on deposits at all, so the implied cost of the deposit base it produces is a ceiling rather than a measurement. A line invented to fill that gap would produce a number that wears the same clothes as a reported one.

What can this computation not tell?

The computation cannot say what a bank should pay a depositor, what mix a bank should hold, or whether one bank's mix reads better than another's. A cash reserve requirementThe idea that a bank must keep a share of what it takes in as deposits with the central bank rather than lending it out. The share itself is set by the regulator and moves. and a statutory liquidity requirementThe idea that a bank must hold a share of its deposit base in a specified class of assets. Which assets and what share are set by the regulator and move. each take a bite out of the deposit base before any of it is lent, and both belong to the Reserve Bank of India. The computation cannot say how much of that base is actually available to lend. A figure written down from memory does a reader more harm than an empty box ever does, so where a requirement decides the answer, the row below is drawn, named and then deliberately left blank.

A printed requirement stops being merely out of date on the morning the requirement moves. The printed figure becomes incorrect, and a reader who copied it carries the error much further than the original will ever travel. The form below is the useful version: a blank the reader can fill from the source, and it cannot go wrong on its own.

There is a second limit, and it is about what is simply not here. One bank, one year, and nothing underneath either of them. Which industries the lending went to, how much of it comes due inside twelve months, what was rescheduled or given up on during the year, how many counters the bank runs: none of that is here. A manufactured line looks exactly as convincing on a screen as a reported one, so where a figure was never published, saying so is the whole of the correct move.