Capital Adequacy Calculator: Capital Over What, Exactly

A capital adequacy ratio measures an institution's own capital against its risk weighted assets, never against its total assets. Set the same Rs 24,000 crore over both denominators and the distance between them stops being a definition and becomes a number: the readings run from 8.33 to 40.00 per cent. The level the ratio must clear, and the weight applied to each asset, are set by the Reserve Bank of India.

Which components, which classes, and what does the division come to?

The panel opens on Suvarna Commercial Bank Limited, invented, at one stated date, and every figure in it is one a published statement could carry. Capital of Rs 24,000 crore goes in as a single component because that is how this record carries it, with the other two capital lines opening at nothing. Advances of Rs 1,44,000 crore, investments of Rs 60,000 crore and everything else on the deploying side at Rs 36,000 crore go in as three classes. Those three come to Rs 2,40,000 crore, and that total is the balance sheet figure the panel divides into rather than a fourth entered one. Neither invented lender carries a commitments schedule, so the commitments row opens at nothing.

Every weight row opens at one hundred, and that is the absence of a schedule rather than one of them: the weighted total comes back at Rs 2,40,000 crore, both readings land on 10.00 per cent, and what is on screen at that moment is capital over total assets wearing no other name. The panel says so on its own face. Advances carry 60.00 per cent of that weighted total, investments 25.00 per cent and everything else 15.00 per cent. Nothing has been restated yet, so the weighted shares repeat the shape of the balance sheet.

Moving the weight column puts the arithmetic on display. Set at one hundred, sixty and nothing across the three balance sheet classes, the weighted total falls to Rs 1,80,000 crore, so the reading rises to 13.33 per cent. Set instead at seventy five, ninety and fifty, a wholly different column, the weighted total is Rs 1,80,000 crore again and the reading is 13.33 per cent again. Two columns that agree about nothing produced one identical answer. A weighted ratio cannot be read backwards into the book that produced it.

Two more moves are worth making before any of this is explained. Commitments brought in at Rs 48,000 crore with every weight left where it opened take the weighted total to Rs 2,88,000 crore, above the balance sheet total; the reading falls to 8.33 per cent, and capital over total assets sits exactly where it always was at 10.00 per cent. With the commitments back at nothing and Rs 6,000 crore taken off capital instead, capital becomes Rs 18,000 crore and both readings fall together to 7.50 per cent. A movement on the asset side shifts one reading and a movement on the capital side shifts both. Watching which readings move is the quickest way to tell which side of the division something came from.

Consider a division already familiar. A shopkeeper keeps Rs 40,000/- of her own money in the till and in the shelves, and she has borrowed Rs 3,60,000/- more to fill those shelves. Asked what share of the shop is hers, she answers ten per cent without reaching for a calculator. The harder question is whether Rs 40,000/- is enough. Enough depends entirely on what is on the shelves. Rs 4,00,000/- of sealed rice sacks that will sell whatever happens is one situation. Rs 4,00,000/- of fresh flowers is another. The rupees on the shelves are identical in both. The chance of losing them is not remotely identical, and it is losses that her Rs 40,000/- has to absorb.

The rice and the flowers are the entire idea behind weighting a balance sheet before anything is divided by it. A capital ratio that treats rice and flowers as the same rupee has answered a question about size when the question asked was about exposure.

What does a capital adequacy ratio actually measure?

Capital on top. Risk weighted assets underneath. One stated date for both. A balance sheet is a position rather than a flow, and a ratio struck across two dates is not a ratio of anything. The question the arithmetic is asking is whether the institution's own money is large enough to absorb losses on the exposures it is presently carrying, once each class of those exposures has been restated by how much of a loss it is capable of producing.

The denominator is neither total assets nor the loan book, and quietly substituting either of those produces a figure that looks exactly like a capital adequacy ratio and is not one. This matters more than it sounds. Both substitutes are readily available. Total assets is printed on every balance sheet in existence, advances is printed right above it, and both of them will divide into a capital number perfectly happily and return something in the eight to twenty per cent region. Nothing about the output announces which denominator went in. The naming discipline around a capital adequacy ratio therefore has to be heavier than the arithmetic.

So the tool asks for three things and guesses none of them. The capital amount comes off the balance sheet. Total assets comes off the same balance sheet. The weighted figure comes off neither, for reasons taken up below.

Why are the assets weighted before anything is divided?

Because a rupee lent against a house that the lender can take and sell, and a rupee lent to somebody on nothing but a signature, are the same rupee on the balance sheet and are nowhere near the same exposure. Adding them up gives a size. Adding them up does not give a quantity of the losses capital exists to absorb. Weighting restates the balance sheet in units of exposure instead of units of rupees, and only after that restatement does dividing capital into it mean anything at all.

And the consequence shapes everything that follows: the weight attaching to each class of asset is set by the Reserve Bank of India at rbi.org.in, those weights are revised, and so a risk weighted asset figure cannot be derived from a balance sheet alone. The arithmetic is not hard. The schedule is simply not ours to write. The weighted figure is therefore an input on this calculator rather than an output of it, and the box for it below is drawn empty with an address inside it.

Where does the weighted figure come from, and what if the record has none?

An institution publishes its own risk weighted assets. The figure sits in its disclosureThe institution's own published statement of its position, put out on its own authority for anyone to read. A disclosure is where a reader goes for a figure the institution alone computes., which is the same place a profit figure or a provision figure comes from, and the figure is taken from there and entered. The whole answer is unglamorous: the figure is read, not built.

Now the awkward part. There is no risk weighted asset figure on record for Suvarna Commercial Bank Limited or for Rukmini Finance Limited. Both carry a full balance sheet and a full income statement, and neither carries a weighted total. Supplying one would have meant choosing a weight schedule and writing it into the example.

An invented lender can report its own ratio and nobody is harmed. A weighted total invented for it is different: it would carry a set of assumed weights inside it, and nothing on the face of the number would reveal that a schedule had been guessed at upstream. An invented weighted total would behave exactly like a disclosed one. An empty box is the better outcome, and the field is empty.

What does one unchanged capital amount read against different denominators?

Hold Suvarna Commercial Bank Limited's capital at Rs 24,000 crore and refuse to touch it. Now change only what sits underneath. Rs 24,000 crore divided by a balance sheet total of Rs 2,40,000 crore gives 10.00 per cent exactly. Set it over Rs 1,80,000 crore and the division yields 13.3333 per cent, whose two place print of 13.33 lands a shade under the true figure. Over Rs 1,20,000 crore it is 20.00 per cent exactly. Over Rs 60,000 crore it is 40.00 per cent exactly. One denominator sits above the balance sheet total: Rs 2,88,000 crore, reachable once commitments that never sat on the balance sheet at all are weighted in. The division yields 8.3333 per cent, whose two place print of 8.33 again lands a shade under it.

One unchanged Rs 24,000 crore produced readings from 8.33 to 40.00 per cent, and every bit of that travel belongs to the denominator. Read that list again with an eye on what stayed still. Not one rupee of capital was raised, spent, written off or revalued between the first reading and the last. The institution did not change. The only thing that changed was the question being asked of it.

Every figure in the first column except Rs 2,40,000 crore is an illustration chosen to make the movement legible, and none of them is anybody's weighted total. Say that out loud. A table of five denominators reads very easily as a range that real institutions occupy, and it is nothing of the kind. The five rows are the span this control can reach. The 8.33 per cent at the bottom is a floor on what the control can produce and not a floor on anything in the world; the 40.00 per cent at the top is a ceiling in exactly the same limited sense.

Why the calculator opens with both readings on the same number

Because there is no weighted figure to open it with. Set the weighted input equal to total assets, at Rs 2,40,000 crore, and both readings come out at 10.00 per cent with the two markers exactly on top of one another. One denominator can produce only one reading, so the coincidence says nothing about Suvarna Commercial Bank Limited. The alternative would have been a plausible second number invented to make the two markers separate.

Move the denominator and the two separate at once. Only then is one of them a capital adequacy ratio and the other a capital to total assets figure. At the opening position they are one division done twice under two names, which is precisely where one of those two names is being misapplied.

How are the capital share and the leverage multiple the same fact?

Suvarna Commercial Bank Limited holds capital worth 10.0 per cent of what sits on its balance sheet. The balance sheet runs at 10.0 times the capital. The share and the multiple are not two findings but one sentence written in two directions, and one hundred divided by either of them gives the other. At Rukmini Finance Limited, invented, capital is 20.0 per cent of assets under managementThe total book a lender runs, used the way total assets is used for a bank. Assets under management is the denominator that lender's own ratios are struck on. of Rs 18,000 crore, so assets are 5.0 times capital. Same inversion, a different position on the same curve.

The multiple is the leverage limb of the return decomposition. Holding more capital therefore moves an institution's return on equity directly and moves its return on assets not at all. The asset return divides profit by the book, and capital appears nowhere inside it. The multiple divides the book by capital, and capital is the only thing inside it. Raise capital without changing the profit or the book, and the first limb sits still while the second one shrinks.

The equality that was built on purpose, and the rounding that comes with it

Both lenders earn 9.38 per cent on equity. The match is not a coincidence and not a transcription slip. The equality was constructed, and it was constructed to be walked into: rank these two lenders on the equity return by itself and the ranking has nothing to say about either. Suvarna Commercial Bank Limited reaches it on 0.9375 per cent of assets, reported as 0.94, multiplied by assets at 10.0 times capital. Rukmini Finance Limited reaches it on 1.875 per cent of assets, reported as 1.88, multiplied by assets at 5.0 times capital. Each rupee on the bank's balance sheet earns it half what a rupee earns the finance company, the bank carries twice as many of those rupees per rupee of capital, and the two halves cancel into one identical answer.

Print the two limbs to two places and the multiplication stops closing: 0.94 taken ten times reaches 9.40, 1.88 taken five times reaches 9.40, and 9.38 is neither of them. Both printed asset returns were rounded upward. Take the exact limbs instead, 0.9375 per cent at 10.0 times capital and 1.875 per cent at 5.0 times capital, and both land on 9.375 per cent, whose own two place print of 9.38 sits a shade above it. The printed limbs give 9.40; the exact ones give the printed answer. The arithmetic has not gone wrong. A presentation showing 0.94, 10.0 times and 9.38 without this percentage pointThe unit a gap between two percentages is measured in. A move from 9.375 up to 9.40 covers 0.025 of one, a different quantity from 0.025 per cent of anything. of housekeeping would look as though it could not add up.

Who sets the minimum, and why is no figure for it given?

The values needed here and held by the regulator are these. How much capital a bank has to carry against its risk weighted assets. Every bufferAn amount required to be held above a stated minimum, so that touching it is a warning rather than a breach. The amount, and the conditions for each, are set by the authority that writes it. required above that minimum, together with the conditions for each. Which instruments count as capital at all, and in what order they absorb a loss. The weight applied to each class of asset. The leverage limit and the exposure measure it is struck on. A non-banking finance company's own requirement, and how it differs from a bank's. And how often the whole thing is reported, and the date it is struck at. Seven items, and every one of them belongs to the Reserve Bank of India at rbi.org.in.

The international standard these arrangements descend from comes from the Basel Committee at bis.org. Naming that origin is not the same as knowing what applies here. The rule that applies in India is the Reserve Bank of India's own implementation, and that implementation carries the actual figure.

A reference that prints a minimum is not merely stale the day it moves, it is wrong, and a reader who copied the number has no way of knowing which day that was. A site name behaves differently. A site name can go out of date too, but it goes out of date visibly: following it turns up something else. A number sitting in a working file gives no such signal at all. So the rows below are drawn, named and left empty, with the address inside them.

What does this calculator leave unstated?

Whether a ratio is enough is the minimum plus the buffers, and both of those belong to the Reserve Bank of India. Whether one institution is better capitalised than another is the same question wearing a comparison, so it has the same owner. Risk weighted assets are not derivable from anything on a balance sheet, for the reason worked through above. And one stated date at one invented lender supports no view about that lender.

Equal returns on equity were built into the two lenders on purpose. The two invented lenders carry the same return on equity, so neither way of running a lender comes out preferred here. Carrying more leverage is not recklessness, and earning a wider spread is not skill. Each is one invented institution in one year, with no downturn, no later year and no failure on record. One year settles nothing about what either approach is worth.