Risk Adjusted Return: Return Measured Against Capital Held

A risk adjusted return is income less an expected loss charge, divided by capital. The adjustment recognises that income earned by taking more risk is not worth the same as income earned by taking less. At Vindhya Commercial Bank Limited, invented, one numerator of Rs 2,232 crore over four different capital bases gives four answers between 3.72 and 33.8 per cent.

The spread between those two answers is faintly unsettling. One bank, one year, one set of books, one arithmetic operation performed correctly every time, and the answer comes out anywhere between 3.72 per cent and 33.8 per cent depending on which figure the person doing the dividing reached for. Nobody has made a mistake. Nobody has been dishonest. The measure simply has more than one lawful form, and the person quoting it did not say which one they built.

What is a risk adjusted return actually adjusting for?

The mechanism is easier to feel at the scale of a street than at Rs 96,000 crore. Consider two shopkeepers on the same street. One sells rice and lentils for cash, takes no credit, and clears Rs 40,000 a month. The other sells the same goods but lets half the neighbourhood buy on account, and clears Rs 60,000 a month. On the month's takings the second shopkeeper is winning by half. But some of those accounts will never be collected. The second shopkeeper has been selling on account for eleven years and knows roughly how many. Subtract that, and the two are much closer. A risk adjusted return is nothing more sophisticated than that subtraction, done deliberately and written down.

A risk adjusted returnIncome less a charge for expected losses, divided by capital, so that income earned by taking more risk is not treated as equal to income earned by taking less. therefore does two things at once, and they are usually described as one. First it takes something off the income for the losses the risk is expected to produce. Second it divides what is left by the capital that had to be held to run the position at all. The first step deals with the fact that risky income is worth less than safe income of the same size. The second deals with the fact that risky business consumes more of the institution's own money before it can be written, so two activities earning the same rupees are not equally attractive if one of them ties up twice the capital.

Vindhya Commercial Bank Limited, invented, supplies the arithmetic from here on. Every figure below is that bank's own working number and none of them is a requirement placed on it by anybody. The bank earned net interest income of Rs 2,880 crore over twelve numbered months, and month 12 is the reporting date. The numerator starts at that Rs 2,880 crore, and almost immediately the choices begin.

What goes into the numerator, and what is a loss charge?

The numerator is income less a charge for losses. The word that does the work there is charge, and a charge is not a loss that has happened. The charge is a subtraction made in advance for losses the institution believes the position will produce, on average, before anybody knows which particular borrower will fail. The advance subtraction is an expected loss chargeThe loss the institution own model says an exposure will produce on average, subtracted before the return is computed rather than after a default occurs., and subtracting it is the single idea that separates a risk adjusted return from an ordinary one.

Why subtract something that has not happened? Because the alternative subtracts nothing until it does, and by then the comparison being attempted is years out of date. The shopkeeper again. If the bad accounts are left until they are formally written off, the month in which they are written off looks terrible and every month before it looked wonderful, and neither picture said anything useful about how the business was actually being run. Subtracting an expected loss moves the cost of the risk into the same period as the income the risk earned. No other arrangement allows the two to be compared at all.

The expected loss is a modelled number. Somebody built the model, somebody chose its assumptions, and somebody else may have chosen differently. So the numerator is not read off the accounts. The numerator is assembled, and the assembly is visible to the person doing it and invisible to everybody who receives the answer.

Which of this bank's three loss numbers is subtracted?

Vindhya Commercial Bank Limited carries three separate loss figures for the same twelve months, and this is not disorder. Each of them answers a genuinely different question, and each of them is defensible.

The first is what its own credit model expects. Run grade by grade across the performing book, the model produces an expected loss of Rs 343.6 crore. The second is the same computation restated. The model assumes it will lose 40.0 per cent of an exposure when a borrower defaults, but the bank actually holds provision coverage of 68.0 per cent against the exposures that have already defaulted. The 40.0 per cent assumption and the 68.0 per cent coverage have never been reconciled with each other, and neither of them is wrong. Run the same grade by grade sum at the coverage the bank actually provides and it asks for Rs 584.1 crore. The third is the plainest of the three: the credit costThe charge an institution actually took to its income statement for the year, which is a different number from what its model expects to lose. the bank charged to its income statement for the year, Rs 648 crore.

None of the three is the true one. Subtracting the model figure gives a forward looking number, one that says what this book should cost to run. Subtracting the restatement gives the same forward looking number at the bank's own harsher assumption. Subtracting the charged figure gives a number that ties, rupee for rupee, to the year that was actually reported. All three are honest, and the difference between the largest and the smallest is Rs 304.4 crore of numerator, produced by nothing except which figure somebody reached for.

What goes into the denominator, and why is there more than one?

Now the other half, and it is where the spread really opens. The denominator is capital, and this bank has four figures that a reasonable person would call capital. The four are not competing versions of one quantity. Each is a different object, and the four happen to sit in the same part of the balance sheet.

Tier 1 capitalThe strongest layer of an institution capital, being the part that absorbs losses first and while the institution is still running. is Rs 6,600 crore at month 12. Tier 1 is the strongest layer, the part that takes losses first while the institution is still trading. Total capitalTier 1 capital plus the additional layers an institution counts, being a larger denominator and therefore a smaller answer. is Rs 9,000 crore, being tier 1 plus the Rs 2,400 crore of subordinated bonds the bank counts in its second layer. Equity, the accounting figure, is Rs 7,680 crore, being share capital of Rs 1,200 crore plus reserves and surplus of Rs 6,480 crore. And risk weighted assetsExposures scaled by risk weights, used as a denominator when comparing activities that carry different amounts of risk for the same rupees. are Rs 60,000 crore, being the bank own scaling of its exposures by how risky each is, made up of Rs 50,400 crore for credit risk, Rs 4,800 crore for market risk and Rs 4,800 crore for operational risk.

The last of those four is a different kind of animal from the first three, and it is worth saying why. Tier 1, total capital and equity are all amounts of money somebody put in or the institution retained. Risk weighted assets are not money at all; they are a measure of how much risk is being carried. Dividing by them asks what the bank earns for the risk it takes. Dividing by the other three asks what it earns for the money its providers left in. Earning for risk and earning for money are two different questions, and the fact that both are called a risk adjusted return is exactly why the figure travels so badly.

What do the four answers actually come out at?

Take the charged credit cost, the one figure that ties to the reported year, and build the numerator once: Rs 2,880 crore less Rs 648 crore is Rs 2,232 crore. Now divide it four times. Over tier 1 capital of Rs 6,600 crore, 33.8 per cent. Over total capital of Rs 9,000 crore, 24.8 per cent. Over equity of Rs 7,680 crore, 29.1 per cent. Over risk weighted assets of Rs 60,000 crore, 3.72 per cent.

One numerator, four answers, from 3.72 to 33.8 per cent, and every single one of them is correctly computed from the same set of books. The largest is 9.09 times the smallest, and it is 9.09 times for the plainest reason available: Rs 60,000 crore is 9.09 times Rs 6,600 crore. Nothing subtle is happening. The information is entirely in the denominator baseWhich capital figure the return is divided by, without which a percentage cannot be interpreted or compared with anything., and a percentage quoted without it has told the listener almost nothing.

There is one more thing the arithmetic throws up here, and it is a small trap rather than a large one. The bank sets its own internal floor for its total capital ratio at 11.0 per cent, and 11.0 per cent of Rs 60,000 crore of risk weighted assets is Rs 6,600 crore. Tier 1 capital is also Rs 6,600 crore. Two entirely different objects, an amount the bank holds and an amount its own policy asks it to hold, wearing the same figure. Nothing connects them except arithmetic, and setting them side by side without saying which is which invites a reader to supply a relationship that was never there.

What is the measure actually for?

If the level moves this much on choices nobody sees, what survives? The answer is that a risk adjusted return is a comparison measureA number whose value lies in the difference between two of it, computed the same way, rather than in its own level. and not a level. Its whole value is in the difference between two of them built identically.

Computed the same way for the wholesale lending business and for the retail deposit franchise, it says which of the two earns more for the capital it consumes. Computed the same way for this year and last, it says whether the institution got better or worse at converting capital into income after paying for the risk. Computed once, in isolation, and put on a slide as a percentage, it is a number that cannot be checked, cannot be compared and cannot be argued with. Producing nothing at all would have left the reader better off.

The level of a risk adjusted return is a statement about the person who built it. The difference between two of them is a statement about the business. The discipline the measure demands is therefore not really arithmetic. Everything hard about it lies in holding both halves still, so that the quantity under comparison is the only one that moves.

What does the whole relationship look like when the loss charge moves?

Hold the denominator at tier 1 capital of Rs 6,600 crore and move the numerator instead, and the shape is the least surprising one in finance: a straight falling line. The denominator never moves, so every extra rupee of loss charge takes exactly the same fraction off the answer, and the line has to come out straight. Rs 66 crore of extra loss charge takes exactly one percentage point off the tier 1 basis, every time, anywhere on the line.

Reading across it shows where the bank's own three figures land, and where its severe scenario lands. At no loss charge at all the answer is 43.6 per cent. At the model Rs 343.6 crore it is 38.4 per cent. At the Rs 584.1 crore restatement it is 34.8 per cent. At the charged Rs 648 crore it is 33.8 per cent. And under the bank's own severe scenario ST3, at a credit cost of Rs 1,944 crore, it is 14.2 per cent. A severe scenario cuts this measure by more than half without a single capital figure moving, and the sensitivity in the fraction therefore lives entirely in the numerator.

The solved table, for a reader who never touches the control

Every figure in that table is in per cent, every one is correctly computed, and the twenty of them describe one bank in one year. The shaded row is the worked default the control opens on.

Where does this return fall to fifteen per cent, and what does it land on?

Solve the line backwards. The tier 1 basis reaches 15.0 per cent when the numerator is 15.0 per cent of Rs 6,600 crore, or exactly Rs 990 crore. Getting there needs a loss charge of Rs 2,880 crore less Rs 990 crore, being Rs 1,890 crore. The crossing is clean, and it lands on two figures that already mean something else in this same bank.

Rs 990 crore is the cap on limit L8, the bank sensitivity limit on the economic value of its equity. Here it is a numerator that fell out of a subtraction. And 15.0 per cent is the bank total capital ratio at month 12. Here it is a return. A third collision waits one column across: the same Rs 990 crore over total capital of Rs 9,000 crore is 11.0 per cent, and 11.0 per cent is the bank own internal total capital floor. None of the three collisions means anything whatsoever. An unlabelled one is dangerous for precisely that reason: a reader will hunt for the connection and eventually supply one.

What is missing from the numerator, and what does that forbid?

What has to travel with the number for it to mean anything?

Four things, and all four fit on one line. The numerator, stated as the arithmetic rather than the label. The denominator, stated as a figure and a name. The period. And what has been excluded. Written out, that is: two thousand eight hundred and eighty less six hundred and forty eight, over six thousand six hundred, for twelve months, excluding operating expenses, fee income and tax. In figures that is 2,880 less 648 over 6,600, and anybody in the room can check it against the accounts in about four minutes.

Writing only 33.8 per cent produces a figure nobody in the room can check, disagree with usefully or reproduce next quarter. The difference between those two sentences is not rigour for its own sake. One number survives being moved between two meetings and the other quietly changes meaning on the way.

Who actually picks this figure up, and what do they do with it?

Four people read a risk adjusted return, and none of them reads it the way the person who built it expects.

A business head inside the institution reads it against the same measure for another business. Manjari Sondhi, who runs the wholesale book, cares whether her portfolio earns more or less for the capital it consumes than the retail book does, and she does not care at all about the level. Her only real question is whether the two were computed the same way, and if the retail figure divides by risk weighted assets while hers divides by tier 1, the comparison is worthless and no amount of care about the arithmetic rescues it.

A credit analyst at another institution, sizing up Vindhya Commercial Bank Limited as a counterparty, reads it for the trend and for what it excludes. The excluded line tells her what the figure has been built to flatter, so she has learned to read it before the number. A numerator with no operating expense in it is not dishonest, but it is not a profit measure and she will not put it beside one.

An investor is the reader most likely to mistake a risk adjusted return for a return on equity, and the harm concentrates there. Twenty nine point one per cent on equity of Rs 7,680 crore looks exactly like the sort of figure that belongs on a comparison table, and it does not belong there at all.

The mechanism does not change with scale, so there is a household version too. A person deciding whether to keep money in a recurring deposit or lend it to a cousin who runs a hardware shop is doing the same computation. The deposit pays what it pays. The cousin pays more, and some fraction of the time the cousin pays nothing. Subtracting the expected shortfall before comparing, and naming what was subtracted, builds a risk adjusted return at the scale of one household savings decision. The bank version has more zeroes and exactly the same three moving parts.

Where do the capital figures come from?

Every figure in the arithmetic above is the invented bank own computation. A real one would be read from the documents named below, and the capital figures are the only part of the measure any external body touches.