# What makes banks fragile?

Deposit insurance has been in the spotlight, with the release of the recent report of the RBI working group on deposit insurance. There is now considerable agreement about three propositions: (a) The implicit, free guarantee that the government is now giving banks should be withdrawn, (b) This should be replaced by a formal deposit insurance to protect `small depositors', which is backed by an insurance premium that is sensitive to the probability of bankruptcy of the bank in question and (c) The deposit insurance corporation should trigger off closure of a bank, and supervise an orderly liquidation process.

We now ask the question: how large will this "risk--based insurance premium" prove to be? What drives the size of the insurance premium, and what kinds of values do we obtain under various assumptions?

```
Deposit Insurance Rates (% of assets)
--------------------------------------------------------
Equity (%)
--------------------------------
Daily Sigma (%)           10       8       5       2
--------------------------------------------------------
0.75                    0.0154  0.0469  0.1915  0.5898
1.0                     0.4325  0.6030  0.9509  1.4322
1.7                     2.4675  2.9071  3.6594  4.5273
--------------------------------------------------------
```

Economic theory gives us clear ideas about how to apply techniques of option pricing to compute deposit insurance rates. The calculation of the premium requires knowing (a) the true value of assets of the bank and (b) the true volatility of the assets. These are hard to measure in practice. However, a back--of--the--envelope calculation is feasible and highly revealing.

For this purpose, we look at a bank with 10% equity and 90% deposits. Reserve requirements imply that 35% of the assets of the bank are invested into government securities. If we assume that the remainder (65%) of the assets of the bank have a portfolio risk like the NSE-50 index, the volatility (sigma) of the banks' assets proves to be 1% per day. This gives us an annualised deposit insurance premium of 0.43%. A bank with Rs.100 crore in assets would have to pay an insurance premium of Rs.0.43 crore per year. For this bank, the subsidy that's implicit in the free insurance given by the government today, is worth roughly 0.4%.

We have assumed that 65% of the assets of the bank are as risky as a Nifty index fund. In practice, banks hold a complex portfolio of loans and securities. Many loans have a quasi-equity flavour in the character of their risks. Many a bank is not as well diversified as Nifty. Finally, bank portfolios are typically highly illiquid and non--transparent, in contrast with Nifty which enjoys very high levels of liquidity and perfect transparency. Hence, our assumption, that the risk of the bank portfolio is similar to that of Nifty, may place us in the correct ballpark. Calculations are also shown using a lower daily sigma of 0.75% for the purpose of comparison.

When we say that 10% of the bank assets are equity, we assume that this is in the true sense of the term: i.e. where all loans are valued at their secondary market prices. For example, a bank that started off with Rs.10 of equity and Rs.90 of deposits, that experienced Rs.5 of NPAs which are worth 0, is left with Rs.5 of equity and Rs.90 of deposits. This is equity of 5.3%: i.e. enormously greater leverage.

The insurance premium rises dramatically with leverage: to 0.6% (at 8% equity) to 0.95% (at 5% equity) to 1.43% (at 2% equity). The real problem with NPAs is that after they are written off, most banks are incredibly risky leveraged entities. When ICICI recently issued fresh equity, they were reducing their risk by deleveraging, which is an entirely sensible thing to do.

The complacence of the banking industry with leverage is in sharp contrast with the knowledge and healthy respect for leverage that is found in the securities industry. Derivatives are widely touted as "highly leveraged products", but the Nifty futures which will soon trade at NSE involve up--front cash collateral of 5-8% coupled with daily pay-in of losses. The derivatives industry views leverage with fear and respect, even though the futures clearing corporation is the most sophisticated and well-articulated risk management mechanism which deals with leverage. If we think that derivatives trading involves walking on the high wire, and that most banks are not equipped to walk on the high wire, then banks should be targeting equity capital of 30% to 50% of their total assets.

Deposit insurance is also a window through which we can understand debates about reserve requirements. When I first started thinking about Indian banking, I used to think of reserve requirements as a pure tax: an appropriation of bank assets by the State. However, reserve requirements also serve to reduce the risk of banks. The calculations above used a sigma of 1%, which is obtained by assuming 35% of assets invested in government securities and the remainder in Nifty. If, instead, all the assets of the bank were invested in Nifty, the sigma would rise to 1.7%, which gives us much higher risk and hence deposit insurance premia: to levels ranging from 2.47% (at 10% equity) to 4.53% (at 2% equity).

This illustrates the dilemma in reducing reserve requirements. On the one hand, the appropriation of resources by the State in this fashion should end. At the same time, we should recognise that this could (in general) lead to more fragile banks. If reserve requirements are reduced without first putting in a framework for orderly and routine bank closure, it could generate macro-economic disruptions either through disorderly bank failure or through expensive bank bailouts. Hence, the desirable sequencing is to first put a sound framework for deposit insurance and bank closure into place, and then remove reserve requirements.

How can we obtain better risk management at banks, so as to minimise these problems? The RBI has thus far tried to obtain improvements in the risk management of banks by fiat. While there is a strong role for prudential regulation in some aspects of risk management (e.g. market valuation of assets), the knowledge and culture of risk measurement and risk management cannot come out of regulatory fiat: it can only come from the pressures of competition.

An environment with deposit insurance (which charges higher premia to high-risk banks), a steady pace of bank closure (which generates exit), zero reserve requirements (which gives banks full freedom to do asset management) and a steady pace of entry of new banks would add up to strong competitive pressure. Banks who succeed in this would be most able to raise equity capital and hence grow; banks who are unable to persuade the equity market that they understand risk management would be unable to sell equity and their deposit growth would stall.

In summary, the most basic forces at work in India's banking system today are the extent to which NPAs and equity issuance determine leverage, the risk of the banks portfolio, the premia charged by the DIC, the process of bank closure, and the extent to which success in these factors makes possible the phaseout of reserve requirements. We are in for an exciting few years.

Back up to Ajay Shah's media page