# RDP 9302: A Decade of Australian Banking Risk: Evidence from Share Prices 4. Data, Assumptions and Methods

## 4.1 Data

Our sample is comprised of eleven banks that were listed on the Australian Stock Exchange between January 1983 and March 1992. This includes the three major private banks and, from September 1991, the Commonwealth Bank. The banks included in our sample account for about 55 percent (80 percent following the inclusion of the Commonwealth Bank) of all deposits repayable in Australia. This group of banks does not, however, include the state banks which have been most troubled in recent times. The remainder of the banks omitted from our sample are primarily wholly owned subsidiaries of foreign banks. For more details see the Data Appendix.

## 4.2 The Value of a Banking Licence

The value of a banking licence is likely to be seen in non market interest rate spreads. On the liability side a bank licence may enable banks to set a rate on their liabilities which is less than the rate on government securities. Similarly, on the asset side, the licence may allow banks to earn a rate of return on bank loans in excess of the rate required on the open market for securities of comparable risk. Using an alternative formulation of the contingent claim model presented in equation (5), Levonian (1991b) demonstrates that the licence value can be approximated by

where Δ is the loan spread – the rate of return on loans held by the bank minus the required rate of return for assets with the same level of risk, rf is the rate on government securities, rd is the average cost of banks' liabilities, and k denotes the capital ratio.

The spread rf − rd was proxied by the difference between the rate on 26-week Treasury Notes and a measure of banks' weighted average cost of funds (see the Data Appendix). Investigation of a number of loan spreads leads us to postulate that Δ is about 0.015 to 0.02 on average. Combining the interest spreads with values of k between 2 and 12 percent produces estimates of ϕ in the range of 0.05 and 0.06. Since substantial approximation error is likely these estimates should be taken only as a rough guide of the licence value ratio. Although not strictly comparable, this is somewhat higher than the range of licence value ratios calculated for US banks by Levonian (1991b).

While the model assumes that the licence value is constant over time, it may be expected that the process of deregulation, in particular the entry of new banks into the Australian market, would have eroded bank licence values in the face of increased competition. Consistent with this the cost of funds spread exhibits a negative trend. However, it has been observed that the spread between the loan rate and other rates has increased over the past few years (such spreads do not include risk premia, which make interpretation of these spreads as a reflection of licence value difficult). These trends in interest rates coincided with a downward trend in operating costs which may have stemmed the erosion of banks' licence value in the face of deregulation. Thus it is likely that in total licence value has not exhibited any significant trend during the 1980s.

Given the differences in size, geographical location and business strategies across the banks in our sample it is likely that there are, in fact, interbank differences in ϕ. However, it is not possible to measure ϕ for each individual bank with the data available. Hence the licence value ratio is assumed to be identical across all banks in the sample.

## 4.3 The Closure Threshold

Solutions for the system of equations could not be obtained for some banks at closure thresholds above −0.02. This suggests that closure thresholds greater than −0.02 are not consistent with the data; that is, stock market participants regard bank closure as being extremely unlikely at any positive level of capital or even at small negative values of capital. This suggests that c = −0.02 should be considered a maximum value for the assumed closure threshold.

Levonian (1991a and 1991b) argues that a lower bound on c exists, related to the licence value ratio. Levonian notes that the value ET realised by shareholders in (2) can never be negative, since they can always exercise their right as corporate owners with limited liability to walk away from a losing proposition. Thus it must be true that banks are closed at capital ratios above the level at which the licence value would be completely offset by negative net worth; that is, at the closure point k=c, it must also be true that A−B+ϕB ≥ 0. Rewriting this restriction using the definition of the capital ratio, the closure threshold must satisfy c ≥ −ϕ/(1−ϕ). If the closure threshold were set lower, banking supervisors or the deposit guarantor would be forced to inject funds to induce banks with c < k < −ϕ/(1−ϕ) not to close voluntarily. The injection would have to be large enough to bring the capital ratio back up to the minimum level of −ϕ/(1−ϕ).

Licence values in the range of 0.05 to 0.06 imply a minimum closure threshold of about −0.06. Consistent with this, analysis of the final annual report of the State Bank of Victoria gives a capital-asset ratio of about −0.06 when considering the State Bank group as a whole (0.02 for the State Bank alone) in the absence of government assistance.

## 4.4 Estimation

In the light of the previous discussion of the licence value and closure threshold four cases are considered:

Early Closure Late Closure Case 1 c = −0.02, ϕ = 0.05 Case 2 c = −0.05, ϕ = 0.05 Case 3 c = −0.05, ϕ = 0.06 Case 4 c = −0.06, ϕ = 0.06

In case 1 the banking licence value is low, and a bank is closed when it is insolvent as judged by market value, that is, when the market value of the bank's assets falls below the book value of its liabilities, but the value of the banking licence has not been exhausted. In case 2 the banking licence value is also low, and banks are closed when their licence value has been exhausted, that is, when the market value of the bank's assets falls below liabilities by an amount equal to the value of the banking licence. The banking licence value is relatively high, and banks are closed before their licence value has been exhausted in case 3. Finally, for case 4 the banking licence value is high, and banks are closed when their licence value has been exhausted.

In each of these cases the monitoring interval is set equal to one year. The market value of bank liabilities is assumed to be equal to book value. Actual dividends paid by each bank semi-annually are used to compute the dividend rate, hence it is assumed that market participants perfectly forecast future dividends. The standard deviation of rates of return on equity is estimated from share prices over the past 52 days, using daily data.

The system of equations was solved using the GAUSS 1.49B procedure for solving non-linear equations. The algorithm employed is a modification of Broyden's secant method (Edlefsen and Jones (1986), Dennis and Schnabel (1983)), which combines Broyden's method with Newton's method, Newton's method being used when Broyden's approximation does not move towards the system's solutions.

## Footnotes

See, for instance, Reserve Bank of Australia (1992). 

It is possible that regulators might systematically vary the monitoring interval and closure threshold according to the condition of each bank. The maximum closure threshold at which solutions could be obtained varied across time and between banks, suggesting that this is in fact the case. Variation of the monitoring interval between three months and one year made no noticeable difference to the results. The weighted average of asset volatility increases a little as the monitoring time increases, as does the market capital – asset ratio. 

Special dividends, such as those paid out at the time of the introduction of dividend imputation, are excluded when calculating the dividend rate.