# **Appendix II: Sensitivity Analysis**

The results of the practitioner approach that are described in section 2 are conditional on assumptions made about the allocation of line items in the balance sheet and income statement, as well as on specific interest rates. Thus, sensitivity analysis is undertaken for key variables that are not fully corroborated<sup>53</sup> in order to identify the robustness and relative contribution of the different assumptions to the results. The outcomes of the different tests are reported in Tables II.1a and b below.

We have tested the relative share of _deposits_ between the Retail and Corporate business lines. As discussed above, an important part of the allocation was based on the assumption – based on bank interviews and banks’ 20F reports – of an even allocation for of demand deposits among the two key business lines and a majority of time deposits kept in Corporate, after allocating to Government or other specific rules. We have tested the effect of this assumption by shifting 10 percent of total Retail deposits to Corporate (and vice versa). In both cases, the key result of the returns of Retail being higher than those of Corporate is maintained. While in the base case the relation of ROC between Retail and Corporate is 39/16, in the first test the relationship moves to 38/17 and in the other test to 41/14. In fact, one needs to assume that the Retail business has less than 20% of time and demand deposits – an unlikely assumption, which would itself cast doubt on one of the main reasons for having a branch network – in order for the two business lines to have a similar rate of return.

Results are also fairly insensitive to changes in _deposit rates_ . We have tested for different assumed rates for time deposits, reverse repos and acceptances such that the total interest expense which is already known from Bacen reports remains the same. The variability in the relationship of ROCs between the Retail and Corporate businesses is between 37/8 and 42/24 (Treasury actually exhibits volatility in ROC across the two scenarios), thus confirming the robustness of our key result.

We have tested the results of changes in the relative share of _gross loans_ . In the above analysis, we have assumed that around 15 percent of loans to companies were actually loans to small firms that come under the Retail business line. We tested this assumption in two ways: firstly, by assuming that no loans to these companies belong to Retail; and secondly, by assuming that a larger number of loans to firms (25 percent) are actually served by the branch network and should therefore come under Retail. The results of the tests show that the contribution of small businesses to profitability is fairly small. In fact, the ratio of ROCs between Retail/Corporate moves from 39/16 in the base case to 40/16 and 38/16 in the respective scenarios.

Sensitivity analysis was also undertaken with respect to the distribution of _loan loss provisions_ (LLP) among different loan products, while ensuring that the overall LLP rate remains the same as the one reported by Bacen. One test increased LLP of Retail compared to Corporate, and the other did the reverse. Results are fairly insensitive to

> 53 Sensitivity analysis on variables whose values are confirmed – for example, the average interest rate of Selic for 2007 – is not undertaken, even though these may also represent key drivers of performance.

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