# Exchange Rate Risk

Exchange rate risk is the risk that exchange rate changes can affect the value of an institu­tion’s assets and liabilities, as well as its off-balance-sheet items. Exchange rate risk can be direct (a financial institution takes or holds a position in foreign currency) or indirect (a foreign exchange position taken by one of the financial institution’s borrowers or by coun­terparties may affect their creditworthiness). The most commonly used measure of foreign exchange exposure is an institution’s net open foreign exchange position. Under the Basel methodology, a bank’s net open position is calculated as the sum of the following items:8 the net spot position (i. e., all asset items less all liability items, including accrued interest, which is denominated in the currency in question), the net forward-position, guaran­tees that are certain to be called and are likely to be irrecoverable, net future income or expenses not yet accrued but already fully hedged, any other item representing a profit or

loss in foreign currencies, and the net delta-based equivalent of the total book of foreign currency options. The resulting net open position in each currency can be stress tested against variations in the exchange rate of a particular currency (sensitivity analysis). For example, the change in net open position on account of a change in exchange rate can help determine the sensitivity of the position to exchange rate risk.

To illustrate the relation between the net open position and the direct exchange rate stress test, let F denote the net open position in foreign exchange, C be the capital, ARW be the risk-weighted assets (all in domestic currency units), and e be the exchange rate in units of foreign currency per a unit of domestic currency. A depreciation (a decline) in the exchange rate leads to a proportional decline in the domestic currency value of the foreign exchange exposure, that is, Ae/e=AF/F.9 Assume, as is often done, that a decline in the value of the net open position translates directly into a decline in capital, that is, AC/AF = 1.10 The effect of the exchange rate shock on the ratio of capital to risk-weighted assets would then be calculated as

(1)

where we used the fact that AC/Ae = AF/Ae = F/e. The operator A denotes change, and the symbol = means that the equation holds only approximately for larger than infinitesimal changes. Equation 1 can be rewritten as

(2)

The straightforward relationship between the net open position and the direct exchange rate stress test holds only under certain assumptions. Equation 2 summarizes the relation­ship between the basic exchange rate stress test and the respective FSIs. The term AARW /AC can have values from 0 to 1, reflecting the degree of co-movement of capital and the risk-weighted assets. In the special case of AARW /AC = 0, that is, if the risk-weighted assets do not change, then the change in the capital adequacy ratio (in percentage points) equals simply the exchange rate shock (in percent) times the exposure, which is measured as a product of the two core FSIs (F/C and C/A ). This relationship is sometimes used as a shorthand calculation of the direct exchange rate stress test. The calculation high­lights the assumptions behind such approximations, in particular the assumption of no change in Arw.11 Also, equation 2 holds only as a linear approximation, which works well if foreign exchange portfolios are essentially linear, that is, the banking sector is not very active in options markets. If banks have large positions in foreign exchange options, the relation between the exchange rate change and the effect on capital can become highly nonlinear. In such cases, a stress test that is based on a more detailed decomposition of banks’ positions in foreign exchange would be a clearly superior analytical tool.12

The net open position captures the direct foreign exchange risk. In practice, this risk tends to be rather small compared with other risks that banks face, given that the expo­
sure is relatively easy to measure and, therefore, to manage or regulate by setting limits. It is typically much more difficult to monitor foreign exchange vulnerabilities of banks’ counterparties and, therefore, the aggregate risk banks would face through changes in credit risk resulting from changes in the exchange rate. The corporate sector’s net for­eign exchange exposure to equity is one of the encouraged indicators in the set endorsed by the Executive Board in June 2001. However, no FSAP mission so far has been able to provide this indicator, and only a few FSAP missions have been able to address the indirect foreign exchange risks in the stress-testing calculation. Several FSAP missions recommended improvements in the collection of data on foreign exchange exposures in the corporate sector.

It is important to incorporate the indirect exchange risk in the stability assessment. Although FSAP missions have not been able to collect comprehensive data on corporate sectors’ foreign exchange exposure, several FSAP missions that analyzed the corporate sector in detail generally found that the banking sectors’ indirect exchange rate risk was more important than its direct exchange rate risk. To illustrate the significance of the indirect risk in overall banking sector risk, denote the corporate sector’s debt, equity, and open foreign exchange position as DC(e), EC(e), and FC(e), respectively.13 Assume that, similar to the case of banks’ net open position, a percentage change in the exchange rate will translate into the same percentage change in the domestic currency value of the net open position, which will, in turn, lead to an equivalent change in the corporate sector’s equity, that is, AEC/Ae=AFC/Ae = F/e. The effect of the exchange rate on the corporate leverage (DC/EC) is then given by (3)

Thus, if the corporate sector is short in foreign exchange, a depreciation (decline) in the exchange rate would lead to an increase in its leverage. Corporate leverage typically is positively correlated with the share of banks’ nonperforming loans (NPL) in total loans (TL), denoted as NPL/TL, that is, A(NPL/TL)/ A(DC/EC) = a > 0.14 The effect of a change in the exchange rate on the NPL/TL ratio can then be expressed as

A(NPL/TL) s aA[Dc(e)/Ec(e)] *

e Ec [Ec

In the special case when ADC/AEC = 0, the change in the NPL/TL ratio would equal the exchange rate change times the respective FSI (the net open position), times the param­eter a, which can be estimated empirically, as shown in chapter 3. To find the effect on capital adequacy, we can assume—as done in several assessments—that the credit shock has the form of a transition of performing loans into the nonperforming category. By dif­ferentiating C/Arw with respect to NPL/TL, and by substituting for NPL/TL from equa­tion 4, we obtain

(5)

where we assume (as is commonly done) that provisions are expressed as a fixed percent­age (n) of NPLs and that they are deducted directly from capital.

The incorporation of the indirect effect makes the analysis—and the relationship between the FSIs and the stress test calculations—more complex and dependent on addi­tional assumptions or regression analysis. The presentation of the direct effect in equation 2 and the indirect effect in equation 5 may appear similar, given that in both cases, the change in the capital adequacy FSI is expressed as the shock times an FSI that character­izes the exposure (the net open position). However, the calculation of the indirect effect in equation 5 is perhaps the simplest possible expression for the indirect exchange rate effect using FSIs. It relies on additional assumptions and parameters that would need to be estimated or determined, such as the sensitivity parameter, reflecting the effect of the corporate sector on the banking sector, the provisioning rate, and the ratio of TLs to risk – weighted assets.

The complexity of the indirect exchange rate stress test is greater because it should include the effects on stocks as well as on flows. The calculation of the indirect effect shown in equation 5 would need to reflect the effect of exchange rate changes on the net present value of the corporate sector, which means taking into account changes in the net present value of future earnings. For example, in export-oriented companies, a depre­ciation could generally be expected to increase their future earnings. In terms of the net present value, the effect would be essentially equivalent to the effect of a long position in foreign currency. However, it may be more practical to calculate the effect on flows by estimating the elasticity of earnings to interest and principal expenses (an encouraged FSI) with respect to the exchange rate and then to estimate the relationship between this FSI and the NPL/TL ratio.

Alternatively, it would be useful to compile an indicator measuring the corporate sector’s flow exposure, for example, a ratio of foreign exchange earnings to total earnings or (ideally) a ratio of earnings in foreign exchange to interest and principal expenses in foreign exchange. Subject to further developmental work and analysis, such an indicator could be included in the set of encouraged FSIs.