1 Theory and Practice of International Financial Management Assessing the Risk of Foreign Exchange Exposure

2 Foreign Exchange Risk Foreign exchange risk is defined as the variability in the value of the firm, subsidiary, or investment position that is caused by uncertainty about exchange rate changes. A firm’s foreign exchange risk is a function of two variables: the firm’s degree of exposure and the volatility of the exchange rates relevant to this exposure. We have examined various measures of exposure, but have yet to integrate them with measures of exchange rate volatility.

3 Foreign Exchange Risk A firm’s degree of foreign exchange risk from period t to t+n can be expressed as: SD(X S t+n ) = X S t SD(%  S t ), where: - SD ( ) is the measure of standard deviation. - X is degree of foreign exchange exposure of the firm. - %  S t is the percent change in the spot exchange rate. The measure can be in either real or nominal units. Example.

4 Multiple Currencies Main problem: due to non-zero correlations, exposures cannot simply be added together. Correlations can be quite high between certain currencies. This is quite an important point, but one that is generally neglected in courses and by managers (i.e. Tektronix). From statistics, we know the variance of a portfolio of n- assets can be expressed as:

5 Multiple Currencies Main problem: due to non-zero correlations, exposures cannot simply be added together. Correlations can be quite high between certain currencies. This is quite an important point, but one that is generally neglected in courses and by managers (i.e. Tektronix). From statistics, we know the variance of a portfolio of n- assets can be expressed as: n i=1 Q i 2 Var(R i ) + n i=1 n j=1 Q i Q j Cov(R i R j ) (for i = j)

6 Multiple Currencies Since covariance equals correlation times standard deviations, we can write: n i=1 Q i 2 Var(R i ) + n i=1 n j=1 Q i Q j Corr(R i R j ) Var(R i ) Var(R j ) (for i = j) Examples.

7 Nominal vs. Real Exchange Rate Risk Recall that the real exchange rate is defined as: e t = S t P* t /P t. Percent changes in the real exchange rate will be simply deviations from relative purchasing power parity: %  e t = %  S t +  * t,t+n -  t,t+n The variance of percent real exchange rate changes can be expressed as: Var(%  e t ) = Var(%  S t ) + Var(  * t,t+n -  t,t+n ) + 2 Cov(%  S t,  * t,t+n -  t,t+n )

8 Compare variability of nominal and real exchange rates. For most developed currencies, variances are roughly similar. Why? Var(%  e t ) = Var(%  S t ) + Var(  * t,t+n -  t,t+n ) + 2 Cov(%  S t,  * t,t+n -  t,t+n ) In developed countries, inflation differentials are low and not terribly variable relative to spot exchange rate changes. Most of the variability in spot rates is unrelated to inflation differentials. Nominal vs. Real Exchange Rate Risk

9 Compare variability of nominal and real exchange rates. For most developed currencies, variances are roughly similar. Why? Var(%  e t ) = Var(%  S t ) + Var(  * t,t+n -  t,t+n ) + 2 Cov(%  S t,  * t,t+n -  t,t+n ) In developed countries, inflation differentials are low and not terribly variable relative to spot exchange rate changes. Most of the variability in spot rates is unrelated to inflation differentials. Nominal vs. Real Exchange Rate Risk near zero

10 Nominal vs. Real Exchange Rate Risk For developing countries in general and Mexico in particular, real exchange rate variability is considerably lower than nominal exchange rate variability. Why? Var(%  e t ) = Var(%  S t ) + Var(  * t,t+n -  t,t+n ) + 2 Cov(%  S t,  * t,t+n -  t,t+n ) In developing counties, inflation differentials are causing nominal exchange rate movements.

11 Nominal vs. Real Exchange Rate Risk For developing countries in general and Mexico in particular, real exchange rate variability is considerably lower than nominal exchange rate variability. Why? Var(%  e t ) = Var(%  S t ) + Var(  * t,t+n -  t,t+n ) + 2 Cov(%  S t,  * t,t+n -  t,t+n ) In developing counties, inflation differentials are causing nominal exchange rate movements. highly negative

12 Centralized Exchange Risk Management A firm which considers the exchange risk facing the firm as a whole rather than each operation individually is said to centralize exchange risk management. A major advantage of centralizing exchange risk management is that it can take advantage of the portfolio diversification effect. A centralized manager is able to net exposure positions of subsidiaries against one another and thereby identify from where the main sources of aggregate risk arise. Example.

13 The Minimum-Variance Portfolio In centralized risk management it is generally useful to identify the minimum-variance portfolio with respect to a set of currencies. A minimum-variance program solves for optimal currency weights given a variance-covariance matrix. Formally, the program minimizes:

14 The Minimum-Variance Portfolio In centralized risk management it is generally useful to identify the minimum-variance portfolio with respect to a set of currencies. A minimum-variance program solves for optimal currency weights given a variance-covariance matrix. Formally, the program minimizes: n i=1 Q i 2 Var(R i ) + n i=1 n j=1 Q i Q j Cov(R i R j ) n i=1 subject to: Q i = 1

15 The Minimum-Variance Portfolio Clearly, the manager be constrained in terms of which currencies can and cannot be held. In other words, there will be costs in achieving the minimum-variance portfolio. Of course, with no constraints, the minimum-variance portfolio will consist entirely of the home currency. The minimum-variance portfolio should be interpreted as the minimum attainable risk level for a given portfolio of currencies. The minimum-variance portfolio should serve as a benchmark to gauge the degree of risk of a given portfolio of exposures.

16 Exchange Risk and Cash Flow Variability Now that we have measures of foreign exchange exposure and can measure the risk of a given portfolio of exposures, the next task is to relate the foreign exchange risk to the overall volatility of the firm. Ultimately, we want some comparison of the foreign exchange exposure portfolio standard deviation to the standard deviation of the total value of the firm. How do we do this?

17 Exchange Risk and Cash Flow Variability Run the regression from Chapter 7 of real cash flows (or net worth or market value) on all real exchange rates that might impact firm value. RCF t =  +  1 e 1t +  2 e 2t + … + u t Now, the R 2 statistic will give a measure of the fraction of variability in firm value that is accounted for by the firm’s portfolio of real exchange rate exposures. As we have seen, some real exchange rates are highly correlated. Hence, in order to avoid multicollinearity problems, only truly distinct currencies should be included in the regression.

18 Exchange Risk and Cash Management Cash management refers to the manipulation of short-term financial assets which serve as a store of wealth for the firm. Since the focus here is on a portfolio of cash rather than a portfolio of exposures, managers may be inclined to pay attention to nominal rates of return. Since nominal interest rates vary by currency, it might be natural to consider the tradeoff between the return on a particular deposit and the associated riskiness of that currency. In particular, the problem will become a mean-variance optimization problem which incorporates interest rate volatility and covariances of interest rates and exchange rates.

19 Exchange Risk and Cash Management However, from earlier in this course, we know that if uncovered interest parity is expected to hold, dollar- denominated returns in all currencies should be the same: R* t,t+n + E(%  S t,t+n ) = R t,t+n Although there may exist expected deviations from UIP, in short-term offshore deposit markets (where there are few frictions) UIP should hold reasonably well ex-ante. Hence, to the extent UIP holds, ex-ante, mean-variance optimization will produce the minimum-variance portfolio - it will minimize variation in ex-post deviations from UIP.

20 Exchange Risk and Cash Management In Chapter 7, we argued that exposure of both physical and monetary assets and liabilities are best measured in terms of unanticipated deviations from RPPP. This discussion points out that the proper measure of monetary asset risk is really unanticipated deviations from UIP. Recalling from Chapter 3, one component of ex-post deviations from UIP is deviations from RPPP. If this component is large, then we are really saying the same thing. Is it?

21 Exchange Risk and Cash Management As it turns out, for most currencies, the volatility and correlations of ex-post deviations from UIP are highly similar to those of deviations from RPPP. Why? Recall that ex-post UIP deviations are really a combination of deviations from RPPP, inflation surprises, and real interest differentials. What the correlations suggest is that most of the variability and co-movements are coming from RPPP and not from variable and highly correlated inflation surprises or interest differentials. This suggests we can usually ignore interest volatility and focus on real currency changes as the significant component of risk in international cash management. Example.

22 Key Points 1.To accurately measure a firm’s foreign exchange risk, its exposures to various currencies must be integrated with the variabilities of those currencies and the correlations among them. 2.Real exchange rate variances and correlations are not terribly different from nominal counterparts for developed countries, as inflation differentials are of low variability and not terribly correlated to nominal movements. 3.For developed countries, inflation differentials are highly negatively correlated with nominal movements, and hence analysis must focus on real exchange rates. 4.Centralized risk management can take advantage of portfolio diversification effects by identifying minimum- variance portfolios with respect to a given set of currencies.

23 Key Points 5.To measure the importance of exchange risk relative to the total variability of a firm, the R 2 from regressing real cash flows on all relevant real exchange rates will describe the fraction of variability in firm value that is due to exchange risk. 6.In international cash management, if UIP holds ex-ante, the focus will be on minimizing ex-post deviations from UIP. Since deviations from RPPP account for most of the variance and co-movements, focusing on changes in real currency value is not likely to impair analysis.