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Theory and Practice of International Financial Management

Assessing Economic Exposure

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Summary of Economic Exposure1. Economic exposure, rather than focusing on the

translation of financial statements or exposure of immediate-term finances, measures the extent to which a firm’s market value changes with exchange rates.

2. Economic exposure integrates 3 key aspects of exchange rate risk: cash flow exposure, net worth exposure, and real exchange rate risk.

3. Real exchange rate changes must be used to distinguish between exchange rate fluctuations that simply offset inflation differentials and changes that impact a subsidiary’s real home-currency value.

4. Exchange rate risk can be highly pronounced in firms with purely domestic operations and firms operating in countries with fixed nominal exchange rates.

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Summary of Economic Exposure5. Cash flow exposure measures the extent to which a firm’s

real revenues and expenses - absent depreciation and debt repayment - are affected by exchange rate changes.

6. Microeconomic theory is useful in the analysis of cash flow exposure as it allows us to distinguish between price, volume, and margin effects on overall firm profit.

7. Net worth exposure measures the extent to which a company’s real net asset position - the market value of assets and liabilities - is affected by exchange rate changes.

8. Since prices for assets and liabilities are forward-looking, while prices for inputs or outputs are not, real exchange rate expectations are important.

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Summary of Economic Exposure9. If the currency habitat of price is in a currency different

from the parent company’s currency, the firm must worry also about currency fluctuations with respect to this third currency (or basket of currencies).

10. Monetary assets and liabilities will have real exchange rate expectations built into interest rates.

11. Hence, net worth is only exposed to unanticipated changes in real exchange rates.

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Measuring Economic Exposure

A statistical measure of economic exposure can be obtained by applying linear regression analysis to cash flows or real net asset values.

For cash flow exposure, a regression of the following type can be estimated:

CFt = + st + ut,

where CFt denotes cash flows in home currency units in period t and st is the spot exchange rate in terms of home currency units per foreign currency unit.

The estimated coefficient , will be:

= Cov(CFt st) / Var(st)

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Measuring Economic Exposure

= Cov(CFt st) / Var(st)

Hence, will measure the sensitivity of cash flows to the level of the exchange rate - which is precisely exposure denominated in the foreign currency units.

Example.

The R2 statistic from the regression will measure the fraction of cash flow variability that can be explained by changes in the exchange rate.

The regression should be run in real terms.

- The cash flows should be deflated by the home currency inflation (i.e. converted into constant 2008 dollars).

- The exchange rate should be the real exchange rate.

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Measuring Economic ExposureWhat happens if the regression is run in nominal terms?

As an example, consider the case where the Pound-Dollar real exchange rate is constant.

If inflation is 10% in the U.S. per year and zero in the U.K., the dollar must be depreciating by 10% per year to maintain the constant real exchange rate.

If a nominal regression is run, however, dollar cash flows will be increasing at 10% per year and the spot exchange rate will be rising at 10% per year reflecting the nominal depreciation of the dollar.

will pick up the fact that each side of the regression is increasing at 10% per year - which will be misattributed to exposure.

Run in real terms, the regression correctly delivers = 0

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Measuring Economic Exposure

This measurement technique can be applied in many different ways:

- regressing net asset value on exchange rate to determine net worth exposure.

- regressing total market value, recovered from the stock price, onto exchange rate changes.

- including lagged values of the exchange rate in the regression if an adjustment lag in cash flows might exist.

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Example: American Airlines

Bilson (1994) ran a regression to determine the economic exposure of American Airlines.

He regressed the monthly price of American Airlines stock (from January 1985 to December 1991) on:

- the $/Mark exchange rate (since over 75% of AMR’s revenues outside of the U.S. came from Europe).

- the price of oil (since this directly influences costs).

- the overall performance of the U.S. stockmarket.

The regression was run in log-scale - so coefficients can be interpreted as elasticities (i.e. if the coefficient on oil is 5, a 1% change in the price of oil will result in a 5% change in price of AMR’s stock).

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Example: American Airlines

The regression equation of the price of AMR stock was as follows (with standard errors in parentheses):

ln PAMR =

- 3.5396 + 0.9829 ln PS&P - 0.1793 ln POIL - 0.7753 ln S$/DM

(.9471) (.1107) (.0716) (.1617)

R2 = 0.53

where: ln PAMR is the log of AMR stock

ln PS&P is the log of the S&P 500 index

ln POIL is the log of the price of crude oil futures

ln S$/DM is the log of the $/DM exchange rate

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Example: American Airlines

The coefficients on the S&P 500 and oil futures came in as expected. When the S&P rises, so does AMR. When the price of oil increases, the price of AMR stock falls.

The negative coefficient on the $/DM exchange rate implies that American airlines is hurt by a dollar depreciation.

A one percent increase in the Mark is associated with a 0.77 percent decline in the stock price.

Why?

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Summary of Measuring Economic Exposure

Economic exposure can be measured using linear regression - regressing cash flows, net worth, or stock prices on exchange rates.

a. If conducted in levels, the slope coefficient can be interpreted as the exposure measure. Exchange rate changes times this exposure yield the exchange rate gain/loss.

b. If conducted in logs, the slope can be interpreted as an elasticity - a 1% change in exchange rates yields an x% change in cash flows, net worth, etc.

c. The regression must be run in real terms - real exchange rates and inflation-adjusted cash flows.

d. The R-square can be interpreted as the fraction of cash flow, net worth, or stock price fluctuation that can be accounted for by exchange rate changes.

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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 exposure and the volatility of the exchange rates relevant to this exposure.

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Foreign Exchange Risk

A firm’s degree of foreign exchange risk from period t to t+n can be expressed as:

(X St+n) = X St (% St),

where:

- ( ) is the measure of standard deviation = SQRT (Var).

- X is degree of foreign exchange exposure of the firm.

- % St is the percent change in the spot exchange rate.

The measure can be in either real or nominal units.

Example.

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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:

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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

Qi2 Var(Ri) +

n

i=1

n

j=1

Qi Qj Cov(Ri Rj)

(for i = j)

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Multiple Currencies

Since covariance equals correlation times standard deviations, we can write:

n

i=1

Qi2 Var(Ri) +

n

i=1

n

j=1

Qi Qj Corr(Ri Rj) Var(Ri) Var(Rj)

(for i = j)

Example. Suppose the variance of annualized quarterly percentage changes in the pound/$ exchange rate is 525 points^2, the Euro/$ 540^2, and the pound-euro covariance 520^2. The exchange risk associated with $100 worth of pounds and $100 worth of euros = 100^2 (525)+ 100^2 (562)+2(100^2) (520) = 100^2 (525+562+1040) = 10k (2127)

Hence, s = 4612 points, or $46.12 on an exposure of $200

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Nominal vs. Real Exchange Rate Risk

Recall that the real exchange rate is defined as:

et = St P*t/Pt.

Percent changes in the real exchange rate will be simply deviations from relative purchasing power parity:

% et = % St + *t,t+n - t,t+n

The variance of percent real exchange rate changes can be expressed as:

Var(% et) =

Var(% St) + Var(*t,t+n - t,t+n) + 2 Cov(% St , *t,t+n - t,t+n)

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Compare variability of nominal and real exchange rates.

For most developed currencies, variances are roughly similar. Why?

Var(% et) =

Var(% St) + Var(*t,t+n - t,t+n) + 2 Cov(% St , *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

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Compare variability of nominal and real exchange rates.

For most developed currencies, variances are roughly similar. Why?

Var(% et) =

Var(% St) + Var(*t,t+n - t,t+n) + 2 Cov(% St , *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 near zero

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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(% et) =

Var(% St) + Var(*t,t+n - t,t+n) + 2 Cov(% St , *t,t+n - t,t+n)

In developing counties, inflation differentials are causing nominal exchange rate movements.

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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(% et) =

Var(% St) + Var(*t,t+n - t,t+n) + 2 Cov(% St , *t,t+n - t,t+n)

In developing counties, inflation differentials are causing nominal exchange rate movements.

highly negative

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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.

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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:

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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

Qi2 Var(Ri) +

n

i=1

n

j=1

Qi Qj Cov(Ri Rj)

n

i=1

subject to:

Qi = 1

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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.

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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?

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Exchange Risk and Cash Flow Variability

Run the regression of real cash flows (or net worth or market value) on all real exchange rates that might impact firm value.

RCFt = + 1 e1t + 2 e2t + … + ut

Now, the R2 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.

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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.

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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(% St,t+n) = Rt,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.

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Exchange Risk and Cash ManagementThis 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 exposure of both physical and monetary assets and liabilities is large, then we are really saying both can also be measured in terms of unanticipated deviations from RPPP.

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Exchange Risk and Cash ManagementAs 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.

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Key Points1. 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.

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Key Points5. To measure the importance of exchange risk relative to the total variability of a firm, the R2 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.