Theory and Practice of International Financial Management Assessing Economic Exposure

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Theory and Practice of International Financial
Management Assessing Economic Exposure
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Summary of Economic Exposure
1. Economic exposure, rather than focusing on the
translation of financial statements or exposure
of immediate-term finances, measures the extent
to which a firms 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
subsidiarys 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 Exposure
5. Cash flow exposure measures the extent to
which a firms real revenues and expenses -
absent depreciation and debt repayment - are
affected by exchange rate changes. 6. Microeconomi
c 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 companys 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 Exposure

• If the currency habitat of price is in a currency
  different from the parent companys 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 a b 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 b, will be b
Cov(CFt st) / Var(st)
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Measuring Economic Exposure
b Cov(CFt st) / Var(st) Hence, b 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 Exposure
What 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. b 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 b 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
AMRs 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 AMRs 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
PSP - 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 PSP
is the log of the SP 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 SP 500 and oil futures
came in as expected. When the SP 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.
• 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.
• 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.
• The regression must be run in real terms - real
  exchange rates and inflation-adjusted cash flows.
• 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 firms
foreign exchange risk is a function of two
variables the firms exposure and the volatility
of the exchange rates relevant to this exposure.
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Foreign Exchange Risk
A firms degree of foreign exchange risk from
period t to tn can be expressed as ? (X Stn)
X St ?( D St), where - ? ( ) is the measure of
standard deviation SQRT (Var). - X is degree of
foreign exchange exposure of the firm. - D 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
n
n
Qi2 Var(Ri)
Qi Qj Cov(Ri Rj)
i1
i1
j1
(for i j)
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Multiple Currencies
Since covariance equals correlation times
standard deviations, we can write
n
n
n
Qi2 Var(Ri)
Qi Qj Corr(Ri Rj) Var(Ri) Var(Rj)
i1
i1
j1
(for i j)
Example. Suppose the variance of annualized
quarterly percentage changes in the pound/
exchange rate is 525 points2, the Euro/ 5402,
and the pound-euro covariance 5202. The
exchange risk associated with 100 worth of
pounds and 100 worth of euros 1002 (525)
1002 (562)2(1002) (520) 1002 (5255621040)
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 Pt/Pt. Percent changes in the real
exchange rate will be simply deviations from
relative purchasing power parity D et D St
Pt,tn - Pt,tn The variance of percent real
exchange rate changes can be expressed as Var(
D et) Var( D St) Var(Pt,tn - Pt,tn) 2
Cov( D St , Pt,tn - Pt,tn)
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Nominal vs. Real Exchange Rate Risk
Compare variability of nominal and real exchange
rates. For most developed currencies, variances
are roughly similar. Why? Var( D et) Var( D
St) Var(Pt,tn - Pt,tn) 2 Cov( D St ,
Pt,tn - Pt,tn) 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.
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Nominal vs. Real Exchange Rate Risk
Compare variability of nominal and real exchange
rates. For most developed currencies, variances
are roughly similar. Why? Var( D et) Var( D
St) Var(Pt,tn - Pt,tn) 2 Cov( D St ,
Pt,tn - Pt,tn) 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.
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( D et) Var( D St)
Var(Pt,tn - Pt,tn) 2 Cov( D St , Pt,tn -
Pt,tn) 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( D et) Var( D St)
Var(Pt,tn - Pt,tn) 2 Cov( D St , Pt,tn -
Pt,tn) 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
n
n
Qi2 Var(Ri)
Qi Qj Cov(Ri Rj)
i1
i1
j1
subject to
n
Qi 1
i1
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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 a b1 e1t
b2 e2t ut Now, the R2 statistic will give
a measure of the fraction of variability in firm
value that is accounted for by the firms
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 Rt,tn E( D
St,tn) Rt,tn 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 Management
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 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 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.
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Key Points
1. To accurately measure a firms 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 Points
5. 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.