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Ch 18 Measuring and Managing Operating Exposure to the Exchange Rate

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					International Financial Markets and the Firm             Ch. 18: Operating Exposure              page 18-1




Ch. 18.                  Measuring and Managing
                         Operating Exposure to the
                         Exchange Rate




        1.     Introduction to Operating Exposure
                1.1 Definition of Operating Exposure
                1.2 The Sources of Operating Exposure
        2.     The Importance of the Economic Environment in which the
               Firm Operates
                3.1. Scenario 1: Perfectly Closed Economy
                3.2. Scenario 2: Perfectly Open Economy
                3.3 Scenario 3: Sticky prices and price discrimination
                3.4 Scenario 4: Pass-through pricing
                3.5 Scenario 5: International price-takership
        4.     Measuring and Hedging Operating Exposure
                4.1. The General Approach to Measuring and Hedging
                      Operating Exposure
                4.2 Exposure Measurement with Two Possible Future
                      Exchange Rates
                4.3 Exposure Measurement in a Problem with Residual Risk
                4.4 Exposure Measurement and Hedging in a Multi-State
                      Problem
                4.5 Managing Non-Linear Exposure to the Exchange Rate
        5.     Implications for Treasury Management




P. Sercu and R. Uppal                   Version February 1994              Printed on May 24, 2012
International Financial Markets and the Firm             Ch. 18: Operating Exposure              page 18-2




        1. Introduction to Operating Exposure


1.1       Definition of Operating Exposure

                                                Error!



   Example
   In the 1970’s VW’s profits from exports to the US were
   severely affected by the fall of the USD from DEM/USD 4 to
   about DEM/USD 2.

   In the short run Volkswagen had to decide to what extent it
   should change the USD price of its cars, trading off sales
   volume against profit margin.

   Volkswagen’s long-run problem was to decide whether to
   continue competing in the US market, and, if so, whether or
   not it should move production from Germany to the US, or to
   Latin-America.




P. Sercu and R. Uppal                   Version February 1994              Printed on May 24, 2012
International Financial Markets and the Firm             Ch. 18: Operating Exposure              page 18-3




1.2       The Sources of Operating Exposure

Two misconceptions:

• "Only firms that have foreign operations are exposed to the
  exchange rate". But
  • competition, or potential competition, from foreign firms
  • potential later exports or imports
  • prices of local purchases may depend on S (imported
    inputs)

• "If a firm denominates all its sales and purchases in terms of
  its own currency, there is no exposure".

    See previous chapter for comments.



Conclusion:

• Even a monopolist/exporter cannot simultaneously have both
  stable FC-prices and stable HC revenues

• If there are competitors located in different countries, then a
  change in the exchange rate affects their relative competitive
  position, and therefore, the cashflows of the firms.

• The magnitude of the effect depends on magnitude of PPP-
  deviations; demand and supply elasticities; degree of
  competition; operating leverage; sourcing of inputs; taxes, etc


P. Sercu and R. Uppal                   Version February 1994              Printed on May 24, 2012
International Financial Markets and the Firm             Ch. 18: Operating Exposure              page 18-4




   2. The Importance of the Firm's Economic
                Environment
Dansk AS, a subsidiary of AS Canada, has the following cet.
par. cash flow projection:


    Sales (2m units at DKK 20)                                            DKK 40,000,000
    Direct costs (2m units at DKK 12)                                        <24,000,000>
    Cash overhead expenses                                                    <5,100,000>
    Depreciation                                                               <900,000>
    Profit before taxes                                                       10,000,000
    Taxes (50%)                                                               <5,000,000>
    After-tax profit                                                       DKK 5,000,000
    Add back depreciation                                                        900,000
    Cashflow                                                               DKK 5,900,000

    Cashflow in CAD, at DKK 1 = CAD .2                                     CAD 1,180,000



Effect of unexpected 25% devaluation to CAD/DKK 0.15 (or
33% revaluation of DKK/CAD)?:

• polar cases: perfectly closed (Tibet) or perfectly open
  (Monaco).
• various intermediate cases.

P. Sercu and R. Uppal                   Version February 1994              Printed on May 24, 2012
International Financial Markets and the Firm             Ch. 18: Operating Exposure              page 18-5




3.1. Scenario 1: Perfectly Closed Economy

Internal costs and prices are unaffected by exchange rate
changes. No exports or imports. Then

• DKK cashflows are clearly unaffected.

• DKK value of Dansk AS does not change: exposure, in DKK,
  to DKK/CAD exchange rate is zero.
• CAD value of cashflows and of Dansk AS decreases by 25%:
  exposure, in DKK, to DKK/CAD exchange rate is the current
  value of Dansk AS.



3.2. Scenario 2: Perfectly Open Economy

Small, open economy and an international price taker  DKK
prices for all goods and factors increase by 33.33%. Then,
except for contractual exposure effects (including depreciation
tax shields)

• DKK sales, costs increase by 33.33%; thus, all future DKK
  cashflows increase by 33.33%.

• the CAD value of the cashflows is unaffected.

• the CAD value of Dansk AS is essentially unaltered: exposure
  is 0.


P. Sercu and R. Uppal                   Version February 1994              Printed on May 24, 2012
International Financial Markets and the Firm             Ch. 18: Operating Exposure              page 18-6




Intermediate cases:

• the economy is neither perfectly open or perfectly closed;

• half of the current output of Dansk AS is exported while the
  other half is sold in Denmark.



3.3       Scenario 3: Sticky prices and price discrimination

Assume that

• Dansk AS faces little competition either in Denmark or
  internationally.

• The Danish Government freezes prices: costs are constant,
  home sales price remains at DKK 20.

• Markets are segmented internationally, so that Dansk AS can
  maintain its export price at CAD 4.



From exhibit:

the (one-year) cashflow of Dansk AS rises dramatically both in
terms of DKK as well as CAD when compared to the initial
situation: Dansk AS has a positive exposure to the exchange rate
in both CAD and DKK terms.



P. Sercu and R. Uppal                   Version February 1994              Printed on May 24, 2012
International Financial Markets and the Firm             Ch. 18: Operating Exposure              page 18-7




3.4       Scenario 4: Pass-through pricing

Assume:
• many producers inside Denmark, but hardly any outside.
• price freeze in Denmark
• Intense competition leads to a drop of 25% in FC export
  prices (CAD 3—DKK 20), and exports rise by 50%.
• overtime, night shift; unit variable cost jumps to DKK 13.



From Exhibit:
• increase in the cashflows of Dansk AS, when measured in
  terms of DKK, but less than in previous case
• in terms of CAD, there is a decrease in the cashflows of
  Dansk AS compared to the CAD cashflows in the initial
  situation.



3.5       Scenario 5: International price-takership, sticky CAD
          prices.

Assume:

• P* = CAD 4, P = DKK 26.67 (+33%)
• Low demand elasticity

P. Sercu and R. Uppal                   Version February 1994              Printed on May 24, 2012
International Financial Markets and the Firm             Ch. 18: Operating Exposure              page 18-8


(in 1,000)
                               Scenario 1                  Scenario 2                   Scenario 3
                           Sticky prices and              Pass-through                 International
                          price discrimination              pricing                   price-takership


         SALES

    Denmark             1m                           1.5m                 1m
                         x 20 = 20,000                x 20 = 30,000x 26.67 = 26,667
    exports             1m                           1.5m                 1m
                         x 26.67 = 26,667              x 20 = 30,000      x 26.67 = 26,667
    total sales                    46,667                     60,000                53,334

          COSTS

    direct              2m                           3m                           2m
                         x 12      = 24,000           x 13 = 39,000               x 12     = 24,000
    overhead                          5,100                   5,100                           5,100
    deprec.                             900                     900                             900
    total cost                       30,000                  45,000                          30,000

    INCOME
    before tax                        16,667                     15,000                        23,334
    after tax                          8,333                      7,500                        11,667

    CASHFLOW
    add back depreciation                 900                       900                           900
    change in work. cap.°               <666>                    <2000>                        <1,333>
                                        8,567                     6,400                        11,234


    change (in DKK)                  + 2,667                      + 500                       + 5,334
    change (in CAD)                    + 105                      - 220                         + 505
                              °(crudely) approximated as 10% of change in sales.




P. Sercu and R. Uppal                   Version February 1994              Printed on May 24, 2012
International Financial Markets and the Firm             Ch. 18: Operating Exposure              page 18-9




General conclusions:



• The effect of the devaluation on the firm's value depends on
  (i) the openness of the economy, (ii) the openness of the firm's
  domestic market sector, (iii) the competitive position of the
  firm abroad and at home, and (iv) the firm's strategy.



• Forecasting the effect of changes in the exchange rate on
  future cashflows requires assumptions about competitors'
  reactions, and other variables such as inflation.



• From the Danish point of view, the devaluation is a boon; that
  is, the DKK value of Dansk AS is positively related to the
  DKK value of the CAD under all three scenarios, or, in DKK,
  the economic exposure of Dansk AS is positive.



• Depending on the environment, the CAD value of Dansk AS
  may be either be positively related to the value of the DKK (as
  in Scenario’s 3 and 5), or negatively (as in Scenario 4).




P. Sercu and R. Uppal                   Version February 1994              Printed on May 24, 2012
International Financial Markets and the Firm             Ch. 18: Operating Exposure            page 18-10




         4. Measuring and Hedging Operating
                     Exposure
4.1. General Approach to Measuring and Hedging of
     Linear Operating Exposure

• Simulations: pick a number of possible future possible values
  for the spot exchange rate ST(i), and compute the (HC) value
  of the cashflows for each possible future exchange rate value.



• Run a cross-sectional (as opposed to time-series) regression.

(1)                          ˜                    ˜
                             V T(i) = at,T + bt,T S T(i) + ˜ T(i)
                                                           e

    • bt,T has dimension [FC] and measures the exposure.

    • at,T + ˜ T(i) has dimension [HC] and is the unexposed
             e
      amount: at,T is a cross-sectional constant, ˜ T(i) is
                                                   e
                        ˜
      uncorrelated with S T.



• Hedge—e.g. by selling forward the amount bt,T.

    ˜               ˜             ˜
(2) V T,hedged(i) = V T(i) – bt,T ST(i) – Ft,T                                 
                                                                                


                          ˜
           = at,T + bt,T ST(i) + ˜T(i)
                                 e                             
                                                                          ˜
                                                                    – bt,T ST(i) – Ft,T               
                                                                                                       



P. Sercu and R. Uppal                   Version February 1994              Printed on May 24, 2012
International Financial Markets and the Firm             Ch. 18: Operating Exposure            page 18-11



(3)                            = at,T + bt,T Ft,T + ˜ T(i)
                                                    e




P. Sercu and R. Uppal                   Version February 1994              Printed on May 24, 2012
International Financial Markets and the Firm             Ch. 18: Operating Exposure               page 18-12




4.2       Exposure Measurement with Two Possible Future
          Exchange Rates

The binomial model.

Example
A Belgian company has a marketing affiliate located in the UK.
The UK has experienced a sudden surge in inflation. Possible
implications:

    • Outcome #1: a strongly deflationary policy, and S remains
      at BEF/GBP 60. The value of the marketing affiliate is
      GBP 1.55m.

    • Outcome #2: The pound devalues to BEF/GBP 55. The
      value of the firm would be GBP 1.8m.


                         VT (i)
              (millions of BEF)


                     1.8 x 55
                     = BEF 99
                                                                  Exposure Line

                    1.55 x 60
                    = BEF 93




                                                                                              S (i)
                                                          55             60                    T
                                                                                          BEF/GBP




P. Sercu and R. Uppal                   Version February 1994                 Printed on May 24, 2012
International Financial Markets and the Firm             Ch. 18: Operating Exposure            page 18-13




                                     93m - 99m
                         bt,T =        60 - 55              = –GBP 1.2m

                                  at,T = BEF 93m – bt,T 60

                                         = BEF 93m – (–1.2  60)

                                        = BEF 165.

   Hedge:



                                           Value at time T of …
    ST          Unhedged              Forward                  Hedged firm
BEF/GBP           firm                contract     = value of unhedged firm + value of
                                    = –b[St–Ft,T]                forward

    60           BEF 93m            1.2[60 – 58]                       BEF 95.4

    55           BEF 99m            1.2[55 – 58]                       BEF 95.4




P. Sercu and R. Uppal                   Version February 1994              Printed on May 24, 2012
International Financial Markets and the Firm             Ch. 18: Operating Exposure            page 18-14




4.3       Exposure Measurement in a Problem with Residual
          Risk

Example:
• cashflow is FRK 150 (boom) or FRK 100 (recession)

• S is either GBP/FRK 1.2 or 0.8.

• Recession is more likely when S is high, as follows:

                                               boom                     recession             cond.
                                     FRK cashflow: 150            FRK cashflow: 100           xpctd
                                           prob: 0.50                   prob: 0.50            cash-
                                                                                              flows


         GBP/FRK 1.2                 cashflow: GBP 180            cashflow: GBP 120            138
         prob: 0.50                     joint prob: 0.15             joint prob: 0.35
    ST
         GBP/FRK 0.8                 cashflow: GBP 120             cashflow: GBP 80            108
         prob 0.50                     joint prob: 0.35              joint prob: 0.15



                                          1800.15 + 1200.35
            ˜
         Et(V T |ST=1.2) =                        0.5         = GBP 138

                                           1200.35 + 800.15
             ˜
          Et(V T |ST=0.8) =                       0.5         = GBP 108



P. Sercu and R. Uppal                   Version February 1994              Printed on May 24, 2012
International Financial Markets and the Firm             Ch. 18: Operating Exposure            page 18-15




                                  138 – 108
                           bt,T = 1.2 – 0.8                = FRK 75

Suppose the forward rate is GBP/FRK 0.96:

• Forward profit of 75  [0.96 – 0.80] = 12 when S is low

• Forward profit of 75  [0.96 – 1.20] = –18 when S is high



                           Hedged cashflows of the subsidiary
                                          boom                       recession                cond.
                                     FRK cashflow: 150            FRK cashflow: 100           xpctd
                                        prob: 0.50                   prob: 0.50               cash-
                                                                                              flows

         GBP/FRK 1.2               hedged CF: GBP 162            hedged CF: GBP 102            120
         probability: 0.50            joint prob: 0.15             joint prob: 0.35
    ST
         GBP/FRK 0.8               hedged CF: GBP 132             hedged CF: GBP 92            120
         probability: 0.50           joint prob: 0.35               joint prob: 0.15




Effect of hedging
• The conditional expectations of the hedged GBP cashflows
  no longer depend on the spot rate

• The value of the subsidiary still depends on ‘boom’ or ‘bust’,
  but the remaining uncertainty is uncorrelated with the
  exchange rate uncertainty and cannot be further reduced by
  forex contracts.

P. Sercu and R. Uppal                   Version February 1994              Printed on May 24, 2012
International Financial Markets and the Firm               Ch. 18: Operating Exposure            page 18-16




4.4        Exposure Measurement and Linear Hedging in a
           Multi-State Problem with Non-Linearities

When considering more than two possible exchange rate
outcomes, we will often not be able to fit a straight line through
all the combinations of firm values and exchange rates that we
will consider.

Example
          Item                Simulation 1         Simulation 2        Simulation 3        Simulation 4
                             ST = BEF/USD 20      ST = BEF/USD 22     ST = BEF/USD 24     ST = BEF/USD 28
                             Probability = 1/4    Probability = 1/4   Probability = 1/4   Probability = 1/4

SALES (in BEF)
                             2000  20 = 40000    2000  22 = 44000   2000  24 = 48000     2000  28= 56000
exports to US

COSTS (in BEF)
                              2000  10= 20000    2000  10 = 20000   2000  11 = 22000    2000  14 = 28000
cost of inputs
other costs                               6000                 6000                6000                 6000
Total costs                              26000                26000               28000                34000

CASHFLOWS (in BEF)
before tax (sales – costs)               14000                18000               20000                22000
after tax (50%)                       BEF 7000             BEF 9000           BEF 10000            BEF 11000


Two solutions:
• Hedge with a linear instrument, on the basis of the best-fit
  (regression) line.

                        ˜                    ˜
                        V T(i) = at,T + bt,T S T(i)BEF/USD + ˜ T(i)
                                                             e

                                        ˜
                    = -1828.57 + 471.43 S T(i)BEF/USD + ˜ T(i)
                                                        e

                                                 R2 = 0.89,


P. Sercu and R. Uppal                   Version February 1994                Printed on May 24, 2012
International Financial Markets and the Firm             Ch. 18: Operating Exposure            page 18-17



• [Hedge using options.]




P. Sercu and R. Uppal                   Version February 1994              Printed on May 24, 2012
International Financial Markets and the Firm                   Ch. 18: Operating Exposure            page 18-18




Linear hedge:

                                               fitted casfhlows                  actual cashflows


                            12000

                            11000
            BEF cashflows




                            10000

                             9000

                             8000

                             7000

                             6000
                                    18   20               22              24            26            28

                                                   BEF/USD spot rate at T




P. Sercu and R. Uppal                    Version February 1994                   Printed on May 24, 2012
International Financial Markets and the Firm             Ch. 18: Operating Exposure            page 18-19




4.5       Managing Non-Linear Exposure to the Exchange Rate

• select a portfolio of options that approximates the true
  relationship in a piece-wise linear way.

• or create synthetic options through a dynamic (e.g. binomial)
  hedge




P. Sercu and R. Uppal                   Version February 1994              Printed on May 24, 2012
International Financial Markets and the Firm                                 Ch. 18: Operating Exposure             page 18-20



    Example

                                                5
              DEM cashflow s
                               (in m illions)




                                                4




                                                3
                                                    2                    3                      4                         5

                                                             Spot rate at 6-months (DEM/USD)




                                                                                                    DEM Cashflows
                                                                                  S        =5             5m
                                                                                      22
                                                        S        = 4.5
                                                            11
                    S =4                                                          S2 1 = 4                 4m
                               0
                                                        S        = 3.5
                                                            10
                                                                                  S2 0 = 3                4m

                       1+r = 1.01; 1+r* = 1.0202;
                                        1+r
                       forward factor        = 0.99
                                       1+r*




P. Sercu and R. Uppal                                   Version February 1994                   Printed on May 24, 2012
International Financial Markets and the Firm             Ch. 18: Operating Exposure            page 18-21




• If S1 = 4.5, the exposure is
                                               5m – 4m
                                  b11 =         5 – 4 = USD 1m

    and the unexposed part is a11 = 4.4108m = value replicating
    portfolio.




• If S1 = 3.5, the exposure is
                                               4m – 4m
                                    b11 =       4 – 3 = USD 0

    and the unexposed part is a11 = 3.9604m = value replicating
    portfolio.




• Right now, the exposure is
                            4.4108m – 3.9604m
                  b11 =          4.5 – 3.5    = USD = 0.4504m

    and the unexposed part is a11 = 3.4.1264m= value replicating
    portfolio (or of the call that should be written).




P. Sercu and R. Uppal                   Version February 1994              Printed on May 24, 2012
International Financial Markets and the Firm             Ch. 18: Operating Exposure            page 18-22




    5. Implications for Treasury Management
General points:
• Contractual exposure is very visible, and easy to measure.
  Still, for many firms operating exposure is more important in
  the long run than contractual exposure.

• Contractual exposure is very pervasive, and is not eliminated
  by hedging the outstanding FC contracts.




P. Sercu and R. Uppal                   Version February 1994              Printed on May 24, 2012
International Financial Markets and the Firm             Ch. 18: Operating Exposure            page 18-23




Four Caveats
• Linear hedging is a double-edged sword: you lose on the
  forward hedge if the exchange rate change improves the value
  of your operations. So you might consider hedging with
  options rather than forwards.

• When using short-term forward contracts to hedge long-term
  exposure, there is the possibility of liquidity problems:
  mismatch between the maturity of the underlying position and
  the hedging instrument.

• The estimate of exposure that one obtains changes over time,
  and may not be very precise at any given moment. Still,
  estimating the exposure forces us to think about the way
  exchange rates affect the firm’s operations.

• Hedging does not reduce the operating losses. We also need
  an operational response—like revising the marketing mix,
  reallocating production, choosing sourcing policies to reduce
  exposure, etc.

    When making scenario projections about the possible future
    exchange rates, we should therefore also make contingency
    plans for various possible future exchange rates.




P. Sercu and R. Uppal                   Version February 1994              Printed on May 24, 2012

				
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