FX Derivatives by xumiaomaio


									FX Derivatives

3. Hedging Exposure
               FX Risk Management
 Exposure
At the firm level, currency risk is called exposure.

Three areas
(1) Transaction exposure: Risk of transactions denominated in FX with a
payment date or maturity.
(2) Economic exposure: Degree to which a firm's expected cash flows
are affected by unexpected changes in St.
(3) Translation exposure: Accounting-based changes in a firm's
consolidated statements that result from a change in St. Translation rules
are complicated: not all items are translated using the same St. These
rules create accounting gains/losses due to changes in St.

We will say a firm is “exposed” or has exposure if it faces currency risk.
Q: How can FX changes affect the firm?
- Transaction Exposure
       - Short-term CFs: Existing contract obligations.

- Economic Exposure
      - Future CFs: Erosion of competitive position.

- Translation Exposure
       - Revaluation of balance sheet (Book Value vs Market Value).
Example: Exposure.
A. Transaction exposure.
Swiss Cruises, a Swiss firm, sells cruise packages priced in USD to a
broker. Payment in 30 days.

B. Economic exposure.
Swiss Cruises has 50% of its revenue denominated in USD and only
20% of its cost denominated in USD. A depreciation of the USD will
affect future CHF cash flows.

C. Translation exposure.
Swiss Cruises obtains a USD loan from a U.S. bank. This liability has to
be translated into CHF. ¶
   Measuring Transaction Exposure
Transaction exposure (TE) is very easy to identify and measure:
       TE = Value of a fixed future transaction in FC x St

For a MNC  TE: consolidation of contractually fixed future currency
  inflows and outflows for all subsidiaries, by currency. (Net TE!)

Example: Swiss Cruises.
Sold cruise packages for USD 2.5 million. Payment: 30 days.
Bought fuel oil for USD 1.5 million. Payment: 30 days.
St = 1.45 CHF/USD.
Thus, the net transaction exposure in USD is:

Net TE = (USD 2.5M -USD 1.5M) x 1.45 CHF/USD =CHF 1,450,000. ¶
 Netting
MNC take into account the correlations among the major currencies to
   calculate Net TE  Portfolio Approach.

  A U.S. MNC:       Subsidiary A with CF(in EUR) > 0
                    Subsidiary B with CF(in GBP) < 0
                    GBP,EUR is very high and positive.
                    Net TE might be very low for this MNC.

• Hedging decisions are usually not made transaction by transaction.
  Rather, they are made based on the exposure of the portfolio.
Example: Swiss Cruises.
Net TE (in USD):      USD 1 million. Due: 30 days.
Loan repayment:       CAD 1.50 million. Due: 30 days.
St = 1.47 CAD/USD.
CAD,USD = .924 (from 1990 to 2001)

Swiss Cruises considers the Net TE (overall) to be close to zero. ¶

Note 1: Correlations vary a lot across currencies. In general, regional
currencies are highly correlated. From 2000-2007, the GBP and EUR
had an average correlation of .71, while the GBP and the MXN had an
average correlation of -.01.

Note 2: Correlations also vary over time.
Currencies from developed countries tend to move together... But,
not always!
                              Correlation: GBP/US D and MXN/US D

4-year Correlation


                       1985        1990      1995      2000        2005

• Q: How does TE affect a firm in the future?
MNCs are interested in how TE will change in the future (T days). After
all, it is in the future that the transaction will be settled.
          - MNCs do not know the future St+T, they need to forecast St+T.
          - Et[St+T] has an associated standard error, which produces a
           range for (or an interval around ) St+T and, thus, TE.
          - From a risk management perspective, it is important to know
          how much will be received from a FC inflow or how much will
          be needed to cover a FC outflow.
              Range Estimates of TE
• Exchange rates are very difficult to forecast. Thus, a range estimate of
  the Net TE will provide a more useful number for risk managers.

  The smaller the range, the lower the sensitivity of the Net TE.

• Three popular methods for estimating a range for transaction
  (1) Ad-hoc rule (±10%)
  (2) Sensitivity Analysis (or simulating exchange rates)
  (3) Assuming a statistical distribution for exchange rates.
 Ad-hoc Rule
Instead of using a specific confidence interval (C.I.), which requires
(complicated calculations and/or unrealistic assumptions) many firms use
an ad-hoc rule to get a range: ±10% rule

It’s a simple and easy to understand: Get TE and add/subtract ±10% .

Example: Swiss Cruises has a Net TE= CHF 1.45 M due in 30 days
=> if St changes by ±10%, Net TE changes by ± CHF 145,000. ¶

Note: This example gives a range for NTE:
 NTE ∈ [CHF 1.305M; CHF 1.595 M]
=> the wider the range, the riskier an exposure is.

Risk Management Interpretation: If SC is counting on the USD 1M to
pay CHF expenses, these expenses should not exceed CHF 1.305M. ¶
 Sensitivity Analysis
Goal: Measure the sensitivity of TE to different exchange rates.
Examples: Sensitivity of TE to extreme forecasts of St.
      Sensitivity of TE to randomly simulate thousands of St.
Data: 5-years of monthly CHF/USD percentage changes
                     1-mo Changes in CHF/USD
                  Mean                 0.0004005
                  Standard Error       0.0027497
                  Median               -0.0022862
                  Mode                  #N/A
                  Standard Deviation   0.0329961
                  Sample Variance      0.0010887
                  Kurtosis             0.4632713
                  Skewness             0.4298708
                  Range                0.2070586
                  Minimum              -0.0893638
                  Maximum              0.1176948
                  Sum                  0.0576765
                  Count                        144
Example: Sensitivity analysis of Swiss Cruises Net TE (CHF/USD)
Empirical distribution (ED) of St monthly changes over the past 12 years.
 Extremes: 11.77% (on November 92) and –8.94% (on April 95).

(A) Best case scenario.
Net TE: USD 1M x 1.45 CHF/USD x (1 + 0.1177) = CHF 1,620,665.

(B) Worst case scenario.
Net TE: USD 1M x 1.45 CHF/USD x (1 - 0.0894) = CHF 1,320,370.

Note: If Swiss Cruises is counting on the USD 1M to cover CHF
expenses, from a risk management perspective, the expenses to cover
should not exceed CHF 1,320,370. ¶
Note: Some managers may consider the range, based on extremes, too
conservative: NTE ∈ [CHF 1,320,370; CHF 1,620,665].
=> The probability of the worst case scenario to happen is very low (only
once in 144 months!)

Under more likely scenarios, we may be able to cover more expenses
with the lower bound.

A different range can be constructed through sampling from the ED.

Example: Simulation for SC’s Net TE (CHF/USD) over one month.
(i) Randomly pick 1,000 monthly st+30’s from the empirical distribution.
(ii) Calculate St+30 for each st+30 selected in (i). (Recall: St+30 = 1.45
CHF/USD x (1 + st+30))
(iii) Calculate TE for each St+30. (Recall: TE = USD 1M x St+30)
(iv) Plot the 1,000 TE’s in a histogram. (Simulated TE distribution.)
                                      TE Simulate d Dis tribution









                                                 Trans action Expos ure (in CHF)

Based on this simulated distribution, we can estimate a 95% range
(leaving 2.5% observations to the left and 2.5% observations to the right)
      => NTE ∈ [CHF 1.3661 M; CHF 1.5443 M]

Practical Application: If SC expects to cover expenses with this USD
inflow, the maximum amount in CHF to cover, using this 95% CI, should
be CHF 1,366,100. ¶
 Assuming a Distribution
Confidence intervals (CI) based on an assumed distribution provide a
range for TE.

For example, a firm can assume that St changes, st, follow a normal
distribution and based on this distribution construct a 95% CI.

Recall that a 95% confidence interval is given by [  1.96 ].
Example: CI range based on a Normal distribution.
Assume Swiss Cruises believes that CHF/USD monthly changes follow
a normal distribution. Swiss Cruises estimates the mean and the variance.
 = Monthly mean = 0
2 = Monthly variance = 0.00107       =>  = 0.03271 (3.27%)
st ~ N(0,0.00107).      st = CHF/USD monthly changes.

Swiss Cruises constructs a 95% CI for CHF/USD monthly changes.

Recall that a 95% confidence interval is given by [  1.96 ].
Thus, st will be between -0.0641 and 0.0641 (with 95% confidence).

Based on this range for st, we derive bounds for the net TE:
(A) Upper bound
Net TE: USD 1M x 1.45 CHF/USD x (1 + 0.0641) = CHF 1,542,945.

(B) Lower bound
Net TE: USD 1M x 1.45 CHF/USD x (1 - 0.0641) = CHF 1,357,055.
=> TE ∈ [CHF 1,357,055; CHF 1,542,945]

• The lower bound, for a receivable, represents the worst case scenario
within the confidence interval.

There is a Value-at-Risk (VaR) interpretation:

VaR: Maximum expected loss in a given time interval within a (one-
sided) confidence interval.

Going back to the previous example.

CHF 1,357,055 is the minimum revenue to be received by Swiss Cruises
in the next 30 days, within a 97.5% CI.

If Swiss Cruises expects to cover expenses with this USD inflow, the
maximum amount in CHF to cover, within a 97.5% CI, should be CHF
1,357,055. ¶
● Summary NTE for Swiss francs:

- NTE = CHF 1.45M

- NTE Range:
- Ad-hoc:
                     NTE ∈ [CHF 1.305M; CHF 1.595 M].

- Simulation:
       - Extremes: NTE ∈ [CHF 1,320,370; CHF 1,620,665]
       - Simulation: NTE ∈ [CHF 1.3661 M; CHF 1.5443 M]

- Statistical Distribution (normal):
                         NTE ∈ [CHF 1,357,055; CHF 1,542,945]
 Approximating returns
In general, we use arithmetic returns: st = St/St-1-1. Changing the
frequency is not straightforward.

But, if we use logarithmic returns –i.e., st=log(St)-log(St-1)-, changing the
frequency of the mean return () and return variance (2) is simple. Let
 and 2 be measured in a given base frequency. Then,
f =  T,
2f = 2 T,

Example: From Table VII.1: m= 0.0004 and m=.0329961. (These are
arithmetic returns.) We want to calculate the daily and annual percentage
mean change and standard deviation for the CHF/USD exchange rate.

 We will approximate them using the logarithmic rule.
(1) Daily (i.e., f=d=daily and T=1/5)
d = (0.0004005) x (1/30) = .000013         (0.0013%)
d = (0.0329961) x (1/30)1/2 = .00602       (0.60%)
 Approximating returns
(2) Annual (i.e., f=a=annual and T =52)
a = (0.0004005) x (12) = .004806          (0.48%)
a = (0.0329961) x (12)1/2 = .11430        (11.43%)

The annual compounded arithmetic return is .004817 =(1+.0004005)12-1.
When the arithmetic returns are low, these approximations work well. ¶

Note I: Using these annualized numbers, we can approximate an
annualized VaR(97.5), if needed:
USD 1M x 1.45 CHF/USD x [1 +(.004806-1.96 0.1143)] =
= CHF 1,132,128.1. ¶

Note II: Using logarithmic returns rules, we can approximate USD/CHF
monthly changes by changing the sign of the CHF/USD. The variance
remains the same. Then, annual USD/CHF mean percentage change is
approximately -0.48%, with an 11.43% annualized volatility.
● Sensitivity Analysis for portfolio approach
Do a simulation: assume different scenarios -- attention to correlations!

Example: IBM has the following CFs in the next 90 days
Outflows Inflows           St             Net Inflows
GBP 100,000        25,000        1.60 USD/GBP          (75,000)
EUR 80,000         200,000       1.05 USD/EUR          120,000

NTE (USD)= EUR 120K*1.05 USD/EUR+(GBP 75K)*1.60 USD/GBP
   = USD 6,000 (this is our baseline case)

Situation 1: Assume GBP,EUR = 1. (EUR and GBP correlation is high.)
Scenario (i): EUR appreciates by 10% against the USD
Since GBP,EUR = 1, St = 1.05 USD/EUR * (1+.10) = 1.155 USD/EUR
             St = 1.60 USD/GBP * (1+.10) = 1.76 USD/GBP

NTE (USD) =EUR 120K*1.155 USD/EUR+(GBP 75K)*1.76 USD/GBP
          = USD 6,600. (10% change)
Example (continuation):
Scenario (ii): EUR depreciates by 10% against the USD
Since GBP,EUR = 1, St = 1.05 USD/EUR * (1-.10) = 0.945 USD/EUR
                St = 1.60 USD/GBP * (1-.10) = 1.44 USD/GBP

NTE (USD)=EUR 120K*0.945 USD/EUR+(GBP 75K)*1.44 USD/GBP
   = USD 5,400. (-10% change)

Now, we can specify a range for NTE
      NTE ∈ [USD 5,400, USD 6,600]

Note: The NTE change is exactly the same as the change in St. If a firm
has matching inflows and outflows in highly positively correlated
currencies –i.e., the NTE is equal to zero-, then changes in St do not
affect NTE. That’s very good.
Example (continuation):
Situation 2: Suppose the GBP,EUR = -1 (NOT a realistic assumption!)
Scenario (i): EUR appreciates by 10% against the USD
Since GBP,EUR = -1, St = 1.05 USD/EUR * (1+.10) = 1.155 USD/EUR
               St = 1.60 USD/GBP * (1-.10) = 1.44 USD/GBP

NTE (USD)= EUR 120K*1.155 USD/EUR+(GBP 75K)*1.44 USD/GBP
   = USD 30,600. (410% change)

Scenario (ii): EUR depreciates by 10% against the USD
Since GBP,EUR = -1, St = 1.05 USD/EUR * (1-.10) = 0.945 USD/EUR
                St = 1.60 USD/GBP * (1+.10) = 1.76 USD/GBP

NTE (USD)=EUR 120K*0.945 USD/EUR+(GBP 75K)*1.76 USD/GBP
   = (USD 18,600). (-410% change)

Now, we can specify a range for NTE
 NTE ∈ [(USD 18,600), USD 30,600]
Example (continuation):
Note: The NTE has ballooned. A 10% change in exchange rates produces
a dramatic increase in the NTE range.
  Having non-matching exposures in different currencies with
negative correlation is very dangerous.

IBM will assume a correlation (estimated from the data) and, then, draw
many scenarios for St to generate an empirical distribution for the NTE.
From this ED, IBM will get a range –and a VaR- for the NTE. ¶
                       Managing TE

• A Comparison of External Hedging Tools
Transaction exposure: Risk from the settlement of transactions
  denominated in foreign currency.
Example: Imports, exports, acquisition of foreign assets.

• Tools:      Futures/forwards (FH)
              Options (OH)
              Money market (MMH)

• Q: Which hedging tool is better?
• New tool: MMH
A money market hedge is based on a replication of IRPT arbitrage.
Let’s take the case of receivables denominated in FC
1) Borrow FC
2) Convert to DC
3) Deposit DC in domestic bank
4) Transfer FC receivable to cover loan from (1).

Under IRPT, step 4) involves buying FC forward, to repay loan in (1)
  => This step is not needed, instead, we just transfer the FC receivable.

Q: Why MMH instead of FH?
   - under perfect market conditions          MMH = FH
   - under less than perfect conditions       MMH  FH
Iris Oil Inc., a Houston-based energy company, has a large foreign
currency exposure in the form of a CAD cash flow from its Canadian
operations. The exchange rate risk to Iris is that the CAD may depreciate
against the USD. In this case, Iris’ CAD revenues, transferred to its USD
account will diminish and its total USD revenues will fall.

Situation: Iris will have to transfer CAD 300M into its USD account in
90 days.

St = 0.8451 USD/CAD
Ft,90-day = 0.8493 USD/CAD
iUSD = 3.92%
iCAD = 2.03%
Example (continuation):
Date     Spot market        Forward market            Money market
t        St = .8451 USD/CAD Ft,90-day = .8493 USD/CAD iUSD=3.92%;
t+90     Receive CAD 300M and transfer into USD.

Hedging Strategies:
1. Do Nothing:
Do not hedge and exchange the CAD 300M at St+90.

2. Forward Market:
At t, sell the CAD 300M forward and at time t+90 guarantee:
(CAD 300M) x (.8493 USD/CAD) = USD 254,790,000
Example (continuation):
3. Money Market
At t, Iris Oil takes the following three steps, simultaneously:
1) Borrow from Canadian bank at 2.03% for 90 days :
CAD 300M / [1+.0203x(90/360)] = CAD 298,485,188.
2) Convert to USD at St:
CAD 298,485,188 x 0.8451 USD/CAD = USD 252,249,832
3) Deposit in US bank at 3.92% for 90 days to guarantee at time t+90:
      USD 252,249,832 x [1 + .0392x(90/360)] = USD 254,721,880.

Note: Both the FH and the MMH guarantee certainty at time t+90
FH delivers to Iris Oil:      USD 254,790,000
MMH delivers to Iris Oil: USD 254,721,880
=> Iris Oil will select the FH.
Example (continuation):
4. Option Market:
At t, buy a put. Use the options market. Available 90-day options
       X                  Calls           Puts
  .82 USD/CAD             ----            0.21
  .84 USD/CAD             1.58            0.68
  .88 USD/CAD             0.23            ----
  Buy the .84 USD/CAD put => Total premium cost of USD 2.04M.

                           St+90 < .84 USD/CAD    St+90 > .84 USD/CAD
 In 90 days, the CF is:    (.84 – St+90) CAD 300M                0
 Plus                      St+90 CAD 300M         St+90 CAD 300M
 Total                     USD 252M               St+90 CAD 300M

 Net CF at t+90:     USD 249,960,000              for all St+90 < .84 USD/CAD
 or                  St+90 CAD 300M – USD 2.04M   for all St+90 > .84 USD/CAD
Example (continuation):
5. Collar:
At time t, buy a put and sell a call.
Buy the .84 put at USD 0.0068 and finance it by selling the .88 call at
USD 0.0023. Thus, initial cost is reduced to USD 0.0045 per put
=> Total cost: USD 1.35M
               St+90 < .84 USD/CAD   .84 < St+90 < .88     St+90     >          .88
Put (.84)     (.84 – St+90 ) CAD 300M      0                  0
Call (.88)             0                   0             (.88– St+90) CAD 300M
Plus          St+90 CAD 300M          St+90 CAD 300M     St+90 CAD 300M
Total         USD 252 M               St+90 CAD 300M     USD 264M

Net CF at t+90: USD 250.65M                       for all St+90 < .84 USD/CAD
or              St+90 CAD 300M – USD 1.35M        for all .84 < St+90 < .88
or              USD 262.65M                       for all St+90 > .88 USD/CAD
Example (continuation):
6. Alternative: Zero cost insurance:
At time t, buy puts and sell calls with overall (or almost) matching

Buy the .84 put and finance it buy selling 3, .88 calls. Thus, no initial
cost (actually, it’s a small profit, which we’ll ignore). In 90 days:

              St+90 < .84 USD/CAD .84 < St+90 < .88     St+90 > .88 USD/CAD
Put (.84)     (.84 – St+90) CAD 300M 0                  0
3 Calls (.88)       0                        0      3 (.88–St+90) CAD 300M
Plus          St+90 CAD 300M        St+90 CAD 300M St+90 CAD 300M
Total         USD 252 M             St+90 CAD 300M USD 792M–2St+90CAD 300M

Net CF at t+90: USD 252M                        for all St+90 < .84 USD/CAD
or              St+90 CAD 300M                  for all .84 < St+90 < .88
or              USD 792 M – 2 St+90 CAD 300M    for all St+90 > .88 USD/CAD
• Let’s plot all strategies:

    Received in                                    Do Nothing
USD 264M
USD 262.65M                                                     Collar

USD 254.79M
USD 252M
USD 250.65M
USD 249.96M
                                                       Zero-cost Collar

                               .84   .8562   .88                         St+90
• In order to make a decision regarding a hedging strategy, we need to
say something about St+90. For example, we can assume a distribution.

• We can use the ED to say something about future changes in St.

Example: Distribution for monthly USD/SGD changes from 1981-2009.
Then, we get the distribution for St+30 (USD/SGD).

                        0.4                                                                         0.4
                       0.35                                                                        0.35

                                                                              Relative Frequency
  Relative Frequency

                        0.3                                                                         0.3
                       0.25                                                                        0.25
                        0.2                                                                         0.2

                       0.15                                                                        0.15

                        0.1                                                                         0.1
                              More   -5    -3      -1     0      1    3   5                               M o re   0.6185   0.631 0.6445
                                                                                                                                 5         0.651   0.6575 0.6705 0.6835
                                          C hanges in USD / SGD (%)                                                                 USD/SGD
Example (continuation): Distribution for monthly USD/SGD changes
from 1981-2009. Raw data, and relative frequency for St+30 (USD/SGD).
       st (SGD/USD)      Frequency   Rel frequency      St =1/.65*(1+st)
       -0.0494 or less      2              0.0058    1.462          0.6838
          -0.0431           2           0.0058       1.472          0.6793
          -0.0369           1          S
                                        0.0029       1.482          0.6749
          -0.0306           3          t
                                        0.0087       1.491          0.6705
          -0.0243           6          =0.0174       1.501          0.6662
          -0.0181           20         /0.0580       1.511          0.6620
          -0.0118           36         60.1043       1.520          0.6578
          -0.0056           49         *0.1420       1.530          0.6536
          0.0007            86         +
                                        0.2493       1.540          0.6495
          0.0070            52         (0.1507       1.549          0.6455
          0.0132            41         )0.1188       1.559          0.6415
          0.0195            29          0.0841       1.568          0.6376
          0.0258            5           0.0145       1.578          0.6337
          0.0320            7           0.0203       1.588          0.6298
          0.0383            5           0.0145       1.597          0.6260
          0.0446            0           0.0000       1.607          0.6223
        0.0508 or +         3           0.0058       1.617          0.6186
• Examples assuming an explicit distribution for St+T
Example–Receivables: Evaluate (1) FH, (2) MMH, (3) OH and (4) NH.
Cud Corp will receive SGD 500,000 in 30 days. (SGD Receivable.)
• St = .6500 - .6507 USD/SGD.
• Ft,30 = .6510 - .6519 USD/SGD.
• 30-day interest rates:   iSGD: 2.65% - 2.75% & iUSD: 3.20% - 3.25%
• A 30-day put option on SGD: X = .65 USD/SGD and Pt= USD.01.
• Forecasted St+30:
   Possible Outcomes       Probability
      USD .63              18%
      USD .64              24%
      USD .65              34%
      USD .66              21%
      USD .68              3%
(1) FH: Sell SGD 30 days forward
    USD received in 30 days = Receivables in SGD x Ft,30
    = SGD 500,000 x .651 USD/SGD = USD 325,500.

(2) MMH: Borrow SGD for 30 days, Convert to USD, Deposit USD,
Repay SGD loan in 30 days with SGD payable

   Amount to borrow = SGD 500,000/(1 + .0275x30/360) =
   = SGD 498,856.79

   Convert to USD (Amount to deposit in U.S. bank) =
   = SGD 498,856.79 x .65 USD/SGD = USD 324256.91

   Amount received in 30 days from U.S. bank deposit =
   = USD 324256.91 x (1 + .032x30/360) = USD 325,121.60
(3) OH: Purchase put option.           X= .65 USD/CHF
                               Pt = premium = USD .01

Note: In the Total Amount Received (in USD) we have subtracted the
opportunity cost involved in the upfront payment of a premium:
USD .01 x .032 x 30/360 = USD .000027 (Total = USD 13.50)
=> Total Premium Cost: USD 5,013.50
E[Amount Received in USD] = 319,986.5 x .76 + 324,986.50 x .21 +
+ 329,986.50 x .03 = USD 321,336.5
(4) No Hedge: Sell SGD 500,000 in the spot market in 30 days.

Note: When we compare (1) to (4), it’s not clear which one is better.
Preferences will matter. We can calculate and expected value:
E[Amount Received in USD] = 315K x .18 + 320K x .24 + 325K x .34+
+ 330K x .21+ 335K x . 03 = USD 323,350

Conclusion: Cud Corporation is likely to choose the FH. But, risk
preferences matter. ¶
Example–Payables: Evaluate (1) FH, (2) MMH, (3) OH, (4) No Hedge
Situation: Cud Corp needs CHF 100,000 in 180 days. (CHF Payable.)
• St = .675-.680 USD/CHF.
• Ft,180 = .695-.700 USD/CHF.
• 180-day interest rates are as follows: iCHF: 9%-10%; iUSD: 13%-14.0%
• A 180-day call option on CHF: X=.70 USD/CHF and Pt=USD.02.

• Cud forecasted St+180:
   Possible Outcomes         Probability
    USD .67                  30%
    USD .70                  50%
    USD .75                  20%
(1) FH: Purchase CHF 180 days forward
    USD needed in 180 days = Payables in CHF x Ft,180
    = CHF 100,000 x .70 USD/CHF = USD 70,000.

(2) MMH: Borrow USD for 180 days, Convert to CHF, Invest CHF,
Repay USD loan in 180 days

   Amount in CHF to be invested = CHF 100,000/(1 + .09x180/360)
   = CHF 95,693.78

   Amount in USD needed to convert into CHF for deposit =
   = CHF 95,693.78 x .680 USD/CHF = USD 65,071.77

   Interest and principal owed on USD loan after 180 days =
   = USD 65,071.77 x (1 + .14x180/360) = USD 69,626.79
(3) OH: Purchase call option.   X= .70 USD/CHF
    Ct = premium = USD .02.

Note: In the Total USD Cost we have included the opportunity cost
involved in the upfront payment of a premium = USD 130.

• Preferences matter: A risk taker may like the 30% chance of doing
better with the OH than with the MMH.
(4) Remain Unhedged: Purchase CHF 100,000 in 180 days.

Preferences matter: Again, a risk taker may like the 30% chance of doing
better with the NH than with the MMH. (Actually, there is also an
additional 50% chance of being very close to the MMH.)

E[Amount to Pay in USD] = USD 70,100

Conclusion: Cud Corporation is likely to choose the MMH. ¶
                    Internal Methods

• These are hedging methods that do not involve financial instruments.

• Risk Shifting
Q: Can firms completely avoid exposure to exchange rate movements?
A: Yes! By pricing all foreign transactions in the domestic currency.

Example: Bossio Co., a U.S. firm, sells naturally colored cotton. Asuni,
a Japanese company, buys Bossio's cotton. Bossio Co. prices all exports
in USD. ¶
       => Currency risk is not eliminated. The foreign company bears it.

• Problem with risk-shifting: Reduces firm flexibility.
• Currency Risk Sharing
Two parties can agree -using a customized hedge contract- to share the
FX risk involved in the transaction.

Example: Asuni buys cotton for USD 1 million from Bossio Co.
Risk Sharing agreement:
• If St  [98 JPY/USD, 140 JPY/USD]  transaction unchanged.
(Asuni pays USD 1 M to Bossio Co.)

The range where the transaction is unchanged is called neutral zone.

• If St < 98 JPY/USD or St > 140 JPY/USD  both companies share
the risk equally.

Suppose that when Asuni has to pay Bossio Co., St = 180 JPY/USD.
The St used in settling the transaction is 160 JPY/USD (180 - 40/2).

Asuni's final cost = JPY 160 million = USD 888,889 < USD 1M. ¶
• Leading and Lagging (L&L)
Firms can reduce FX exposure by accelerating or decelerating the timing
of payments that must be made in different currencies:
 leading or lagging the movement of funds.

L&L is done between the parent company and its subsidiaries or between
two subsidiaries.

Example: Parent company: HAL (U.S. company).
   Subsidiaries: Mexico, Brazil, and Hong Kong.
HAL Hong Kong's exposure is too large.
HAL orders HAL Mexico and HAL Brazil to accelerate (lead) its
payments to HAL Hong Kong. ¶

• L&L changes the assets or liabilities in one firm, with the reverse effect
on the other firm.
 L&L changes balance sheet positions.
Might be a good tool for achieving a hedged balance sheet position.
• Funds Adjustments
Key to hedging:
Match inflows and outflows denominated in the foreign currency.

Chinese subsidiary in U.S.         Italian subsidiary in U.S.
has positive CFs in USD            has negative CFs in USD
Increase USD purchases                  Decrease USD purchases
Decrease CNY purchases                  Increase EUR purchases
Decrease USD sales                      Increase USD sales
Increase CNY sales                      Decrease EUR sales
Increase USD borrowing                  Reduce USD borrowing
Reduce CNY borrowing                    Increase EUR borrowing

Example: Japanese and German carmakers have plants in the U.S.
               Translation Exposure

Translation exposure: Risk from consolidating assets and liabilities
  measured in foreign currencies with those in the reporting currency.

Assets and liabilities in a FC must be restated in terms of a DC.

This translation follows rules set up by a parent firm's government, an
  accounting association, or by the firm itself.

Problem: The translation involves complex rules that sometimes reflect a
  compromise between historical and current exchange rates.

  => The translation might not end up with Assets=Liabilities.
• Examples of exchange rates used for translation:

- Historical rates may be used for some equity accounts, fixed assets,

- Current exchange rates are used for current assets, liabilities, expenses
   and income.

- Different exchange rates are used, imbalances will occur.

• Key issue: what to do with the resulting imbalance? It is taken to
  either current income or equity reserves.

Note: Translation exposure does not directly affect cash flows, but some
  firms are concerned about it because of its potential impact on
  reported consolidated earnings.
    Measuring Translation Exposure

There are several methods to translate foreign currency accounts into the
  reporting currency. Two methods that predominate:
  - Temporal method (monetary/nonmonetary method)
  - Current rate method

Useful Terminology:
Monetary: there is a date (maturity) attached to the asset or liability.
Nonmonetary: items with no maturity (fixed assets, inventory).
Three exchange rates can be used:
  S0: Historical exchange rate.
  St: Current exchange rate at the date of balance.
  SAVERAGE: Average exchange rate for the period.
FASB #8 - Temporal Method (U.S.: used from 1976-1982)
Premise: Historical-cost accounting

  - Translate nonmonetary assets at S0, assets and liabilities use St
  - Translate most income statements items at the SAVERAGE
  - Translate shareholder equity at S0
  - Bookkeeping exchange gains or losses are passed to the Income
FASB #52 - Current Rate Method (U.S.: used since 12/15/1982)
- Translate most amounts at St
- Income statement items are translated at S0 or SAVERAGE
- Translate shareholder equity at S0
- Exchange gains or losses are not reflected in income statement rather
   accumulate in an adjustment account in stockholders' equity:
   Cumulative translation adjustment (CTA).
- Distinguished between functional currency (usually local currency) and
   reporting currency (currency in which the parent firm prepares its own
   financial statements)

- Exceptions to FASB #52
1. Accounts of subsidiaries whose operations are mostly with the parent
   use parent’s currency as functional currency, translate using temporal
2. Accounts of subsidiaries operating in hyperinflationary countries (over
   100% over a three year period), functional currency must be the USD.
Summary of U.S. accounting standards

                          1975-81           1981-today
                          FASB #8           FASB #52
                      Temporal Method    Current Rate Method
Monetary                  St                St
(Assets, debt, etc)

(P&E, inventory)          S0                 St

reported:             Income statement   Separate equity account
     Managing Translation Exposure

• Most popular method: balance sheet hedge.

Perfect balance sheet hedge: have an equal amount of exposed foreign
  currency assets and liabilities on a firm's consolidated balance sheet.

   net translation exposure will be zero.

• Translation exposure is measured by currency: equality of exposed
   balance sheet's items can be achieved on a worldwide basis.
Example: HAL HK has the following balance sheet (in HKD M).
                                   Balance    CR     M/NM
                                   accounts    exposures
Cash                               300        300     300
Accounts receivable                850        850     850
Inventory                          400        400     N.ex.
Net fixed plant and equip.         1,000      1,000   N.ex.
   Total assets                    2,550
   Total exposed assets                       2,550   1,150
Liabilities and Capital
Accounts payable                   200        200     200
Notes payable                      300        300     300
Long-term debt                     900        900     900
Shareholder's equity               1,150      N.ex.   N.ex.
   Total liabilities and capitsl   2,550
   Total exposed liabilities                  1,400   1,400
Net exposed assets                            1,150   -250
Example (Continuation):
Net exposed assets                       1,150 -250

St=.128 USD/HKD.
Exposure in USD - CR method:
   HKD 1,150,000,000 x .128 USD/HKD = USD 147,200,000.
Exposure in USD - M/NM method:
   HKD -250,000,000 x .128 USD/HKD = USD -32,000,000.

Management believes the HKD will depreciate 10% against the USD.
If St   HAL will have:
(1)     Translation loss = USD 14.72 million under the CR Method.
(2)     Translation gain = USD 3.2 million under the M/NM Method.
Example (Continuation):
Note: Under the CR Method the loss will go to the CTA.
      Under the Temporal Method the gain will go to the income
      statement and increase earnings.

HAL HK's functional currency is the HKD, HAL uses the CR Method.

HAL wants to avoid translation exposure in HKD:

HAL HK should borrow HKD 1,150,000,000, and then:
(1)  HAL HK could exchange the HKD for USD, or
(2)  HAL HK could transfer the borrowed HKD to HAL. ¶
                 Economic Exposure

Economic exposure (EE): Risk associated with a change in the NPV of a
  firm's expected cash flows, due to an unexpected change in St.

• Economic exposure is:       Subjective.
                              Difficult to measure.

• We can use accounting data (changes in EAT) or financial/economic
  data (returns) to measure EE. Economists tend to like more economic
  data measures.

• Note: Since St is very difficult to forecast, the actual change in St can
  be considered “unexpected.”
      Measuring Economic Exposure
An Easy Measure of EE Based on Financial Data
We can easily measure how CF and St move together: correlation.

Example: Kellogg’s and IBM’s EE.
Using monthly stock returns for Kellogg’s (Krett) and monthly changes
in St (USD/EUR) from 1/1994-2/2008, we estimate ρK,s (correlation
between Krett and st) = 0.154.

It looks small, but away from zero. We do the same exercise for IBM,
obtaining ρIBM,s=0.056, small and close to zero. ¶

• Better measure: 1) Run a regression on CF against (unexpected) St.
                  2) Check statistical significance of regression coeff’s.
• Testing and Evaluating EE with a regression
    (1) Collect data on CF and St (available from the firm's past)

   (2) Estimate the regression:       CFt =  + ß St + t,
        ß measures the sensitivity of CF to changes in St.
        the higher ß, the greater the impact of St on CF.

   (3) Test for EE           H0 (no EE): β = 0
                              H1 (EE): β ≠ 0

   (4) Evaluation of this regression: t-statistic of ß and R2.
       Rule: |tβ= ß/SE(ß)| > 1.96     => ß is significantly different than
                                      zero at 5% level.
Example: Kellogg’s EE.
Now, using the data from the previous example, we run the regression:
  Krett =  + ß st + t

R2 = 0.023717
Standard Error = 0.05944
Observations = 169
                   Coefficients   Standard Error   t-Stat      P-value
Intercept (α)      0.003991       0.004637         0.860756    0.390607
Changes in St (β) 0.551059        0.273589         2.014185    0.045595

We reject H0, since |tβ = 2.01| > 1.96 (significantly different than zero).

Note, however, that the R2 is very low! (The variability of st explains less
  than 2.4% of the variability of Kellogg’s returns.) ¶
Example: IBM’s EE.
Now, using the IBM data, we run the regression:
   IBMrett =  + ß st + t

R2 = 0.003102
Standard Error = 0.09462
Observations = 169
                    Coefficients   Standard Error    t-Stat    P-value
Intercept (α)       0.016283       0.007297         2.231439   0.026983
Changes in St (β) -0.20322         0.2819           -0.72089   0.471986

We cannot reject H0, since |tβ = -0.72| < 1.96 (not significantly different
than zero).

Again, the R2 is very low. (The variability of st explains less than 0.3%
of the variability of IBM’s returns.) ¶
• Sometimes the impact of St is not felt immediately by a firm.
    contracts and short-run costs (short-term adjustment difficult).

Example: For an exporting U.S. company a sudden appreciation of the
  USD increases CF in the short term.

Run a modified regression:
  CFt =  + ß0 St + ß1 St-1 + ß2 St-2 + ß3 St-3 + ... + t.

The sum of the ßs measures the sensitivity of CF to St.

• Practical issue: number of lags?
  Usual practice: include at most two years of information.
Example: HAL runs the following regression.
CFt = .456 + .421 St + .251 St-1 +.052 St-2.           R2= .168.
      (.89) (2.79)       (2.01)     (0.77)

HAL's HKD CF (in USD) sensitivity to St is 0.672 (.421+.251). 
      a 1% appreciation of the HKD will increase HKD CF
      (translated into USD) by 0.672%. ¶

Evidence: For large companies (MNCs, Fortune 500),  is not
  significantly different than zero. We cannot reject Ho: No EE.
A Measure Based on Accounting Data
It requires to estimate the net cash flows of the firm (EAT or EBT) under
    several FX scenarios. (Easy with an excel spreadsheet.)

Example: IBM HK provides the following info:
Sales and cost of goods are dependent on St
                      St = 7 HKD/USD        St = 7.70 HKD/USD
Sales (in HKD)                300M          400M
Cost of goods (in HKD)        150M          200M
Gross profits (in HKD)        150M          200M
Interest expense (in HKD) 20M               20M
EBT (in HKD)                  130M          180M

EBT (in USD at St=7) : HKD 130M/7 HKD/USD = USD 18.57M
EBT (in USD at St = 7.7): HKD 180M/7.70 HKD/USD = USD 23.38M
Example (continuation):
A 10% depreciation of the HKD, increases the HKD cash flows from
HKD 130M to HKD 180M, and the USD cash flows from USD 18.57M
to USD 23.38.

Q: Is EE significant?
A: We can calculate the elasticity of CF to changes in St.

For example, in USD, a 10% depreciation of the HKD produces a change
of 25.9% in EBT. Quite significant. But you should note that the change
in exposure is USD 4.81M.

This amount might not be significant for IBM! (Judgment call needed.) ¶

Note: Obviously, firms will simulate many scenarios to gauge the
sensitivity of EBT to changes in exchange rates.
      Managing Economic Exposure

• If EE is significant => a firm should try to manage it.

• Ideal Situation: A firm would like to have constant CFs at different
exchange rates. If this is possible, there will not be EE.

• Matching Inflows and Outflows
Severe problems show up when there is a currency gap (= inflows in FC
- ouflows in FC).

A very simple approach: Avoid currency gaps between inflows
denominated in FC and ouflows denominated in FC
      => match inflows in FC and outflows in FC
Case Study: Laker Airways (Skytrain) (1977-1982)
After a long legal battle in the U.S. and the U.K, Sir Freddie Laker was
allow to let his low cost carrier, no-frills
airline to fly from LON to NY (1977). Big
success. Rapid expansion, financed with debt.
Situation: Rapid expansion: Laker buys planes
from MD, financed in USD.

• Cost
(i) fuel, typically paid for in USD
(ii) operating costs incurred in GBP, but with a small USD cost
component (advertising and booking in the U.S.)
(iii) financing costs from the purchase of aircraft, denominated in USD.
• Revenue
Sale of airfare (probably, evenly divided between GBP and USD), plus
other GBP revenue.
Currency mismatch (gap):
Revenues                                                        Payables
mainly GBP, USD                                                 mainly USD, GBP

• What happened to St?                                              USD/GBP Exchange Rate
1977-1981: Big USD depreciation.         3

1981-1982: Big USD appreciation.        2.5
1982: Laker Airlines bankrupt.           1






                                                                                                                      Ja 2



































Solutions to Laker Airlines problem (economic exposure):
       - Sales in US
       - Borrow in GBP
       - Diversification
       - Transfer cost out to GBP/Shift expenses to GBP
• The Laker case study presents a very simple approach to managing EE:
Avoid currency gaps between inflows and ouflows.
       => match inflows in FC and outflows in FC as much as possible.

• European and Japanese car makers have been matching inflows and
outflows by moving production to the U.S.

• But, not all companies can have a very good match between inflows
and outflows. Importing and Exporting companies will always be
operationally exposed.
Example: A U.S. firm exports to the European Union. Two different FX
(1) St = 1.00 USD/EUR
        Sales in US USD 10M
               in EU EUR 15M
        Cost of goods in US USD 5M
                      in EU EUR 8M
(2) St = 1.10 USD/EUR
        Sales in US USD 11M
               in EU EUR 20M
        Cost of goods in US USD 5.5M
                      in EU EUR 10M
Taxes: US      30%
        EU     40%
Interest:      US     USD 4M
               EU     EUR 1M
Example (continuation):
            CFs under the Different Scenarios (in USD)
             St=1 USD/EUR         St=1.1 USD/EUR
Sales        10M+15M=25M         11M+22M=33M
CGS          5M+8M= 13M          5.5M+11M=16.5M
Gross profit 5M+7M=12M           5.5M+11M=16.5M
Int          4M+1M=5M            4M+1.1M=5.1M
EBT          7M                  11.4M
Tax          0.3M+2.4M=2.7M 0.45M+3.96M=4.41M
EAT          4.3M                6.99M

Q: Is the change in EAT significant?
Elasticity: For a 10% depreciation of the USD, EAT increases by 63%
(probably very significant!). That is, this company benefits by an
appreciation of the Euro against the USD. The firm faces economic
exposure. ¶
Example (continuation):
Q: How can the US exporting firm avoid economic exposure? (match!)
- Increase US sales
- Borrow more in Euros (increase outflows in EUR)
- Increase purchases of inputs from Europe (increase CGS in EUR)

(A) US firm increases US sales by 25% (unrealistic!)
EAT (St=1 USD/EUR) = USD 6.05M
EAT (St=1.1 USD/EUR) = USD 8.915M
   => a 10% depreciation of the USD, EAT increases by only 47%.

(B) US firm borrows only in EUR: EUR 5M
EAT (St=1 USD/EUR) = USD 4.7M
EAT (St=1.1 USD/EUR) = USD 7.15M
    => a 10% depreciation of the USD, EAT increases by 52%.
Example (continuation):
(C) US firm increases EU purchases by 30% (decreasing US purchases
    by 30%)
EAT (St=1 USD/EUR) = USD 3.91M
EAT (St=1.1 USD/EUR) = USD 6.165M
    => a 10% depreciation of the USD, EAT increases by 58%.

(D) US firm does (A), (B) and (C) together
EAT (St=1 USD/EUR) = USD 6.06M
EAT (St=1.1 USD/EUR) = USD 8.25M
   => a 10% depreciation of the USD, EAT increases by 36%. ¶

Note: Some firms will always be exposed!
• International Diversification
For the firms that cannot do matching. They still have a very good FX
risk management tool: Diversifying internationally the firm. (Portfolio

True international diversification means to diversify:
location of production, sales, input sources, borrowing of funds, etc.

• In general, the variability of CF is reduced by diversification:
        St is likely to increase the firm's competitiveness in some
markets while reducing it in others.
                         EE should be low.

• Not surprisingly big MNF do not have EE.
• Observation taken from Bloomberg.com (November 20, 2007)
(Dollar Will Weather the Whines, Jeers and Jokes: John M. Berry)
[...] As for jokes, one attempt really wasn't very funny. A cartoon by
Mike Luckovich of the Atlanta Journal-Constitution reprinted in the
Nov. 18 New York Times showed Treasury Secretary Henry Paulson, in
the Oval Office with President George W. Bush, asking, ``Can I get paid
in euros?'‘

Paying in Euros
Actually, Zodiac SA, Europe's biggest maker of airplane seats, would
like to get paid in euros.
Zodiac sells both to Boeing Co. and its European competitor Airbus
SAS, the world's two largest manufacturers of commercial aircraft. It's
hardly surprising that Boeing insists on paying its suppliers in dollars.
However, so does Airbus because so many of its own sales are priced in
              Should a Firm Hedge?

• Fundamental question: Does hedging add value to a firm?

There are two views:
(1) Modigliani-Miller Theorem (MMT):         hedging adds no value.
(2) MMT assumptions are violated             hedging adds value.

The MMT depends on a set of assumptions:
  MM requires that a firm operates in perfect markets.
• Hedging is Irrelevant: The MMT
Intuition: What is the value of your car?
Example: You bought a last year car using a bank loan.
Q: Is the value of your car affected by the loan you took to pay for it?

• MMT provides a similar story to value a firm.
  - Firms make money if they make good investments.
  - The financing source of those good investments is irrelevant.
  - Different mechanisms of financing will determine how the cash
  flows are divided among shareholders or bondholders.

• MMT's hedging implications.
If the methods of financing and the character of financial risks do not
    matter, managing them is not important:
                hedging should not add any value to a firm.
• On the contrary, since hedging is not free, hedging might reduce the
  value of a firm.

• MM also say that investors can diversify their portfolio of holding.

Example: Ms. Sternin holds shares of a U.S. exporting firm and shares
  of a U.S. importing firm. Ms. Sternin's portfolio is hedged.

A USD depreciation will negatively affect the importing firm and will
  positively affect the exporting firm.

Hedging at the firm level -since it is expensive- will negatively affect the
  value of Ms. Sternin portfolio. ¶
• Hedging Adds Value
Key: MMT assumptions are violated in the "real-world.“

(1) Investors might not be able to replicate an optimal hedge
Sometimes firms can do a better job at hedging than individuals.
   Example: Investors might not        be big enough
                                       have enough information

(2) Hedging as a tool to reduce the risk of bankruptcy
If cash flows are very volatile, a firm might be faced with the problem of
   needing cash to meet its debt obligations.

Conclusion: Firms with little debt or with good access to credit have no
  need to hedge.

Note: Under this view, large corporations may be wasting their capital.
(3) Hedging as a tool to reduce investment uncertainty
Firms should hedge to ensure they always have sufficient cash flow to
   fund their planned investment plan.
For example, an exporting firm might have cash flows problems in
   periods when the USD appreciates.

Example: Merk, a U.S. pharmaceutical firm, has used derivatives to
  ensure that investment (R&D) plans can always be financed. ¶

(4) Stable CFs to get bank financing.

(5) Herding: “Everybody else is hedging. I should hedge too; otherwise, I
   may not look good.”
• Do U.S. Firms Hedge?
From a survey of the largest 250 U.S. MNCs, taken in (2001):
(1) Most of the MNCs in the survey understood
translation, transactions, and economic exposure
completely or substantially.
(2) A large percentage (32% - 44%) hedged
themselves substantially or partially. However, a
larger percentage did not cover themselves at all
against transactions and economic exposure.
(3) A significant percentage of the firms' hedging decisions depended on
future FX fluctuations.
(4) Over 25% of firms indicated that they used the forward hedge.
(5) The majority of the firms surveyed have a better understanding of
transactions and translation exposure than of economic exposure.
• Canadian Evidence
The Bank of Canada conducts an annual survey
of FX hedging. The main findings from the 2011
survey are:

• Companies hedge approximately 50% of their FX risk.
• Usually, hedging is for maturities of six months or less.
• Use of FX options is relatively low, mainly because of accounting rules
   and restrictions imposed by treasury mandate, rules or policies.
• Growing tendency for banks to pass down the cost of credit (credit
   valuation adjustment) to their clients.
• Exporters were reluctant to hedge because they were anticipating that
   the CAD would depreciate. On the other hand, importers increased
   both their hedging ratio and duration.
Joke: Talking About Accounting
Never trust your Accountant or Stockbroker - The Franciscan

The Godfather, accompanied by his stockbroker, walks into a room to meet with his
accountant. The Godfather asks the accountant, “Where’s the three million bucks you
embezzled from me?” The accountant doesn’t answer. The Godfather asks again,
“Where’s the three million bucks you embezzled from me?”
The stockbroker interrupts, “Sir, the man is a deaf-mute and cannot understand you, but
I can interpret for you.” The Godfather says, “Well, ask him where the @#!* money is.”
The stockbroker, using sign language, asks the accountant where the three million
dollars is. The accountant signs back, “I don’t know what you’re talking about.” The
stockbroker interprets to the Godfather, “He doesn’t know what you’re talking about.”
The Godfather pulls out a pistol, puts it to the temple of the accountant, cocks the
trigger and says, “Ask him again where the @#!* money is!”
The stockbroker signs to the accountant, “He wants to know where it is!” The
accountant signs back, “Okay! Okay! The money’s hidden in a suitcase behind the shed
in my backyard!”
The Godfather says, “Well, what did he say?” The stockbroker interprets to the
Godfather, “He says that you don’t have the guts to pull the trigger.”

To top