Transcript Assessing Foreign Exchange Exposure

FIN 40500: International
Finance
Assessing Foreign Exchange Risk
There is a “true” probability distribution
that governs the outcome of a coin toss
PrHeads  PrTails   .5
Suppose that we were to flip a coin over and over again
and after each flip, we calculate the percentage of heads
& tails
# of Heads
Total Flips
(Sample Statistic)
.5
(True Probability)
That is, if we collect “enough” data, we can eventually learn the
truth!
Continuous distributions

Probability
N ,
-3
SD
-2
SD
2

-1
SD
Probability distributions
identify the chance of
each possible event
occurring
Mean
65%
95%
99%
1
SD
2
SD
3
SD
Event
Sampling
Suppose that you wanted to learn about the temperature in South Bend
Temperature ~ N
, 
2
We could find this distribution by collecting temperature data for south bend
Sample Mean
(Average)
Sample
Variance
1N
x    xi  
 N  i 1
N
1


2
2
s     xi  x    2
 N  i 1
Conditional Distributions
Obviously, the temperature in
South Bend is different in the
winter and the summer. That
is, temperature has a
conditional distribution
 ,  
N  ,  
Temp (Summer) ~ N
Temp (Winter) ~
s
W
2
s
2
W
Regression is based on the estimation of conditional distributions
Some useful properties of probability distributions

Probability distributions
are scaleable
x  N μ,σ 2
y  kx


y  N k,k 2σ 2

=
3X
Mean = 1
Mean = 3
Variance = 4
Variance = 36 (3*3*4)
Std. Dev. = 2
Std. Dev. = 6
 
y  N  ,σ 
x  y  N    ,σ
x  N μ x ,σ x2
Probability distributions
are additive
y
2
y
x
y
2
x
 σ y2  2 cov xy
=
+
Mean = 1
Mean = 2
Mean = 3
Variance = 1
Variance = 9
Variance = 14 (1 + 9 + 2*2)
Std. Dev. = 1
Std. Dev. = 3
Std. Dev. = 3.7
COV = 2

Suppose we know that your salary is based on your shoe size:
Salary = $20,000 +$2,000 (Shoe Size)
Shoe Size
Salary
Mean = 6
Mean = $ 32,000
Variance = 4
Variance = 16,000,000
Std. Dev. = 2
Std. Dev. = $ 4,000
We could also use this to forecast:
Salary = $20,000 +$2,000 (Shoe Size)
If Bigfoot had a
job…how much would
he make?
Salary = $20,000 +$2,000 (50) = $120,000
Size 50!!!
Searching for the truth….
You believe that there is a relationship between shoe size and
salary, but you don’t know what it is….
1. Collect data on salaries and shoe
sizes
2. Estimate the relationship
between them
Note that while the true distribution of shoe size is N(6,2), our
collected sample will not be N(6,2). This sampling error will
create errors in our estimates!!
70000
60000
Salary
50000
40000
30000
20000
Slope = b
a
10000
0
0
2
4
6
8
10
12
14
Shoe Size
Salary = a +b * (Shoe Size) + error

error  N 0,σ
We want to choose ‘a’ and ‘b’ to minimize the error!
2

Regression Results
Variable
Coefficients
Intercept
Shoe
Standard Error
t Stat
45415.65
1650.76
27.51
1014.75
257.21
3.94
We have our estimate of “the truth”
Salary = $45,415 + $1,014 * (Shoe Size) + error
Intercept (a)
Shoe (b)
Mean = $45,415
Mean = $1,014
Std. Dev. = $1,650
Std. Dev. = $257
T-Stats bigger
than 2 are
considered
statistically
significant!
Regression Statistics
Multiple R
Standard Error
0.17
11673.01
Percentage of income
variance explained by
shoe size
Error Term
Mean = 0
Std, Dev = $11,673
Using regressions to forecast (Remember,
Bigfoot wears a size 50)….
50
Salary = $45,415 + $1,014 * (Shoe Size) + error
Mean = $45,415
Mean = $1,014
Mean = $0
Std. Dev. = $1,650
Std. Dev. = $ 257
Std. Dev. = $11,673
StdDev  (1,650)  (50) (257)  (11,673)  $17,438
2
2
Salary Forecast
Mean = $96,115
Std. Dev. = $17,438
2
2
Given his shoe size, you are
95% sure Bigfoot will earn
between $61,239 and $130,991
We’ve looked at several currency pricing models that have
potential for being “the truth”
%et    NX t
Trade Balance Approach

%et      t   t*

%et     i  i *


Price Level Approach
Interest Rate Approach


%et  E  %f t i 
 i 1



%et  E  %et i 
 i 1

Monetary Approach
Technical Approach
Any combination of these could be “the truth”!!
PPP and the Swiss Franc
10
% Change in Exchange Rate
8
6
4
2
0
-10.0
-5.0
-2
0.0
5.0
10.0
15.0
-4
-6
-8
-10
Inflation Differential


%et  a  b  t     t
*
t
Note: PPP implies that
a = 0 and b = 1
Regression Results
Variable
Coefficients
Standard Error
t Stat
Intercept
.027
.231
.12
Inflation
1.40
.742
1.89
Regression Results
Variable
P-value
Lower 95%
Upper 95%
Intercept
.910
-.49
.43
Inflation
.06
-.065
2.86
Regression Statistics
R Squared
.02
Standard Error
2.69
Observations
155
For every 1% increase in
US inflation over Swiss
inflation, the dollar
depreciates by 1.40%
10
8
6
4
2
0
1
6
11
16
21
26
31
36
41
46
51
56
61
66
71
76
81
86
91
96 101 106 111 116 121 126 131 136 141 146 151
-2
-4
-6
-8
-10
Predicted
Actual
Obviously, we have not explained very much of the volatility in
the CHF/USD exchange rate
UIP and the Swiss Franc
10
8
% Change in e
6
4
2
0
-0.4
-0.3
-0.2
-0.1
-2
0
0.1
0.2
0.3
0.4
0.5
-4
-6
-8
-10
Interest Differential


%et  a  b it  i   t
*
t
Note: UIP implies that
a = 0 and b = 1
Regression Results
Variable
Coefficients
Intercept
Interest Rate
Standard Error
t Stat
.55
.31
1.77
-2.87
1.53
-1.87
Regression Results
Variable
P-value
Lower 95%
Upper 95%
Intercept
.07
-.06
1.18
Interest Rate
.06
-5.89
.15
Regression Statistics
R Squared
.02
Standard Error
2.69
Observations
155
For every 1% increase in US
interest rates over Swiss interest
rates, the dollar appreciates by
2.87%
10
8
6
4
2
0
1
7
13
19
25
31
37
43
49
55
61
67
73
79
85
91
97
103 109 115 121 127 133 139 145 151
-2
-4
-6
-8
-10
Exchange Rate
Predicted Exchange Rate
We still have not explained very much of the volatility in the
CHF/USD exchange rate
Using regressions to forecast….
(3 – 1.5) = 1.5


%et  .55  2.87 it  it*   t
Mean = .55
Mean = -2.87
Mean = 0
Std. Dev. = .31
Std. Dev. = 1.53
Std. Dev. = 2.69
StdDev  (.31) 2  (1.5) 2 (1.53) 2  (2.69) 2  3.58%
Salary Forecast
Mean = -3.755%
Std. Dev. = 3.58%
Given current interest rates, you
are 95% sure that the % change in
the exchange rate will be between
-10.91% and 3.40%!!
Technical Analysis Uses prior movements in the exchange rate
to predict the future
10
8
6
% Change (t)
4
2
0
-10
-8
-6
-4
-2
-2
0
-4
-6
-8
-10
%Change (t-1)
%et  a  b%et 1    t
2
4
6
8
10
Regression Results
Variable
Coefficients
Standard Error
t Stat
Intercept
.12
.21
.57
Prior Change
.29
.07
3.86
Regression Results
Variable
P-value
Intercept
Prior Change
Lower 95%
.56
-.29
.53
.0001
.14
.45
Regression Statistics
R Squared
Upper 95%
.09
Standard Error
2.59
Observations
154
A 1% depreciation of the
dollar is typically followed by
a .29% depreciation
BLADES Board & Skate arrived on the action /
extreme scene in 1990, and quickly became a
trusted source of equipment and service to in-line
skaters, skateboarders, and snowboarders.
BLADES got its start in New York and currently
operates 15 retail stores in New York, New
Jersey, Massachusetts and Pennsylvania.
Blades could cut
costs by importing
lower cost
components from
Thailand
Increasing
competition and
rising costs have
lowered Blades’
profit margins
Suppose that Blades makes an agreement to buy plastic
components sufficient to produce 72,000 pairs of
rollerblades from Thai manufacturers at a price of THB
2,870 per pair. ($1 = THB 38.87). Payment is due in one
month (72,000*2,870 = THB 206.64 M)
Trend
Should Blades import components from
Thailand?
$75 Per Pair
At the current
exchange rate,
Blades could cut
their costs by 1.6%
by importing from
Thailand
THB 2,870 per pair
(THB 1 = $ .0257)
THB 2,870 (.0257) = $73.75
$75 - $73.75
$75
100 = 1.6%
However, importing Thai components
creates a transaction exposure for Blades
THB 2,870 per pair
(THB 1 = $ .0257)
Costs ($) = e ($/THB) * 72,000* Costs (THB)
Random
Variable
Constant
We need to
estimate this!!
Regression Results
Variable
Coefficients
Standard Error
t Stat
Intercept
. 80
.02
40
Inflation
.80
.35
2.28
Regression Statistics
R Squared
.43
Standard Error
2.20
Observations
240
%e  a  b   *  
Every 1% difference between US inflation and Thai inflation
depreciates the dollar by .8%
US inflation is currently 1% (per month) while
inflation in Thailand is 2.25% (per month)
(1 – 2.25) = -1.25
%e  a  b   *  
Mean = . 80
Mean = .80
Mean = 0
Std. Dev. = .02
Std. Dev. = . 35
Std. Dev. = 2.20
StdDev  (.02) 2  (.35) 2 (1.25) 2  (2.20) 2  2.25%
Forecast
Mean = -.2%
Std. Dev. = 2.25%
Your 95% confidence interval for
the (monthly) percentage change
in the exchange rate is
[-4.7% , 4.3% ]
Assessing transaction exposure
THB 2,870 per pair
(THB 1 = $ .0257)
Costs ($) = e ($/THB) * 72,000*2,870 THB
Forecast (% Change)
Mean = -.2%
Std. Dev. = 2.25%
Costs
Mean = 72,000*2,870*.0257(1-.002)
= $5,300,026
Std. Dev. = .0225*72000*2870*.0256
= $119,250
Assessing transaction exposure
THB 2,870 per pair
(THB 1 = $ .0257)
Costs ($) = e ($/THB) * 72,000*2,870 THB
Mean = $5,300,026
Std. Dev. = $119,250
You are 95% sure your costs will
be between:
$5,300,026 + 2*$119,250 = $5,538,526
and
$5,300,026 - 2*$119,250 = $5,061,526
Should Blades import components from
Thailand?
$75 Per Pair
THB 2,870 per pair
(THB 1 = $ .0257)
Mean = $5,400,000
Mean = $5,300,026
Std. Dev. = $0
Std. Dev. = $119,250
What do you do?
Blades is also thinking
about exporting rollerblades
to Thailand
Suppose that Blades makes an agreement to sell 30,000
pairs of roller blades to a Thai sporting goods store for
THB 4,500 apiece.
Trend
Assessing transaction exposure
Net Cash Flows($) = e ($/THB) * ( 72,000*2,870 - 30,000*4,500)
= e ($/THB) * ( 71,640,000THB)
Forecast (% Change)
Mean = -.2%
Std. Dev. = 2.25%
Net Cash Flows($)
Mean = 71,640,000*.0257(1-.002)
= $1,837,465
Std. Dev. = .0225*71,640,000*.0257
= $41,342
Blades could also import
Japanese components.
Japanese components are
slightly more expensive
(Y 8,000 per pair = $74.77)
$1 = Y 107
Suppose that Blades splits its purchases of
components between Thailand and Japan
(Exports to Thailand = 0)
THB 2,870 per pair
(THB 1 = $ .0257)
THB 2,870*.0257*36,000 = $2,655,324
JPY 8,000 per pair
(JPY 1 = $ .0093)
JPY 8,000*.0093*36,000 = $2,678,400
$5,333,724
Forecast (% Change)
Forecast (% Change)
Mean = 0%
Mean = 0%
Std. Dev. = 2.25%
Std. Dev. = 3.50%
CORR = -.65
$2,655,324
= .49
$5,333,724
$2,678,400
$5,333,724
= .51
Net Cash Flows
Mean  $5,333,724
SD 
.492 .02252  (.51) 2 (.035) 2  2(.49)(.51)(.0225)(.035)( .65)  .014  1.4%
Cash flow Situation…
And the Currencies
are…
Equal Inflows/Outflows of Two
Currencies
Positively Correlated
Equal Inflows/Outflows of Two
Currencies
Uncorrelated
Currency
exposure
High
Moderate
Equal Inflows/Outflows of Two
Currencies
Negatively Correlated
Low
Inflow in one currency/outflow
in another
Positively Correlated
Low
Inflow in one currency/outflow
in another
Uncorrelated
Inflow in one currency/outflow
in another
Negatively Correlated
Moderate
High
Importing from both Japan and Thailand can diversify currency
exposure!!
Suppose that Blades is planning to expand sales into
England. Should they try and invoice in dollars or
Pounds?
Current
Forecast (% Change)
GBP 1 = $1.80
Mean = 0
SD = 2.0%
Contracting sales in GBP creates transaction exposure.
However, contracting sales in USD creates economic exposure
Suppose that Blades agrees to sell roller blades
to England for $125 apiece. (GBP 70)
Current
Forecast (% Change)
GBP 1 = $1.80
Mean = 0
SD = 2.0%
Demand in England is as follows:
Q = 400 - 3P
P = Local price of
Roller blades
At a local price of GBP 70, demand equal 500 - 3(70) = 190
Q = 400 – 3P
P
Qd
%Qd
Qd
Qd P
d 


P
%P
P Qd
P
1%
70
1.1%
# Roller Blades
190
Elasticity of Demand refers to
the responsiveness of demand
to price changes
Qd P
 70 
d 
 3
  1.11
P Qd
 190 
Suppose that Blades agrees to sell roller blades to
England for $125 apiece. (GBP 70)
Current
Forecast (% Change)
GBP 1 = $1.80
Mean = 0
SD = 2.0%
Revenues = Price ($) * Quantity
Constant
Forecast (% Change)
Mean = 0
SD = 2.0%(Elasticity) = 2.2%
GBP Pricing (Transaction Exposure)
Revenues = e ($/L)* Price (L) * Quantity
Forecast (% Change)
Mean = 0
Constant
SD = 2.0
USD Pricing (Economic Exposure)
Revenues = Price ($) * Quantity
Constant
Forecast (% Change)
Mean = 0
SD = 2.0%(Elasticity) = 2.2%
Changes in currency prices can have all kinds of economic
impacts. A more general way to estimate economic exposure
would be as follows:
PCFt  a  bet   t
Percentage change in cash
flows (measured in home
currency)
Percentage change in the
exchange rate ($/F)
Regression Results
Variable
Coefficients
Intercept
% Change in
Exchange Rate
Regression Statistics
R Squared
Standard Error
Observations
.63
Standard Error
t Stat
.05
1.5
.03
-3.35
.97
-3.45
PCFt  a  bet  
1.20
1,000
Every 1% depreciation in the dollar relative to the British
pound lowers cash flows from England by 3.35%
Suppose that Blades sets up a Thai subsidiary. The
Thai plant uses locally produced components to
produce roller blades that will be sold to local (Thai)
customers.
Is Blades still exposed to currency risk?
Blades will need to produce consolidated cash flow and income statements as
well as a consolidated balance sheet. Translation exposure refers to the
impact of exchange rate changes on these financial statements.
FASB Rule #52 (for US Based MNCs)
The functional currency of an entity is the currency of the economic
environment in which the entity operates
The current exchange rate as of the reporting date is used to translate
assets/liabilities from the functional currency to the reporting currency
The weighted average exchange rate over the relevant reporting period
is used to translate revenues, expenses, gains, and losses
Translated Gains/Losses are not recognized as current net income, but
are reported as a second component of stockholders’ equity
Should we be worried about this type of
exposure??