# Anatomy of a Currency Crisis

Document Sample

```					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

.5
Total Flips
(Sample Statistic)           (True Probability)

That is, if we collect “enough” data, we can eventually learn the
truth!
Continuous distributions

Probability         
N  ,    2
                     Probability distributions
identify the chance of
each possible event
occurring

Event
-3        -2   -1      Mean   1    2    3
SD        SD   SD             SD   SD   SD

65%

95%

99%
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

1N
Sample Mean         x    xi  
(Average)
 N  i 1

1N
Sample
s     xi  x    2
2                 2
Variance
 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

Temp (Summer) ~ N  ,  
2
s   s

Temp (Winter) ~ N  ,  
2
W       W

Regression is based on the estimation of conditional distributions
Some useful properties of probability distributions


x  N μ,σ 2        
Probability distributions        y  kx
are scaleable

y  N k,k σ      2   2


3X                        =
Mean = 1                   Mean = 3
Variance = 4               Variance = 36 (3*3*4)
Std. Dev. = 2              Std. Dev. = 6
 
x  N μ x ,σ x
2

Probability distributions             y  N  ,σ 
y
2
y

x  y  N    ,σ                             
x       y
2
x    σ y  2 covxy
2

+                          =
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)

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

50000
Salary

40000

30000

20000
a                       Slope = b
10000

0
0       2   4   6      8       10       12       14
Shoe Size

Salary = a +b * (Shoe Size) + error            error  N 0,σ          2

We want to choose ‘a’ and ‘b’ to minimize the error!
Regression Results
Variable            Coefficients     Standard Error            t Stat
Intercept                    45415.65                1650.76           27.51
Shoe                           1014.75                257.21             3.94

We have our estimate of “the truth”
T-Stats bigger
Salary = \$45,415 + \$1,014 * (Shoe Size) + error                than 2 are
considered
statistically
significant!

Intercept (a)              Shoe (b)
Mean = \$45,415             Mean = \$1,014
Std. Dev. = \$1,650         Std. Dev. = \$257
Regression Statistics                  Percentage of income
Multiple R                           0.17       variance explained by
Standard Error                   11673.01       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        2                2

Salary Forecast
Given his shoe size, you are
Mean = \$96,115            95% sure Bigfoot will earn
between \$61,239 and \$130,991
Std. Dev. = \$17,438
We’ve looked at several currency pricing models that have
potential for being “the truth”

%et    NX t               Trade Balance Approach


%et      t   t*       Price Level Approach


%et     i  i *   
Interest Rate Approach
          
%et  E  %f t i 
 i 1                Monetary Approach

         
%et  E  %et i            Technical Approach
 i 1     
Any combination of these could be “the truth”!!
PPP and the Swiss Franc
10

8

6
% Change in Exchange Rate

4

2

0
-10.0   -5.0             0.0        5.0     10.0      15.0
-2

-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
For every 1% increase in
R Squared                        .02     US inflation over Swiss
Standard Error                 2.69      inflation, the dollar
Observations                     155     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

6

4
% Change in e

2

0
-0.4   -0.3   -0.2       -0.1         0   0.1       0.2     0.3   0.4   0.5
-2

-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        Standard Error       t Stat
Intercept                       .55                .31           1.77
Interest Rate                  -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              For every 1% increase in US
R Squared                     .02       interest rates over Swiss interest
rates, the dollar appreciates by
Standard Error               2.69       2.87%
Observations                 155
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
Given current interest rates, you
Mean = -3.755%          are 95% sure that the % change in
the exchange rate will be between
Std. Dev. = 3.58%       -10.91% and 3.40%!!
Technical Analysis Uses prior movements in the exchange rate
to predict the future

10

8

6

4
% Change (t)

2

0
-10   -8   -6   -4   -2           0       2   4   6   8   10
-2

-4

-6

-8

-10
%Change (t-1)

%et  a  b%et 1    t
Regression Results
Variable        Coefficients            Standard Error        t Stat
Intercept                            .12                .21               .57
Prior Change                         .29                .07           3.86

Regression Results
Variable        P-value            Lower 95%          Upper 95%
Intercept                     .56              -.29           .53
Prior Change            .0001                  .14            .45

Regression Statistics                 A 1% depreciation of the
R Squared                           .09     dollar is typically followed by
a .29% depreciation
Standard Error                  2.59

Observations                        154
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.
costs by importing
lower cost
components from
Thailand

Increasing
competition and
rising costs have
profit margins
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
Thailand?

THB 2,870 per pair
\$75 Per Pair
(THB 1 = \$ .0257)

At the current
exchange rate,
their costs by 1.6%               THB 2,870 (.0257) = \$73.75
by importing from
Thailand
\$75 - \$73.75
100 = 1.6%
\$75
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            Constant
Variable

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
%e  a  b   *  
Standard Error                2.20

Observations                   240

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
the (monthly) percentage change
Mean = -.2%                      in the exchange rate is
[-4.7% , 4.3% ]
Std. Dev. = 2.25%
Assessing transaction exposure
THB 2,870 per pair
(THB 1 = \$ .0257)

Costs (\$) = e (\$/THB) * 72,000*2,870 THB

Forecast (% Change)              Costs
Mean = -.2%
Mean = 72,000*2,870*.0257(1-.002)
Std. Dev. = 2.25%
= \$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
You are 95% sure your costs will
Std. Dev. = \$119,250
be between:
\$5,300,026 + 2*\$119,250 = \$5,538,526
and
\$5,300,026 - 2*\$119,250 = \$5,061,526
Thailand?

THB 2,870 per pair
\$75 Per Pair
(THB 1 = \$ .0257)

Mean = \$5,400,000                       Mean = \$5,300,026
Std. Dev. = \$0                          Std. Dev. = \$119,250

What do you do?
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)            Net Cash Flows(\$)
Mean = -.2%
Mean = 71,640,000*.0257(1-.002)
Std. Dev. = 2.25%
= \$1,837,465
Std. Dev. = .0225*71,640,000*.0257
= \$41,342
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 8,000*.0093*36,000 = \$2,678,400
(JPY 1 = \$ .0093)
\$5,333,724
Forecast (% Change)               Forecast (% Change)
Mean = 0%                         Mean = 0%
Std. Dev. = 2.25%                 Std. Dev. = 3.50%

CORR = -.65

\$2,655,324                                            \$2,678,400
= .49                                                         = .51
\$5,333,724                                            \$5,333,724

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%
And the Currencies       Currency
Cash flow Situation…                are…               exposure
Equal Inflows/Outflows of Two
Currencies                    Positively Correlated         High
Equal Inflows/Outflows of Two
Currencies                    Uncorrelated                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             Moderate
Inflow in one currency/outflow
in another                       Negatively Correlated      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
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:
P = Local price of
Q = 400 - 3P              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            
1%                             %P    P    P Qd
70                                            P

1.1%
190

Elasticity of Demand refers to
Qd P     70 
the responsiveness of demand
d         3       1.11
to price changes
P Qd     190 
England for \$125 apiece. (GBP 70)

Current                  Forecast (% Change)

GBP 1 = \$1.80            Mean = 0
SD = 2.0%

Revenues = Price (\$) * Quantity

Forecast (% Change)
Constant
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

Forecast (% Change)
Constant
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     Percentage change in the
flows (measured in home       exchange rate (\$/F)
currency)
Regression Results
Variable          Coefficients          Standard Error    t Stat
Intercept                             .05                1.5            .03
% Change in
Exchange Rate                        -3.35               .97        -3.45

Regression Statistics
PCFt  a  bet  
R Squared                      .63

Standard Error                1.20

Observations                 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