Assessing Foreign Exchange Risk FIN 40500: International Finance

There is a “true” probability distribution that governs the outcome of a coin toss Suppose that we were to flip a coin over and over again and after each flip, we calculate the percentage of heads & tails That is, if we collect “enough” data, we can eventually learn the truth! (Sample Statistic)(True Probability)

Probability Event Mean Probability distributions identify the chance of each possible event occurring 1 SD 2 SD 3 SD -1 SD -2 SD -3 SD 65% 95% 99% Continuous distributions

Sampling Suppose that you wanted to learn about the temperature in South Bend Temperature ~ We could find this distribution by collecting temperature data for south bend Sample Mean (Average) Sample Variance

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) ~ Temp (Winter) ~ Regression is based on the estimation of conditional distributions

Mean = 1 Variance = 4 Std. Dev. = 2 Probability distributions are scaleable 3 X = Mean = 3 Variance = 36 (3*3*4) Std. Dev. = 6 Some useful properties of probability distributions

Mean = 1 Variance = 1 Std. Dev. = 1 Probability distributions are additive + Mean = 2 Variance = 9 Std. Dev. = 3 COV = 2 = Mean = 3 Variance = 14 ( *2) Std. Dev. = 3.7

Mean = 6 Variance = 4 Std. Dev. = 2 Mean = $ 32,000 Variance = 16,000,000 Std. Dev. = $ 4,000 Suppose we know that your salary is based on your shoe size: Salary = $20,000 +$2,000 (Shoe Size) Shoe Size Salary

We could also use this to forecast: Salary = $20,000 +$2,000 (Shoe Size) If Bigfoot had a job…how much would he make ? Size 50!!! Salary = $20,000 +$2,000 (50) = $120,000

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!!

Salary = a +b * (Shoe Size) + error a Slope = b We want to choose ‘a’ and ‘b’ to minimize the error!

Regression Results VariableCoefficientsStandard Errort Stat Intercept Shoe Salary = $45,415 + $1,014 * (Shoe Size) + error We have our estimate of “the truth” Intercept (a) Mean = $45,415 Std. Dev. = $1,650 Shoe (b) Mean = $1,014 Std. Dev. = $257 T-Stats bigger than 2 are considered statistically significant!

Regression Statistics Multiple R0.17 Standard Error Error Term Mean = 0 Std, Dev = $11,673 Percentage of income variance explained by shoe size

Using regressions to forecast (Remember, Bigfoot wears a size 50)…. Salary = $45,415 + $1,014 * (Shoe Size) + error 50 Mean = $45,415 Std. Dev. = $1,650 Mean = $1,014 Std. Dev. = $ 257 Mean = $0 Std. Dev. = $11,673 Salary Forecast Mean = $96,115 Std. Dev. = $17,438 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” Any combination of these could be “the truth”!! Trade Balance Approach Monetary Approach Interest Rate Approach Price Level Approach Technical Approach

Note: PPP implies that a = 0 and b = 1 PPP and the Swiss Franc

Regression Results VariableCoefficientsStandard Errort Stat Intercept Inflation Regression Results VariableP-valueLower 95%Upper 95% Intercept Inflation Regression Statistics R Squared.02 Standard Error2.69 Observations155 For every 1% increase in US inflation over Swiss inflation, the dollar depreciates by 1.40%

Obviously, we have not explained very much of the volatility in the CHF/USD exchange rate

Note: UIP implies that a = 0 and b = 1 UIP and the Swiss Franc

Regression Results VariableCoefficientsStandard Errort Stat Intercept Interest Rate Regression Results VariableP-valueLower 95%Upper 95% Intercept Interest Rate Regression Statistics R Squared.02 Standard Error2.69 Observations155 For every 1% increase in US interest rates over Swiss interest rates, the dollar appreciates by 2.87%

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 Mean =.55 Std. Dev. =.31 Mean = Std. Dev. = 1.53 Mean = 0 Std. Dev. = 2.69 Salary Forecast Mean = % Std. Dev. = 3.58% Given current interest rates, you are 95% sure that the % change in the exchange rate will be between % and 3.40%!!

Technical Analysis Uses prior movements in the exchange rate to predict the future

Regression Results VariableCoefficientsStandard Errort Stat Intercept Prior Change Regression Results VariableP-valueLower 95%Upper 95% Intercept Prior Change Regression Statistics R Squared.09 Standard Error2.59 Observations154 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.

Increasing competition and rising costs have lowered Blades’ profit margins Blades could cut costs by importing lower cost components from Thailand

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 M) Trend

THB 2,870 per pair (THB 1 = $.0257) Should Blades import components from Thailand? $75 Per Pair THB 2,870 (.0257)= $73.75 $75 - $73.75 $ = 1.6% At the current exchange rate, Blades could cut their costs by 1.6% by importing from Thailand

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) Constant Random Variable We need to estimate this!!

Regression Results VariableCoefficientsStandard Errort Stat Intercept Inflation Regression Statistics R Squared.43 Standard Error2.20 Observations240 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) = Mean =. 80 Std. Dev. =.02 Mean =.80 Std. Dev. =. 35 Mean = 0 Std. Dev. = 2.20 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% ]

Forecast (% Change) Mean = -.2% Std. Dev. = 2.25% Assessing transaction exposure Costs ($) = e ($/THB) * 72,000*2,870 THB THB 2,870 per pair (THB 1 = $.0257) Costs Mean = 72,000*2,870*.0257(1-.002) = $5,300,026 Std. Dev. =.0225*72000*2870*.0256 = $119,250

Assessing transaction exposure Costs ($) = e ($/THB) * 72,000*2,870 THB You are 95% sure your costs will be between: $5,300, *$119,250 = $5,538,526 and $5,300, *$119,250 = $5,061,526 THB 2,870 per pair (THB 1 = $.0257) Mean = $5,300,026 Std. Dev. = $119,250

THB 2,870 per pair (THB 1 = $.0257) Should Blades import components from Thailand? $75 Per Pair Mean = $5,300,026 Std. Dev. = $119,250 Mean = $5,400,000 Std. Dev. = $0 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

Forecast (% Change) Mean = -.2% Std. Dev. = 2.25% Assessing transaction exposure Net Cash Flows($) = e ($/THB) * ( 72,000*2, ,000*4,500) Net Cash Flows($) Mean = 71,640,000*.0257(1-.002) = $1,837,465 Std. Dev. =.0225*71,640,000*.0257 = $41,342 = e ($/THB) * ( 71,640,000THB)

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) JPY 8,000 per pair (JPY 1 = $.0093) THB 2,870*.0257*36,000 = $2,655,324 JPY 8,000*.0093*36,000 = $2,678,400 $5,333,724

$2,678,400 $5,333,724 Forecast (% Change) Mean = 0% Std. Dev. = 2.25% Forecast (% Change) Mean = 0% Std. Dev. = 3.50% $2,655,324 $5,333,724 =.49=.51 CORR = -.65 Net Cash Flows

Cash flow Situation… And the Currencies are… Currency exposure Equal Inflows/Outflows of Two CurrenciesPositively CorrelatedHigh Equal Inflows/Outflows of Two CurrenciesUncorrelatedModerate Equal Inflows/Outflows of Two CurrenciesNegatively CorrelatedLow Inflow in one currency/outflow in anotherPositively CorrelatedLow Inflow in one currency/outflow in anotherUncorrelatedModerate Inflow in one currency/outflow in anotherNegatively CorrelatedHigh 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 GBP 1 = $1.80 Forecast (% Change) 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 GBP 1 = $1.80 Forecast (% Change) Mean = 0 SD = 2.0% Demand in England is as follows: Q = P P = Local price of Roller blades At a local price of GBP 70, demand equal (70) = 190

Elasticity of Demand refers to the responsiveness of demand to price changes Q = 400 – 3P # Roller Blades P % 1.1%

Suppose that Blades agrees to sell roller blades to England for $125 apiece. (GBP 70) Current GBP 1 = $1.80 Forecast (% Change) Mean = 0 SD = 2.0% Revenues = Price ($) * Quantity Constant Forecast (% Change) Mean = 0 SD = 2.0%(Elasticity) = 2.2%

Revenues = Price ($) * Quantity Constant Forecast (% Change) Mean = 0 SD = 2.0%(Elasticity) = 2.2% Revenues = e ($/L)* Price (L) * Quantity Constant Forecast (% Change) Mean = 0 SD = 2.0 GBP Pricing (Transaction Exposure) USD Pricing (Economic Exposure)

Changes in currency prices can have all kinds of economic impacts. A more general way to estimate economic exposure would be as follows: Percentage change in the exchange rate ($/F) Percentage change in cash flows (measured in home currency)

Regression Results VariableCoefficientsStandard Errort Stat Intercept % Change in Exchange Rate Regression Statistics R Squared.63 Standard Error1.20 Observations1,000 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??