At the firm level, currency risk is called exposure

By Anthony Davis,2014-11-22 17:49
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At the firm level, currency risk is called exposure

10/2 Ch 10

    Measuring FX Exposure

At the firm level, currency risk is called FX exposure. Recall that currency risk describes

    how the value of an asset/liability fluctuates due to changes in S. t

Three areas of FX exposure:

    (1) Transaction exposure: Risk of transactions denominated in FX.

    (2) Economic exposure: Degree to which a firm's expected cash flows are affected by unexpected changes in S. t

    (3) Translation exposure: Accounting-based changes in a firm's consolidated statements that result from a change in S. t

Example: The different FX exposures.

    A. Transaction exposure.

    Swiss Cruises, a Swiss firm, sells cruise packages to U.S. customers priced in USD. SC also has several U.S. suppliers that price in USD.

B. Economic exposure.

    SC has the majority of its costs denominated in CHF. Almost 50% of its revenue is in USD. The CHF appreciates against the USD. SC cannot increase the USD prices of its cruise packages (competitive business). SC’s net CHF cash flows will be affected.

C. Translation exposure.

    SC has inventories in USD and a USD loan from a U.S. bank of equal USD amounts. These balance sheet items will be translated to CHF. Due to Swiss accounting rules, different exchange rates are used to translate USD inventories and the USD loan to CHF. Thus, an accounting gain/loss will be generated. ?

Q: How can FX changes affect the firm?

     Transaction Exposure

    Short-term CFs: Existing contractual obligations

• Economic Exposure

    Future CFs: Erosion of competitive position

• Translation Exposure

    Revaluation of balance sheet (book value vs market value)

Q #1: How do we measure these FX exposures?

    Q #2: How do we use these measures to manage FX exposures?

Measuring TE

    TE is easy to identify and measure, especially in the short-run, when firms can forecast future CF with high accuracy.

    TE represents today’s value of a future transaction denominated in FC translated to the DC.

    MNCs measure net TE. If a subsidiary has CF>0 in EUR and another subsidiary has CF<0 in EUR, the net transaction exposure (NTE) might be very low.

    The NTE in each currency is converted to the DC. The MNC has a standardized measure for each currency.

Example: Swiss Cruises.

    SC has sold cruise packages to a U.S. wholesaler for USD 2.5 million. SC has bought fuel oil for USD 1.5 million.

    Both cash flows are going to occur in 30 days.

    S = 1.45 CHF/USD. t

NTE (in USD): (USD 2,500,000 - USD 1,500,000) x 1.45 CHF/USD = CHF 1,450,000. ?

    Now, we want not only to measure the TE of a company. We want to know how TE will change with changes in S. That is, we want to measure the FX risk involved with the t


To do this, we need to say something about the variability (volatility) of S. t

Example: SC wants to estimates the sensitivity of NTE to changes in the S. Say a 10% t

    change (e = 0.10). f,t

If the exchange rate changes by 10%, then NTE changes by CHF 145,000. ?

Note: This example presents a range for NTE. NTE Є [USD 1.305M, USD 1.595 M]. The

    wider the range, the riskier an exposure is.

Range Estimates of Transaction Exposure

    Exchange rates are difficult to forecast. A range estimate of NTE will provide a more useful number for risk managers.

    The smaller the range, the lower the sensitivity of the NTE => The lower the FX risk.

    Three popular methods for estimating a range for transaction exposure: (1) Ad-hoc Method, usually assuming a change in e = 0.10. (See example above.) f,t

    (2) Sensitivity Analysis (look at empirical distribution of S, simulating S) tt+T

    (3) Assuming a statistical distribution for exchange rates.

1. Sensitivity Analysis

    Goal: Measure the sensitivity of TE to different exchange rates.

There are different ways to approach sensitivity analysis. Popular approaches: Look at the

    empirical distribution, do a simulation.

Examples: Sensitivity of TE to extreme forecasts of S. t

     Sensitivity of TE to randomly simulated thousands of S. Then, t

     draw a histogram to analyze the empirical distribution of TE.

    Example I: Using the empirical distribution for SC’s Net TE (CHF/USD) over one month. Empirical distribution of monthly e over the past 15 years (1988-2003), for 192 e’s. f,tf

     Extremes: 11.30% (on October 92) and 8.13% (on March 95).

    (A) Best case scenario.

    NTE: USD 1M x 1.45 CHF/USD x (1 + 0.1130) = CHF 1,613,850.

(B) Worst case scenario.

    NTE: USD 1M x 1.45 CHF/USD x (1 - 0.0813) = CHF 1,332,115.

    Based on these extremes, we estimate a range for TE

     => TE Є [CHF 1,332,115, CHF 1,613,850]

    Practical Application: If SC is counting on the USD 1M to cover CHF expenses, from a risk management perspective, the expenses to cover should not exceed CHF 1,332,115. ?

Note: Some firms may feel that this range, based on extremes, is too conservative. After all,

    the probability of the worst case scenario to happen is very low (only once in 192 months!)

Example II: Simulation for SC’s Net TE (CHF/USD) over one month.

    (i) Randomly, we pick 1,000 monthly e’s from the empirical distribution. f

    (ii) Calculate S for each e we selected in (i). (Recall: S= 1.45 CHF/USD x (1 + e)) t+30ft+30 f

    (iii) Calculate TE for each S. (Recall: TE= USD 1M x S) t+30t+30

    (iv) Plot the 1,000 TEs in a histogram. (This is your simulated TE distribution.)

    TE Simulated Distribution







    Transaction Exposure (in CHF)1353851













    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)

     => TE Є [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. ?

2. Assuming a Distribution.

    Confidence intervals (CI) based on a distribution provide a range for TE.

Example: A firm can assume that S changes (e) follow a normal distribution and based tf,t

    on this distribution construct a (1-;)% confidence interval.

A 95% (;=.05) CI is given by [ 1.96 ]. (Instead of 1.96, you can use 2)

Example: CI range based on a Normal distribution.

    Swiss Cruises believes that CHF/USD monthly changes (e) follow a normal distribution. f,t

    SC estimates the mean and the variance from the empirical distribution from past 15 years.

     = Monthly mean = 0.0007 ? 0 2 = Monthly variance = 0.00107 (=> = .03271, or 3.271%)

    e ~ N(0,0.00107). f,t

SC constructs a 95% CI for e. f,t

     1/2Recall that a 95% confidence interval is given by [0 1.96*.00107] = 1.96*.03271.

Thus, e will be between -0.0641 and 0.0641 (with 95% confidence). f,t

Based on this range for e, we derive bounds for the net TE: f,t

    (A) Upper bound

    NTE: USD 1M x 1.45 CHF/USD x (1 + 0.0641) = CHF 1,542,945.

(B) Lower bound

    NTE: USD 1M x 1.45 CHF/USD x (1 - 0.0641) = CHF 1,357,055.

    Note: VAR interpretation (VAR measures the worst case scenario within a one-sided CI):

    CHF 1,357,055 is the minimum revenue to be received by SC in the next 30

    days, within a 97.5% CI.

    If SC 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. ?

     Real World Example: Transaction Exposure: The Case of Ericsson

    Ericsson, the Swedish telecommunications giant, reported total income from sales in 2000 as SEK 273 billion (USD 29 billion). Ericsson reports in Swedish Krona (SEK), but operates in more than 140 countries. Foreign currency denominated assets, liabilities, sales and purchases, together with a large cost base in Sweden, result in substantial foreign exchange exposures.

    An analysis of net transaction exposures for the whole company, including revenues and costs by currency, shows a major net revenue exposure in EUR, but a more balanced position for USD. A +/-10% change in the SEK/EUR or SEK/USD exchange rate would have an approximate impact of +/-SEK 3.0 billion, while a +/-SEK 0.3 billion respectively, before any hedging effects are considered.

    Ericsson hedges transaction exposure using forward contracts and options. Ericsson reported a loss of SEK 508 million (USD 53.8 million) associated with its hedging activities during year 2000. Source: Ericsson Annual Report 2000.


     VAR provides a number, which measures the market risk exposure of a portfolio of a firm over a given length of time. VAR measures the maximum expected loss in a given time interval, within a (one-sided) confidence interval.

    Note: To calculate a VAR of a portfolio, we need to specify a time interval and the significance level for the confidence interval.

Interpretation of VAR: VAR of a FX portfolio.

    Time interval: 1 day

    Level of significance (;): 5%

    VAR of FX portfolio: USD 10,000.

    This VAR amount (USD 10,000) represents the potential loss of the FX portfolio in about one every twenty days within a 95% one-sided confidence interval.

    Example: Microsoft uses a VAR computation, within a 97.5% confidence interval, to estimate the maximum potential 20-day loss in the fair value of its foreign currency denominated investments and account receivables, interest-sensitive investments and equity securities. At the end of June 2001, Microsoft calculated a VAR of negligible for foreign currency instruments, USD 363 million for interest sensitive instruments, and USD 520 million for equity investments. ?

BONUS COVERAGE II: The Normal Distribution

    Suppose the random variable X has a probability distribution function (pdf) given by:

     21/222f(x) = [1/(2,!)] exp{-(x-)/(2)} - < x < , X

    22where and are any number such that -<<, and 0<<. Then X is said to follow a normal 2distribution. We will use the following notation: X ~ N(,). The pdf has the following bell shape:

    If Z follows a standard normal distribution then Z ~ N(0,1), that is the green function in the above graph. Using the formula of the pdf normal distribution, tables for the cdf of the standard normal distribution have been tabulated.

1.B.1 Useful Results of the Normal Distribution

     2Let X ~ N(,). Then,

(i) E[X] = (the mean, , is also the mode and the median) 22(ii) Var(X) = E[(X-)] =

    (iii) The shape of the pdf is a symmetric bell-shaped curve centered on the mean. (iv) Let Z = (X-)/. Then, Z ( N(0,1).

    (v) If and ß are any numbers with < ß, then

     P[< X < ß] = P[(-)/ < Z < (ß-)/] = F[(ß-)/] - F[(-)/], ZZ

where F represents the cdf of Z. Z

    Example: Let X be the annual stock returns (in percentage points) in the U.S. Assume that X ~ 2N(11.44,16.22). (The mean and variance of X have been obtained from annualizing the 1980-1990 U.S. weekly mean return and variance.) Suppose you are the manager of a portfolio that tracks the U.S. Index. You want to find the probability that your portfolio's return (X) is lower than -30% next year (i.e., a market crash).

P[X < -30]= P[Z < (-30-11.44)/16.22]= P[Z < -2.55]= F[-2.55]= 1 - F[2.55]= 1 - .9878 = .0122. ZZ

    That is, the probability that next year stock return is lower than 30% is 1.22%. ?

    Example: Go back to the previous example. Now, suppose you want to determine a minimum return, say %, with probability .95. That is, you want to find the probability that your portfolio's return exceeds a level with probability .05. That is,

.95 = P[X > ]= P[Z > (-11.44)/16.22] = 1 - F[(-11.44)/16.22]. Z

From the Normal Table, we obtain that if F(z) = .05, z = -1.645. Z

Then, (-11.44)/16.22 = -1.645 ? = 11.44 - 1.645 (16.22) = -15.323.

That is, there is a 95% probability that next year's portfolio return will be bigger than -15.323%. ?

Using the above properties, it is very easy to construct confidence intervals for the random variable 2X, which is normally distributed with mean and variance . The key to construct confidence

    intervals is to select an appropriate z value, such that

     X [ z ] with a probability (1-;). α/2

For a 99% confidence interval (i.e, ;=.01) z is equal to 2.58.

    For a 98% confidence interval (i.e, ;=.02) z is equal to 2.33.

    For a 95% confidence interval (i.e, ;=.05) z is equal to 1.96 (~2).

    For a 90% confidence interval (i.e, ;=.10) z is equal to 1.645.

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