International Financial Management 9

CHAPTER 9 – BRIEF ASSESMENT You work in Austin for a local investment bank. You have available quarterly inflation rate (I), interest rate (i), and growth rate (y) data for the U.S. and Europe from 2016:1 to 2016:4. The USD/EUR in 2016:1 was equal to 1.0821 USD/EUR, which you believe is an equilibrium exchange rate. Your job is to do quarterly forecasts of the USD/EUR exchange rate for 2017:1. The investment bank uses the following ad-hoc model: st+1 = St+1/St – 1 = .75 (Id,t+1 – If,t+1) + .25 (yd,t+1 – yf,t+1) (M1). This model is based on the monetary approach. You have the following data: Year yUS – yEUR 2016.1 2016.2 2016.3 2016.4 0.17% 0.24% 0.31% 0.57% IUS-IEUR iUS-iEUR St (EUR/USD) 0.4473% 0.6976% -0.1308% -0.3403% -0.5012% -0.0593% 0.6773% 0.8381% 1.0821 1.1453 1.1183 1.0962 To forecast income growth rates differentials (yt) your firm uses the following regression model (estimated regression is attached below): yUS,t – yEUR,t = α + β (yUS,t-1 – yEUR,t-1) + t. To forecast inflation rates (I) your firm uses a RW model. (A) Use the ad-hoc model (M1) to forecasts the USD/EUR exchange rate for the period 2017:1. (B) Use the forward rate to forecast the USD/EUR exchange rate for the period 2017:1. (C) Use StPPP (long-run PPP, starting with St=2016.1) to forecast the USD/EUR exchange rate for the period 2016:4. (D) Use the random walk to forecast the USD/EUR exchange rate for the period 2017:1. SUMMARY OUTPUT Regression Statistics Multiple R 0.196241 R Square 0.03851 Adjusted R Square 0.032185 Standard Error 1.143971 Observations 154 ANOVA df Regression Residual Total Intercept X Variable 1 1 152 153 SS 7.967219 198.9178 206.885 Coefficients -0.03019 0.19537 Standard Error 0.092218 0.079181 MS 7.967219 1.30867 F 6.088029 Significance F 0.01472 t Stat -0.32737 2.467393 P-value 0.743839 0.01472 Lower 95% -0.21238 0.038933 IFM-LN.122 CHAPTER 9 - BONUS COVERAGE: TAYLOR RULE According to the Taylor rule, the CB raises the target for the short-term interest rate, it, if: (1) Inflation, It, raises above its desired level (2) Output, yt, is above “potential” output The target level of inflation is positive (deflation is thought to be worse than positive inflation for the economy) The target level of the output deviation is 0, since output cannot permanently exceed “potential output.” John Taylor (1993) assumed the following reaction function by the CB: it = It + γ ( It – It* )+ θ y-gapt + r* (Equation BC.1) where y-gapt is the output gap –a percent deviation of actual real GDP from an estimate of its potential level–, and r* is the equilibrium level or the real interest rate, which Taylor assumes equal to 2%. The coefficients θ and γ are weights, which can be estimated (though, Taylor assumes them equal to .5). Let It* and r* in equation BC.1 be combined into one constant term, μ = r* - γ It*. Then, it = μ + λ It + θ y-gapt, where λ = 1 + γ. Using Taylor’s assumed coefficients (γ = θ = 0.5), r* = 2% and I*=2%, we predict that the Fed sets interest rates according to: it = .01 + 1.5 It + 0.5 y-gapt. We graphed this prediction (“Taylor Rule Prescription”) below in Figure 9.2 for the period 2000-2018, along with the actual Fed funds rate. Figure 9.2 Taylor Rule: U.S. Federal Fund Rate (2000 - 2018) IFM-LN.123 A popular variation to the Taylor rule (Equation BC.1) is to allow for gradualism in interest rate policy, reflecting the usual Central Bank practice of gradual, small adjustments in interest rates. This modified Taylor rule is: id,t = ρ id,t-1 + (1 – ρ) [rt* + Id,t +γ (Id,t – Id,t*) + θ y-gapt], where ρ is the smoothing parameter. If there is no gradual adjustment (ρ=0), the modified Taylor rule, reverts to the original rule. For example, using ρ=0.5 and the previous parameter values, in Figure 9.3 we graph the Taylor Rule prediction. It looks better. Figure 9.3 Modified Taylor Rule: U.S. Federal Fund Rate (2000 - 2018) For many countries, whose CB monitors St closely, the Taylor rule is expanded to include the real exchange rate, Rt: it = μ + λ It + γ y-gapt + δ Rt. Estimating this equation for the U.S. and a foreign country can give us a forecast for the interest rate differential, which can be used to forecast exchange rates. IFM-LN.124 Chapter 10 - Measuring FX Exposure – Part 1 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 St.  From Kellogg’s 2014 Annual Report Almost everyone knows Kellogg, but the general public may not be aware that they do more than cereal. Kellogg is the world's largest cereal company; second largest producer of cookies and crackers; a major producer of snacks; and a major North American frozen foods company. “Our operations face significant foreign currency exchange rate exposure and currency restrictions which could negatively impact our operating results. We hold assets and incur liabilities, earn revenue and pay expenses in a variety of currencies other than the U.S. dollar, including the euro, British pound, Australian dollar, Canadian dollar, Mexican peso, Venezuelan bolivar fuerte and Russian ruble. Because our consolidated financial statements are presented in U.S. dollars, we must translate our assets, liabilities, revenue and expenses into U.S. dollars at then-applicable exchange rates. Consequently, changes in the value of the U.S. dollar may unpredictably and negatively affect the value of these items in our consolidated financial statements, even if their value has not changed in their original currency” Three areas of FX exposure: (1) Transaction exposure: Risk of transactions denominated in FX. The transaction should have a settlement or maturity date, T (today, 60 days, 90 days, 1 year, etc.). (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. 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? IFM-LN.125 • 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? 10.1 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, certain transaction denominated in FC translated to the DC: TE = Value of transaction denominated in FC x St Example: Swiss Cruises has sold cruise packages to a U.S. wholesaler for USD 2.5 million. Payment is due in 30 days. St = 1.45 CHF/USD. TE = USD 2.5 M * 1.45 CHF/USD = USD 3.625 M. ¶ MNCs measure Net TE. If a subsidiary has CF>0 in EUR and another subsidiary has CF<0 in EUR, net TE might be very low. 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 T=30 days. St = 1.45 CHF/USD. TEEUR (in USD): (USD 2,500,000 - USD 1,500,000) * 1.45 CHF/USD = CHF 1,450,000. ¶ An MNC, like GE or MSFT, has many transactions denominated in FC, say EUR, GBP, JPY, MXN, etc. Since all net TEs by currencies are translated to DC, TE is easy to aggregate in a single number, the company’s overall NTE: NTE = TEEUR + TEGBP + TEJPY + TEMXN + ... Usually, companies aggregate and report the overall NTE by maturity date, say “less than 90 days,” and “more than 90 days.” MNCs measure Net TE. If a subsidiary has CF>0 in EUR and another subsidiary has CF<0 in EUR, NTE might be very low. IFM-LN.126 If we believe in the RW model, this is what we expect to happen at time T. Now, we know St will likely change at time T. We want to know how TE will be affected by changes in St. That is, we want to measure the FX risk involved with the transaction. To do this, we need to say something about the variability (volatility) of St. • Range Estimates of Transaction Exposure Exchange rates are volatile, 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 Rule: Usually, assume a change in ef,t, for example  0.10. (2) Simulation/Sensitivity Analysis: We look at empirical distribution (ED) of St, simulating St+T. (3) Assuming a statistical distribution for St. 1. Ad-hoc Rule Based on past experiences, a firm assumes that St can change (in either direction) by a fixed percentage. Then, it calculates the range of NTE under the assumed percentage. Example: SC wants to estimates the sensitivity of NTE to changes in the St. They use the 10% rule (ef,t =  0.10). (Recall: receivable USD 1 M due in 30 days.)  if St changes by 10%, then NTE changes by CHF 145,000. ¶ Note: This example presents a range for NTE. NTE  [USD 1.305M, USD 1.595 M]. The wider the range, the riskier an exposure is. The  percentage used depends on the volatility of the portfolio of currencies in NTE: Higher volatility in the currencies in the portfolio  A higher  percentage. 2. Simulation/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 (ED), do a simulation. Examples: Sensitivity of TE to extreme forecasts of St. Sensitivity of TE to randomly simulated thousands of St. Then, draw a histogram to analyze the empirical distribution of TE. Example ED-I: Using the ED for SC’s Net TE (CHF/USD) over one month. Statistics for the Empirical Distribution (ED) of monthly ef,t over the past 27 years (1990-2017), for 325 ef’s: Minimun 0.25 -0.12260 -0.02066 IFM-LN.127 Median -0.00086 0.75 0.00192 Maximun 0.12570 Average () -0.000886 0.03151 Standard Deviation () Skewness 0.21376 Excess Kurtosis 1.35745  Extremes: 12.57% (on September 2011) and –12.26% (on December 2008). (A) Best case scenario: largest appreciation of USD: 0.1509 NTE: USD 1M * 1.45 CHF/USD * (1 + 0.12570) = CHF 1,632,265. (B) Worst case scenario: largest depreciation of USD: -0.1162 NTE: USD 1M * 1.45 CHF/USD * (1 + (-0.12260)) = CHF 1,272,230. Based on these extremes, we estimate a range for TE  TE  [CHF 1,272,230, CHF 1,632,265] 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 1,281,510. ¶ 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 248 months!). Under more likely scenarios, we may be able to cover more expenses with the lower bound. Simulating TE from Empirical Distribution A different range can be constructed through sampling from the ED. Typical simulation: (i) Randomly draw one scenario from the ED -say, ef,t=Jun 1999. (ii) Calculate quantity of interest using simulated scenario -say, TE = USD 1M x St (1+ ef,t=Jun 1999). (iii) Repeat (i)-(ii) R times. This is your simulated distribution. Analyze it as usual (calculate mean, SD, (1α)% C.I., etc.) Example ED-II: Simulation for SC’s Net TE (CHF/USD) over one month. Based on the ED, we will draw R = 1,000 ef,t realizations (past monthly ef,t.). Then, we calculate 1,000 TE for each scenario drawn. Steps: (i) Randomly draw ef,t = esim,1 from ED: Observation 19: ef,t = 0.0034. (ii) Calculate Ssim,1: St+30 = 1.45 CHF/USD * (1 + .0034) = 1.4549 (iii) Calculate TEsim,1: TE = USD 1M * St+30 = 1,454,937.57 (iv) Repeat (i)-(iii) 1,000 times. Plot the 1,000 TEs in a histogram. (This is your simulated TE distribution.) IFM-LN.128 Lookup cell ef,t Random Draw with Randbetween Draw e_sim with Vlookup S_sim TE(sim) 1 2 0.0025 19 0.0034 1.4549 1,454,937.57 3 -0.0027 147 -0.0104 1.4349 1,434,895.83 4 0.0001 99 0.0125 1.4682 1,468,189.96 5 -0.0443 203 -0.0584 1.3653 1,365,272.92 6 -0.0017 82 -0.0727 1.3446 1,344,597.25 7 -0.0031 4 0.0001 1.4502 1,450,168.79 8 -0.0227 67 -0.0226 1.4172 1,417,218.22 9 -0.0099 136 0.0095 1.4638 1,463,838.02 10 0.0098 232 0.0191 1.4777 1,477,749.46 Note: You can find this example in my homepage: www.bauer.uh.edu/rsusmel/4386/chfusd-sim.xls TE: Simulated Distribution (in CHF M) 300 250 200 150 100 50 More 1.6430 1.6172 1.5914 1.5656 1.5397 1.5139 1.4881 1.4623 1.4365 1.4106 1.3848 1.3590 1.3332 1.3074 1.2815 0 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  [CHF 1.356775 M, CHF 1.52688 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 1,356,775. ¶ IFM-LN.129 We can interpret the worst case scenario of the empirical CI as Value-at-Risk or VaR (see Appendix 10). The VaR(mean) measures the maximum expected loss in a given time interval, within a (one-sided) confidence interval. Since VaR can be measured as a percentage or a value, it is common to put a currency sign (say, “$”) before the VaR to make explicit when the VaR is measured as a value. In this latter case, we will put the respective currency in front of the VaR. In the previous example, the CHF VaR(mean) = CHF 1.45M – CHF 1,356,775 = CHF 43.3225 is the maximum expected low in a month within a 97.5% CI. 3. Assuming a Distribution Confidence intervals (CI) based on a distribution provide a range for TE. We will assume a normal distribution to construct a CI. Example: A firm assumes that St changes (ef,t) follow a normal distribution with mean  and variance 2. That is, ef,t ~ N(, 2). Based on this assumption, a firm can construct a (1 – )% CI: [ – zα/2 * ,  + z(1-α/2) * ] = [  |zα/2| ]. Then, a 95% ( = .05, z.025 = -1.96) 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 (ef,t) follow a normal distribution. SC estimates the mean and the variance from the empirical distribution from past 20 years.  = Monthly mean = -0.000886 ≈ -0.09% ( statistically speaking,  =0!) 2 = Monthly variance = 0.000992 (  = 0.03151, or 3.15%) ef,t ~ N(-0.00152, 0.031512). SC decides to construct a 95% CI for ef,t. Then, a 95% confidence interval is given by: [-0.000886  1.96 * 0.03151] = [-0.06365; 0.06087]. Thus, ef,t is expected to be between -0.06365 and 0.06087 (with 95% confidence). Based on this range for ef,t, we derive bounds for the net TE: (A) Upper bound NTE: USD 1M * 1.45 CHF/USD * (1 + 06087) = CHF 1,538,267. (B) Lower bound NTE: USD 1M * 1.45 CHF/USD * (1 – 0.06365) = CHF 1,359,164.  TE  [CHF 1.3592 M, CHF 1.5383 M] Interpretation of CI: If we have 100 transactions, with the same terms, we expect that in 95 of those transactions the TE will lie within the estimated 95% confidence interval. Note 1: VaR interpretation (VaR measures the worst case scenario within a one-sided (1 – ) CI): IFM-LN.130 CHF 1,359,164 is the minimum revenue to be received by SC in the next 30 days, within a 97.5% CI. Notation: CHF VaR(.975) = CHF 1,359,164.. 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 1,359,164. The VaR is often expressed as a potential loss, relative to today’s value of the cash flow at risk (or expected value, using the RWM!). In this case, we call it VaR(mean): CHF VaR(mean, 97.5%) = CHF 1,359,164 – CHF 1,450,000 = CHF -90,836. VaR(97.5%): Minimun revenue within a 97.5% C.I. 2.5% CHF -90,836 CHF 1.359M TE: CHF 1.45M The VaR(mean) can be expressed as: CHF VaR(mean, 97.5%) = CHF 1.45 M * [-0.000886 – 1.96*0.03151] = CHF -0.090836 M Given that the mean is statistically speaking, that is, we can assume  = 0, and, thus, the CHF VaR(mean, 97.5%) ≈ CHF 1.45 M * (-1.96) * 0.03151 = CHF -0.089551 M We can generalize the above result as: VaR(mean, (1 – )) ≈ NTE * (-zα ) * . Note 2: For a given data set, using logarithmic (geometric) returns, it is easy to extend the results to different maturities. Suppose we are interested in building a 95% C.I. for TE in q months, using data based on frequency n (say, n=1 month). Assuming independence of returns, the approximation formulas for mean and SD are: q-mo mean = n-mo mean x q/n q-mo SD = n-mo SD x √ q/n) IFM-LN.131 Suppose, in the above example, the maturity of the cash flows is extended to 3 months. Using the monthly data, we create a 95% C.I. for 3-mo TE. Then, q=3 and n=1: 3-mo mean = -0.000886 x 3 = -0.00266 3-mo SD = 0.03151 x √3 = 0.05458 95% C.I. for ef,t: [-0.00266  1.96*0.05458] = [-0.10963; 0.10431] (A) Upper bound NTE: USD 1M x 1.45 CHF/USD * (1 + 0.10431) = CHF 1,601,254. (B) Lower bound NTE: USD 1M x 1.45 CHF/USD * (1 – 0.10963) = CHF 1,290,960. ¶ In Table 5.1, we noticed that ef,t does not follow a normal distribution, mainly because it has “fat tails,” as shown by an excess kurtosis significantly different from zero. We can introduce departures from normality in different ways; usually, by assuming a fat-tail distribution, like the t-distribution, or using the Cornish-Fisher (CF) approximation. The CF approximation uses a Taylor expansion of the normal density, which makes the approximate density a function of skewness (SK) and excess kurtosis (EK). Under the CF approximation, we have new zα values, 𝑧 : 𝑧 𝑧 𝑧 1 𝑧 Notice that if SK = EK = 0, then, z For  = .025, z.975 = 1.96  z z.025 = -1.96  z 3𝑧 2 𝑧 5𝑧 z . . . 1.96 0.474 ∗ SK 0.069 ∗ EK 1.335 ∗ SK . 1.96 0.474 ∗ SK 0.069 ∗ EK 1.335 ∗ SK . Example: For the CHF/USD used above we have SK = 0.214 & EK = 1.357 (&  = 0). Then, z . 1.96 0.474 ∗ 𝟎. 𝟐𝟏𝟒 0.069 ∗ 𝟏. 𝟑𝟓𝟕 1.335 ∗ 𝟎. 𝟐𝟏𝟒 = 2.216 z . 1.96 0.474 ∗ 𝟎. 𝟐𝟏𝟒 0.069 ∗ 𝟏. 𝟑𝟓𝟕 1.335 ∗ 𝟎. 𝟐𝟏𝟒 = -2.013. Then, CHF VaR(mean, (1 – )) ≈ CHF 1.45M * (-2.013) * 0.03151 = CHF -0.091973. ¶  Real World Example: Transaction Exposure: The Case of Kellogg The Kellogg Company is the world’s largest cereal company; second largest producer of cookies and crackers; and a major producer of snacks and frozen foods. The principal markets for these products include the U.S. and the Europe. Kellogg’s operations are managed in two major divisions –U.S. and International- with International further delineated into Europe, Latin America, Canada, Australia, and Asia. Operating profits for fiscal year 2014 were USD 1,024 million on sales of USD 14.58 billion. Primary exposures include the USD versus the EUR, GBP, MXN, AUD, CAD, VEF, and RUB, and in the case of inter-subsidiary transactions, the British pound versus the euro. IFM-LN.132 The total notional amount of foreign currency derivative instruments at year-end 2014 was USD 764 million, representing a settlement receivable of USD 23 million. The total notional amount of foreign currency derivative instruments at year-end 2013 was USD 517 million, representing a settlement obligation of USD 1 million. All of these derivatives were hedges of anticipated transactions, translational exposure, or existing assets or liabilities, and mature within 18 months. Assuming an unfavorable 10% change in year-end exchange rates, the settlement receivable would have become a settlement obligation of USD 53 million at year-end 2014 and the settlement obligation at year-end 2013 would have increased by approximately USD 52 million. Source: Kellogg Annual Report 2014.  IFM-LN.133 CHAPTER 10 - BONUS COVERAGE I: TE Simulation in R Excel is not a very flexible way to construct a simulated C.I. We can use R to do; for this, you need to install R in your computer (go to https://www.r-project.org to download the latest version). • Code in R (cut and paste; play with parameters R & alpha): chfusd <- read.csv("http://www.bauer.uh.edu/rsusmel/4386/chfusd.csv",sep=",") # Data summary(chfusd) # Distribution of Data (S_t) names(chfusd) # Repeats Header info ("DATA" & "CHF_USD" S <- chfusd$CHF_USD T <- length(S) Tstart <- 229 e <- matrix(0,T-1,1) Val <- 1 S_0 <- 1.45 # Defines S_t as the CHF_USD column of the data # Check total T (1971:1 to 2017:1) # Start of sample period: 1990:1 # create vector of 0 to put the e_f,t # Value of transaction in FC (in M) # Today's S_t for (i in 2:T){ # e[i] <- (S[i]/S[i-1]-1) e[i] <- log(S[i])-log(S[i-1]) } # loop to calculate log (or arithmetic) returns Tsart <- Tsart-1 summary(e) summary(e[Tstart:T-1]) sd(e[Tstart:T-1]) # adjust Tstart (we lost one observation in the above loop # summary stats for the whole sample of e # summary stats for sample of interest of e # Standard Deviation of e during sample of interest # simulation R = 1000 alpha = .05 R_low <- R*alpha/2 R_low R_high = R*(1-alpha/2) R_high x_sam <- sample(e[Tstart:T-1], size=R, replace=TRUE) TE <- Val*S_0*(1+x_sam) # Number of simulations # Specify (1-alpha)% Confidence Interval # generate R e_f draws from ED # calculate R TE values # Sort and Histogram STE <- sort(TE) print(STE[R_low]) print(STE[R_high]) # sort TE (from lowest to highest) # print TE_lower bound # print TE_upper bound hist(TE,main="Histogram for TE", xlab="TE (in CHF)", breaks=30) # TE histogram • You should get something similar to: > print(STE[R_low])# print TE_lower bound IFM-LN.134 [1] 1.356775 > print(STE[R_high])# print TE_upper bound [1] 1.52688 > hist(TE,main="Histogram for TE", + xlab="TE (in CHF)", breaks=30)# TE histogram > IFM-LN.135 CHAPTER 10 - BONUS COVERAGE II: Value-at-Risk (VaR)  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. (This is what we called before VaR(mean).) Let Rt+1 = (Zt+1 - Zt)/Zt be the profit/loss of a financial firm in day t+1 for holding portfolio/asset Zt (say, Zt = St). Then, VaR is defined by: Prob[Rt+1 > VaRt+1(1 – )] = (1 – ) VaR: (1 - ) Confidence Interval  Maximum Expected Loss VaR((1 - ) Today’s valuation of Z Note: To calculate the 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% (zα=1.645, 95% C.I.) 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 C.I. Banks report the VaR for their trading desk. They use =.01% ((zα=-2.33, 99% C.I.) and T=10 days. Regulators use the reported VaR to calculate capital requirements (capital charge). Say, Capital charge = VaR x k, k>3. 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. ¶ IFM-LN.136