




































Indian Journal of Finance and Banking 

 Vol. 5, No. 1; 2021 

                                       ISSN 2574-6081   E-ISSN 2574-609X 

Published by CRIBFB, USA 

 

23 

VALUE-AT-RISK BASED APPROACH FOR CURRENCY 

HEDGING 
 

Rachna Khurana 

Chief Executive Officer 

Southern Ridges Capital 

8 Robinson Road, Singapore 048547, USA 

E-mail: rachna.khurana@southernridgescapital.com 

 

Umang Khetan 

PhD Candidate 

University of Iowa 

Tippie College of Business, Iowa City, IA 52242, USA 

E-mail: umang-khetan@uiowa.edu 

 

ABSTRACT 
Corporate FX risk management has gained complexity with an increased number of currencies 

involved and varying correlations among them. Existing literature has highlighted the need to 

account for cross-currency correlations when optimizing hedge ratios for portfolio management 

(Dowd, 1999). In this paper, we propose a Value-at-Risk (VaR) based model to estimate the 

optimal hedge ratio for a multi-national corporate that aims to minimize the cost of hedging at a 

given tolerance level of expected loss arising out of FX movement. The paper illustrates both 

parametric and historical methods of VaR estimation at a portfolio level as the first step in risk 

management. As a second step, an efficient-frontier is derived based on the expected VaR level at 

various hedge ratios and compared with associated hedge cost. The benefits of this approach 

include: identification of net exposures after correlations among currencies are accounted for in 

order to avoid duplication of hedges, and condensation of the parameters governing hedging 

decision into a single, intuitively-appealing number. The paper also highlights the need to 

frequently update the model’s assumptions as currency correlations and corporate exposures 

remain dynamic. 

Keywords: Value-At-Risk, FX Risk Management, Correlation, International Finance. 

JEL Classification Codes: C10, F31, G32, M20. 

 

INTRODUCTION 

Increase in cross-border flow of capital and trade has diversified the sources of cash flow for 

multi-national corporations. These cash flows tend to be denominated in varying currencies, 

often different from the functional currency of the corporation in which it draws its books of 

accounts. As a result, corporate treasuries have to manage multi-currency exposures while 

controlling for cost of hedging. 

 

mailto:rachna.khurana@southernridgescapital.com
mailto:umang-khetan@uiowa.edu


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Existing literature on corporate FX risk management has focused on the merits of undertaking 

derivative transactions for minimizing cash flow volatility. Dufey and Srinivasulu (1983) were 

among the earliest proponents of corporate FX risk management, arguing that firms can hedge 

more cheaply than individual shareholders and protect the latter in times of financial distress. 

Nain (2004) finds there to be strategic motives for FX risk management that insulates corporate 

from input price fluctuations in markets with inelastic output prices. Smithson and Simkins 

(2005) conducted a survey that found that 92% of Fortune 500 companies believed that financial 

risk management adds value to shareholders. In light of these findings, it is important to adapt 

risk management strategies in line with the evolving complexities in currency markets and 

diversified nature of cash flows. This paper highlights one such approach: the Value-at-Risk. 

Value-at-Risk (VaR) is a globally recognized framework in banks and financial 

institutions. The methodology became an industry standard after Morgan (1996) published the 

Risk Metrics framework in 1992. While the financial industry has adopted variations of the 

framework and several papers and books have been written on implementation and limitations 

(see for instance Dowd, 1999), this paper is the first to apply the framework to corporate FX risk 

management. The strength of the framework lies in its ability to condense various sources of FX 

risk into a single metric that can be understood at various levels in an organization. 

VaR as a risk assessment parameter has also found applicability in asset management 

literature. Marshall and Siegel (1996) consider different approaches to portfolio risk management 

based on the central idea of VaR, as detailed in Morgan’s Risk Metrics. In this paper, we 

illustrate the parametric and historical cash-flow methodologies to estimate VaR when a 

corporate has exposures in multiple currencies that are less-than-perfectly correlated with one 

another. Rockafellar and Uryasev (2000) proposed a conditional VaR model that focuses only on 

downside risk, since that is essentially what an investor tries to protect against. In our paper, 

however, we assume a corporate philosophy of mitigation of volatility while keeping the cost at a 

reasonable level, and hence do not go down the conditional VaR route.  

At the outset, an organization often evaluates the benefits of hedging currency risks. 

Global treasurers typically face a dilemma because hedging and speculating can be two sides of a 

coin depending on the view of the organization or that of the senior management. Copeland and 

Copeland (1999) illustrate that variance minimization is not the only objective way of assessing a 

hedge program; the impact of a hedge program on business disruption and the drift in operating 

cash flow caused by the cost of FX hedging must also be considered. In this paper, we consider 

the example of an Indian exporter that expects to earn USD in the future and can hedge the 

currency risk by selling USD against INR under a forward contract. If INR were to appreciate in 

the future, the mark to market on the contract would be positive and the company would benefit 

by having locked in a rate for its future receivables. On the flip side, if INR depreciates, the mark 

to market on the contract would be negative. The contract was to fix a rate for its future 

receivables, and hence is technically not a loss for the company. However, the senior 

management or shareholders can view it as an opportunity loss where the company could have 

received higher INR value in absence of the forward contract. If the firm were to opt for an 

Option contract instead, to take advantage of a possible favorable currency movement, it would 

have to pay a premium which adds to hedge costs. There are other costs associated with hedging 

as well which need to be considered, including manpower and operational overheads. Therefore, 

it is important for all levels in the organization to clearly set the objectives of a hedging policy to 

avoid any conflicts in the aftermath of a hedge performance. It is also important for the policy 



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25 

and tools to be simple to understand and evaluate. It is with this motivation that a simple metric 

must be used to evaluate hedge decisions against. 

We propose the use of VaR to arrive at an assessment of materiality of risks. The 

simplicity of VaR measurement greatly facilitates reporting of risks to senior managers and 

directors in a standard format. VaR represents the potential loss that can be expected on a 

portfolio of assets, associated with a specified level of confidence, based on the correlations 

among assets and their respective volatilities. The example of an Indian corporate used in this 

paper follows a confidence level of 95%, but variations around it can be easily incorporated 

Hendricks (1996) for other variants of the model. As with any quantitative tool, there are 

limitations such as reliance on historical data and inability to predict fat-tail events. We discuss 

some of these issues in the last section of the paper. 

We set the corporate to centrally manage its FX risks where it can consolidate its 

exposures and optimize the hedge ratio. The first step in the process is risk evaluation. We 

develop a framework here to identify various exposures and quantify the risks in terms of impact 

on the firm’s profitability, using a simple VaR metric. The second step is to decide how much of 

the exposure identified should be hedged using FX derivatives. A conservative approach that 

does not account for cross-currency correlations is to hedge each currency exposure fully – in the 

spirit of complete mitigation of cash flow volatility caused by FX movements. However, this can 

result in large costs for the organization including transaction costs, credit limit utilization, 

margining requirements, and operational overheads. Particularly for companies having exposures 

in emerging market currencies, such costs can be material. We propose a cost-benefit trade-off 

model that obviates hedging of offsetting exposures and focuses on the net currency risk faced 

by the corporate. The cost of hedging this net exposure is assessed against the VaR achieved at 

different levels of hedge ratio. This results in an efficiency frontier along which the corporate can 

determine the cost-efficient optimal hedge ratio and the associated VaR at that level. The model 

also offers flexibility to a corporate that wishes to target a certain VaR level and accordingly 

determine the hedge ratio. Targeting a zero VaR would need 100% hedge ratio of net exposure. 

The paper therefore provides a scientific way to determine optimal hedge ratios for multi-

national corporations and accounts for the key variables of FX exposures, expected cash-flow 

volatility, and hedge cost. 

The paper concludes with a discussion on the limitations of using VaR as a standalone 

quantitative tool. We take the example of COVID-19 crisis, which was a tail-risk event that a 

VaR model can only provide partial protection against. Other limitations of the proposed 

approach include the need to regularly update the model parameters. Companies’ risk profile in 

terms of currency exposures undergoes changes from time to time, and a correlation among 

currencies is also not static. The model, once constructed and implemented, can be updated with 

little effort.  

A potential extension of this model and that of the paper would be to include other asset 

classes that the corporate has exposure to, such as interest rates and commodities, and that have 

non-zero correlation with FX. The rest of this paper is organized as follows: Model, Empirical 

Illustration, and Discussion on limitations of the model and best practices for hedging, and 

Conclusion. This section ends with a brief summary of key foreign exchange risks for a 

corporate, as below. 

 

 

 



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26 

Key Foreign Exchange Risks 

Every transaction or potential transaction which result in an inflow or outflow in foreign 

currency is a risk for a company. Most companies would identify these risks in below broad 

categories: 

 Current Account Transaction Risk: This arises due to current payable/receivable and 

net income in foreign currency. This is part of the consolidated profit and loss statement. 

For instance, a US based machine tools manufacturer selling products in Europe may 

have receivables in EUR and exposure to EURUSD currency volatility as the functional 

currency of the US based manufacturer is US Dollar. Another example could be a US 

based company having a subsidiary in Singapore for its Asia business and consolidating 

the net income from Singapore (in SGD).  

 Capital Account (Foreign Currency Debt) Risk: This is an important risk to consider 

as companies may tap various foreign markets for meeting their borrowing needs. These 

could be long tenor bonds/loans and any significant FX moves could result in a much 

larger liability for the company. 

 Net Investment Risk: This is the risk arising from investments in foreign subsidiaries 

whose reporting currencies may be different from that of its parent. In most cases, this is 

treated as “Other comprehensive Income” thereby affecting Balance Sheet and not the 

Income Statement. 

 

MODEL 

We consider a firm with CARA utility function that seeks to maximize expected wealth in the 

following period. The utility function of the firm is given by 

 

𝑈 = −𝑒𝑥𝑝 −𝑎𝑊  
 

Where a is the coefficient of risk aversion and W is the level of wealth achieved in period 

t+1. We take a as exogenously given and proceed to analyze the determination of wealth W. 

 

Wealth in period t+1 is composed of cash flows arising into or out of currencies other 

than the home currency of the firm. While the cash flow is certain in the currency in which it is 

denominated (for example, export contracts or outbound investment flows), there is uncertainty 

around the future FX rate at which such cash flows will eventually occur
1
. Therefore, the 

corporate attempts to maximize the below wealth function that is parametrized by cash flow in 

foreign currency and the expected spot rate in period t+1 

 

𝑚𝑎𝑥 E[−𝑒𝑥𝑝 −𝑎(𝑥𝑖 ∗ 𝑆𝑡+1
𝑖  ]                                            (1) 

 

Where 𝑥𝑖  is the cash flow in foreign currency I and 𝑆𝑡+1
𝑖  is the expected spot rate at the 

time of actual conversion. Note that we do not place a non-negativity constraint on x because it 

can be both an inflow and an outflow from the corporate’s perspective. However, for the rest of 

the analysis below, we consider the case of a firm that exports in terms of currency i to earn a 

                                                           
1
We assume 100% certainty of cash flow in the foreign currency to keep the model tractable. However, risk of 

contract non-performance can be incorporated by multiplying the cash flow with a certainty factor and proceeding 

with the analysis as described. Our results continue to hold in such scenarios. 

 



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27 

positive cash flow in foreign currency (𝑥𝑖> 0) and benefits from a higher expected spot rate of 

conversion. 

Now let us say that the firm chooses to hedge a certain portion of its expected cash flow 

so as to not depend entirely on the vagaries of FX market in setting the conversion rate when the 

cash flow becomes due. Let 𝛼𝑖  be the proportion of cash flow that is not hedged, and 

consequently (1-𝛼𝑖) is the proportion that is hedged at a certain rate of 𝐹𝑖  with associated hedge 

cost of 𝑚𝑖 . Then, the expected wealth is given by 

 

𝑊𝑖 = E[ 𝑥𝑖 ∗ (𝛼𝑖𝑆𝑡+1
𝑖  +  (1 − 𝛼𝑖)(𝐹𝑖  −  𝑚𝑖))]                    (2) 

 

Subject to the constraints that 

0 ≤  𝑥𝑖 , 0 ≤  𝛼𝑖 ≤ 1 
 

The term (𝐹𝑖  −  𝑚𝑖) can be understood as the net rate realized by the firm that is 

composed of (i) in case of an option, at least the strike price less premium, or (ii) in case of a 

forward, the forward rate less transaction costs. 
 

Further, assume 𝑆𝑡+1
𝑖  to be normally distributed with mean 𝜇 and variance 𝜎2, i.e. 

𝑆𝑡+1
𝑖  ~ 𝑁(𝜇, 𝜎2). Substituting equation (2) and the foregoing distribution parameters into the 

exponential function (1), we arrive at the firm’s objective function as 

 

max
𝛼 𝑖

−𝑒𝑥𝑝  −𝑎𝑥𝑖(𝛼𝑖𝜇 +  (1 − 𝛼𝑖)(𝐹𝑖  −  𝑚𝑖))  +  
1

2
𝑎2𝑥2𝛼𝑖2

𝜎2                 (3) 

 

Maximizing this function is akin to minimizing the power of the exponential. We take the 

first order condition of the power term with respect to 𝛼𝑖  and arrive at its optimal value as below 

 

𝛼𝑖  =  
𝜇 −  𝐹𝑖  +  𝑚𝑖

𝑎𝑥𝑖𝜎2
                                                                (4) 

 

This is the first key result in our paper; the proportion of cash flow in foreign currency 

that the firm chooses to keep unhedged, 𝛼𝑖 , goes up as: (i) the volatility of the FX pair goes 

down, (ii) the difference between the expected spot rate and the hedged rate goes up (in this case, 

the forward premium goes down), (iii) the hedge cost goes up, and (iv) the firm’s coefficient of 

risk aversion goes down. All of these conclusions make intuitive sense. Consequently, the firm 

arrives at the optimal hedge ratio considering the FX volatility, expected spot rate (which may be 

the same as current spot rate), the forward quote available from a dealer bank, and the associated 

option premium or transaction costs. 

Now we can consider these results at an aggregate level for all currency pairs put 

together. The corporate can treat each stream of cash flow affected by an FX pair separately, 

thereby deciding on how much to hedge for each currency pair. Such an approach assumes that 

all the FX pairs that the firm has exposure to are independently and identically distributed (iid). 

While the assumption of identical distribution may be plausible (at least to the extent the 

currency pairs can be classified as G10 or EM), the assumption of independence among FX pairs 

is clearly not. We show in the empirical section below the correlation between a sample of 

currency pairs and find that they are almost always non-zero. This is understood to be the case 



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28 

because similar macro-factors move currencies, such as geopolitical developments, commodity 

prices, risk sentiment that drives portfolio flows, and macro-economic data. Therefore, we refine 

the approach of the corporate to account for cross-currency correlations when determining the 

exposure that needs to be hedged, and then optimizing its hedge ratio of the net exposure. 

We know from literature that portfolio variance is not a simple summation of variances of 

individual securities. We apply the same reasoning in the context of a portfolio of currencies that 

the corporate has exposure to. Consider a portfolio of n currency pairs. Let 𝐶𝑜𝑣(𝑖, 𝑗) be the 

covariance between currencies i and j, derived from a covariance matrix that is empirically 

derived using historical data for all the currencies. Then, the portfolio variance is given by, 

 

                                  𝜎𝑝
2  =  𝑤𝑖

2𝜎𝑖
2

𝑛

𝑖 = 1

 +   𝑤𝑖𝑤𝑗𝐶𝑜𝑣(𝑖, 𝑗)

𝑛

𝑗  = 1

n

𝑖 = 1

                      (5) 

 

Where 𝑤𝑖𝑤𝑗  is the product of the relative weight of the currencies in the portfolio. 

 

Motivated by the portfolio variance theory, we introduce VaR as a condensed numerical 

representation of the risk faced by the corporate considering all currency exposures together. 

This can substitute for the individual currency variance that we considered in equation (4) when 

deciding on the optimal hedge ratio. 

Value-at-Risk is an attempt to provide a single number summarizing the total risk in a 

portfolio of financial assets. It gives the maximum loss that an institution can expect to face with 

a certain confidence level over a specific horizon at a portfolio level. Controlling for a certain 

tolerance level of VaR, the corporate can ascertain how much of the net currency exposure it 

should hedge. Generally, the corporate can compare the level of VaR with associated cost of 

hedging in the numerator of equation (4) to draw an efficient frontier of hedge ratio. We detail 

this approach in the next section. This section concludes with a brief overview of two VaR 

estimation methodologies. 

 

VaR Methodologies 

 

Historical Method  

This method uses historic market data to create theoretical portfolio of the exposure profile at 

various points in the past. It calculates hypothetical returns for the current portfolio using actual 

historic market conditions over a certain period of the past, such as the past one year. For 

instance, we can calculate the change in portfolio value over one year holding period, observed 

daily, which provides the daily market value change of the portfolio. 

Once we arrive at a hypothetical return for each day, we can calculate the average of the 

worst twenty days (from a sample set of 252 working days) for 95% confidence to give us the 

resulting VaR. Other confidence intervals typically used in literature are 97.5% and 99%. 

Historical method requires a significant amount of daily rate history and incorporates tail 

risk only to the extent of what may have actually occurred in history. However, as a concept this 

method is easy to understand and implement, with limited mathematical computation. Also, 

correlations and standard deviations need not be separately estimated because the change in 

portfolio value automatically incorporates them. 

 



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29 

Parametric method (Variance - Covariance) 

This method relies on a variance-covariance matrix for all currencies in the portfolio and 

estimates the portfolio standard deviation using equation (5). 

 

𝑉𝑎𝑅 ($)  = ∝ ∗   𝑡
2

 ∗  𝜎𝑝 ∗  𝐸𝑥𝑝𝑜𝑠𝑢𝑟𝑒 ($) 

Where, 

 

∝  =  Number of standard deviations from the mean for given confidence level 

- 95% confidence interval: 1.65 

- 97.5% confidence interval: 1.96 

- 99% confidence interval: 2.33 

 

t   =  Time period in days 

𝜎𝑝   =  Daily standard deviation 

 

The benefit of parametric method is that it doesn’t involve analyzing extensive historical 

data (only volatility and correlation data is required). This makes it applicability easier across 

new and evolving portfolios. A disadvantage is that it may be less accurate for skewed 

distributions or distributions with fat tails, because of its inability to learn from past events. 

 

EMPIRICAL ILLUSTRATION 

We consider an electronics manufacturer based out of India, with exports and imports 

denominated in EUR, GBP, JPY and USD, and foreign currency debt in EUR and USD. The 

below tables summarize the exposures. All exposures have been converted into USD equivalent 

to enable comparison. 

 

Table 1. exposure summary (amounts in USD million equivalent) 

 

Trade Exposures Exports Imports Net Imports 

EUR 100 10 -90 

JPY 250 0 -250 

USD 300 50 -250 

GBP 50 100 50 

    Foreign Currency Debt Amount Tenor  

EUR 500 10y  

USD 200 5y  

    

Consolidated Exposure affecting the Income 

Statement 

Net Payables   

EUR 410   

JPY -250   

USD -50   

GBP 50   

 



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30 

The company starts with an analysis of its net exposure which is summarized in the third 

table above. In USD terms, the largest exposure is a net EUR payable of 410 million, followed 

by a JPY receivable of 250 million. Smaller exposures are payable of 50 million in GBP and an 

equal amount of receivable in USD. We assume the timing of these exposures to coincide. 

Without looking at currency correlations, the corporate treasury would seek to hedge a certain 

portion of each currency’s exposure individually. However, we have two potential offsets 

available that the VaR model can capture. First, due to current and capital account exposures 

running in opposite directions for both EUR and USD, the company has EUR payable and USD 

receivable. Additionally, there is a net JPY receivable and GBP payable. In all, the net exposure 

of the four currency pairs can be consolidated into a common currency unit (say, INR or USD) to 

arrive at the final, offsetting exposure number. 

Second, there are correlations among currencies which increase or decrease the overall 

risk faced by the corporate. Figure 1 below illustrates rolling correlation for a tenor of 1 year for 

combinations of these currency pairs. 

 

 
 

  Figure 1.  Historical rolling correlation between select currencies 

Data Source: Bloomberg 

 

Looking at correlations, amongst the major exposures, EURINR and JPYINR are 

offsetting exposures and are positively correlated. These two pairs therefore provide an offset to 

the company and obviate the need to hedge separately. Likewise, EURINR and USDINR are 

strongly positively correlated and have offsetting cash flows, thereby further reducing the net 

amount that the company needs to hedge. However, the positive correlation between EURINR 

and GBPINR with same direction of exposure (net payable in both) means that these exposures 

add up to overall risk and must be aggregated. We summarize these results into an intuitively 

appealing VaR measure using both historic and parametric estimation methods in figures 2 and 

3. These figures show, at various levels of confidence, what is the expected daily loss to the 

company at a portfolio level if the currencies were to move from their present levels. All 

correlations and volatilities are encapsulated in a single number that provides the basis for the 

-0.40

-0.20

0.00

0.20

0.40

0.60

0.80

1.00

D
ec

-1
8

Fe
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-1
9

A
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r-
1

9

Ju
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-1
9

A
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1

9

O
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-1
9

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-1
9

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-2
0

A
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r-
2

0

Ju
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-2
0

A
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g-
2

0

O
ct

-2
0

Historical 1y rolling correlation

EURINR&GBPINR GBPINR&JPYINR JPYINR&USDINR

EURINR&USDINR EURINR&JPYINR GBPINR&USDINR



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31 

next step of hedge decision. Historical volatility pattern in these currencies, which drives the 

estimate of VaR under both methods, is displayed in Figure 4. 

 

 

 
 

Figure 2. Daily VaR in USD (million) using Historical method at three levels of confidence  

Data Source: Bloomberg. 

 

 

 
 

 

Figure 3. Daily VaR in USD (million) using Parametric method at three levels of confidence 

Data Source: Bloomberg 

 

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

4.50

95% 97.5% 99%

V
aR

 (
In

 U
SD

 m
ill

io
n

)

Percentile

Historical Method - Daily VaR 

0.00

0.50

1.00

1.50

2.00

2.50

3.00

95% 97.5% 99%

V
aR

 (
in

 U
SD

 m
ill

io
n

)

Percentile

Parametric Method - Daily VaR



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32 

 
 

Figure 4. Historical volatility in four currency pairs for 1 year tenor  

Data Source: Bloomberg. 

 

There is some difference in VaR estimation between historical and parametric methods, 

due to differences in assumptions. Also, given that the historic method in our sample includes the 

COVID-19 sell-off of 2020, it is likely to show higher VaR numbers due to the incorporation of 

this fat-tail event. Annual VaR can be estimated using the below relation 

 

𝐴𝑛𝑛𝑢𝑎𝑙 𝑉𝑎𝑅 =  𝐷𝑎𝑖𝑙𝑦 𝑉𝑎𝑅 ∗   252 
 

Considering a daily VaR estimate of USD 2.4 million at 95% confidence level, we arrive 

at an annual VaR estimate of USD 37.5 million. 

The next step is to address two questions: what specific exposure does the company 

hedge, and how much of it? After netting off offsetting exposures, the company in our example 

is left with the largest exposures to EUR and JPY, which primarily drive VaR up. Given that the 

correlation between the two pairs is significantly and generally positive, with exposures running 

in opposite directions, the net amount of EUR payable remains as the key source of risk for the 

company. Therefore, the rest of the decision is based on what proportion of EUR exposure to 

hedge using FX derivatives, while hedging a small proportion of JPY exposure. It bears 

repeating here that the only way to achieve a zero-VaR is to 100% hedge the net exposure in 

each currency, which is both costly and overly conservative. 

As computed above, the starting level of VaR when all exposures are unhedged is USD 

37.5 million. While EURINR and JPYINR have a strong positive correlation, it is less than one. 

Hence, a small part of JPYINR exposure is likely to remain open even after netting with 

EURINR. In the scenario analysis that follows, we let the company hedge 10% of its JPYINR 

exposure and then decide how much of EURINR exposure to hedge, while keeping the other two 

currencies unhedged. Table 2 shows the various hedge ratios for EUR exposure, the 

corresponding VaR after the hedge is implemented, the associated cost of hedging using 

forwards, and the summation of VaR and cost of hedging. 

 

4.0%

5.0%

6.0%

7.0%

8.0%

9.0%

10.0%

D
ec

-1
8

Fe
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-1
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-1
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A
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-2
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A
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2

0

O
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-2
0

1y rolling historical volatility

EURINR GBPINR JPYINR USDINR



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33 

 

Table 2. comparison of VaR and cost at various hedge ratios for EUR exposure 

 

Hedge Ratio 

(net EUR exposure) 

Annual VaR 

in $ million 

(95% confidence) 

Hedge Cost (Forward) 

in $ million 

VaR plus Hedge Cost 

in $ million 

0.1 34.1 0.9 35.0 

0.2 31.2 3.1 34.3 

0.3 28.8 5.2 34.0 

0.4 26.8 7.4 34.1 

0.5 25.4 9.5 34.9 

0.6 24.7 11.7 36.4 

0.7 24.8 13.8 38.6 

0.8 25.6 16.0 41.6 

0.9 27.2 18.1 45.3 

1.0 29.3 20.3 49.6 

 

Note: the scenario analysis assumes JPY exposure hedge ratio of 10% due to the imperfect 

correlation between EURINR and JPYINR. Forward cost is the net premium paid for EURINR 

and JPYINR hedge, expressed in USD million. 

 

VaR shows a curvilinear trend: it falls as hedge ratio increases but at a slowing pace. The 

first order derivative is negative but the second order derivative is positive, indicating a convex 

function. After a point, VaR stops reducing, flattens out, and then starts increasing again. This is 

because a very high hedge ratio begins to nullify the diversification benefit arising from 

correlations among currencies. Cost of hedge, on the other hand, generally follows a linear trend. 

It rises almost one-to-one with higher hedge ratio, but in cases it could rise faster if large trade 

size begins to adversely affect market liquidity. 

Table 2 gives us two optima: VaR is minimized at a EUR hedge ratio of 60%, at USD 

24.7 million. It has an associated hedge cost of USD 11.7 million. On the other hand, the total 

cost (VaR plus hedge cost) is minimized at a EUR hedge ratio of 30%, at USD 34 million. The 

corresponding VaR is USD 28.8 million. The company can choose to minimize either of the two 

and settle on a hedge ratio accordingly. 

The optimal hedge ratio, as in equation (4), is determined by a trade-off between hedge 

benefit and hedge cost. The equation is re-stated here for reference: 

 

𝛼𝑖  =  
𝜇 −  𝐹𝑖  +  𝑚𝑖

𝑎𝑥𝑖𝜎2
 

 

From this equation, we know that a higher hedge cost, 𝑚𝑖 , should reduce the hedge ratio. 

Therefore, the ideal measure to minimize would be VaR plus hedge cost, as opposed to VaR 

alone. 

Figure 5 converts this into an efficient frontier where it is clear that a hedge ratio of 60% 

achieves the lowest VaR. Note that as the hedge ratio increases beyond 60%, VaR begins to 

increase because the netting benefit against other currencies begins to get undone. This happens 



https://www.cribfb.com/journal/index.php/ijfb                               Indian Journal of Finance and Banking                    Vol. 5, No. 1; 2021 

34 

while there is concurrent increase in hedge cost, which represents an inefficient region for the 

corporate undertaking such hedges. 

Bauwens, Ben Omrane and Rengifo (2006) adopt a similar methodology in determining 

the optimal allocations in an FX portfolio, that maximizes expected returns subject to a VaR 

constraint. Here in the case of a corporate hedger, the cost is minimized subject to a desired VaR. 

 

 
 

Figure 5. Comparison of VaR and cost of Forward hedge at various hedge ratios. Blue dots 

represent VaR-cost combinations and are represented along the left axis. Orange dots represent 

the sum of VaR and hedge cost and are represented along the right axis. 

 

DISCUSSION 

Limitations of the Model 

Value-at-Risk has well-documented limitations as a framework. Huisman, Koedijk, and Pownall 

(1998) highlight how the traditional measure of VaR does not account for fat-tail events 

accurately enough. Given that VaR is a statistical measure of the risk that estimates the 

maximum loss that may be experienced on a portfolio with a given level of confidence, it is 

always connected with a probability that says how likely it is that losses will be smaller than a 

given number. Measuring risk in this manner can result in the corporate being exposed to fat-tail 

risk because VaR does not quantify the potential loss that can occur at the very end of the tail. 

VaR model makes an assumption that markets are behaving normally with some likelihood of 

major movement, while frequently financial markets do not behave normally as we have seen 

historically. It is important to understand that VaR is not designed to measure extreme price 

changes, and would not have been able to fully capture the market movement caused by once-in-

a-decade crises such as the COVID-19 pandemic. Therefore, VaR should always be interpreted 

along with the associated level of confidence, which is less than 100%. 

An organization can supplement a VaR based risk framework with stress testing. 

Financial parameters which demonstrate the greatest risk for the organization can be chosen and 

one can assess the impact of a certain percentage up or down move of that parameter. For 

example, in the case of the Indian exporter explored in this paper, given that the exposure in 

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https://www.cribfb.com/journal/index.php/ijfb                               Indian Journal of Finance and Banking                    Vol. 5, No. 1; 2021 

35 

EUR is the largest, the firm should monitor the impact of a +- 5% daily move in EURINR. 

Taken together with VaR, this can provide a comprehensive measurement framework. 

Another limitation of standalone VaR model arises when looking at multi-asset risks 

together. VaR takes account of how price changes of different assets are related to each other. 

However, the correlations between different assets are constantly changing and one has to be 

mindful to reassess the underlying assumptions of a hedge philosophy. For instance, JPYINR 

and EURINR are offsetting exposures and are positively correlated and hence can provide a good 

offset in our example. However, looking at historical data, the underlying correlations are 

volatile, moving between 0.2 and 0.8 in a year. Hence, it is important to review the correlations 

and resultant hedge ratios on a frequent basis. 

Finally, it is critical for the organization to define hedging goals clearly. Hedging and 

speculating are sometimes indistinguishable (a broader definition of speculation could include 

amending the hedge ratio to allow for some volatility in the cash flow). Inadequate 

understanding of implication of hedging in terms of additional cost or opportunity loss can result 

in problems for treasury professionals. Using VaR as a tool to set these objectives is a step in 

reducing such subjectivity. However, it is important that goals associated with acceptable VaR 

levels are set and understood at senior levels in the organization. We briefly discuss hedging best 

practices in the next section. 

 

Best Practices for Hedging 

Hedging can often be an expensive proposition. Costs typically include hiring qualified 

employees in the treasury who understand the use of derivatives, credit limits with banks and 

associated overheads such as collateral transfer and legal documentation such as ISDA, 

operational costs of tracking mark-to-market on the derivative positions, and the potential gains 

that are foregone when uncertainty of exposure is done away with. Some of these costs can be 

optimized using a few simple techniques that we describe below. 

Exposure optimization: as illustrated in the previous section, the recognition of offsetting 

exposures (within and across asset-classes) can reduce the net exposure that needs to be hedged. 

For instance, companies having long-term exports in USD can choose to raise USD foreign 

currency debt (loan/bond) to act as a natural hedge. Likewise, companies can also seek to restrict 

the number of invoicing currencies for exports or imports in order to keep the scope of currency 

exposures manageable. As a finer point, there are likely to be tenor mismatches that a corporate 

needs to be mindful of, such as the short-term nature of trade exposures compared to longer term 

nature of borrowings. Ideally, exposures should be netted off over the same time horizon when 

they are expected to occur, but in practice there are likely to be mismatches that need to be 

managed carefully. 

Cross-asset correlations: in addition to the fact that currencies are correlated and hence 

provide natural hedge depending on the portfolio of exposures, a corporate can also consider 

cross-asset correlations that include exposures to commodities, fixed income instruments, and 

equities. Such correlations are not static and the company needs to keep monitoring these at a 

reasonable frequency and take an action when the correlations break down. Chen, Kritzman, and 

Turkington (2015) explore strategies such as linear and non-linear relations among asset classes 

to identify second order relationships. The use of machine learning may be particularly helpful in 

identifying non-linearities among financial assets. While adding layers of quantitative analyses to 

optimize hedging may be useful, it is computationally expensive and needs regular monitoring. 



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36 

Risk reward optimization: once the company establishes a framework of looking at 

overall risks by a single measure such as VaR, a risk-reward analysis can be performed 

comparing expected loss at a particular confidence level of VaR and evaluating it against the 

costs of running a hedge program. An optimum ratio can then be arrived at, similar to the Sharpe 

ratio for investment returns versus risk. This provides an objective, consistent parameter that the 

company can track to execute its hedge program. The simplicity of this measure does not 

compromise the quantitative rigor that goes into creating it. 

 

CONCLUSION 

Value-at-Risk is a widely-applied methodology for measuring risks in financial institutions. As 

we demonstrate in this paper, the technique can be adopted by corporate risk management as 

well. The basic tenets of risk measurement remain the same across organizations, whether 

corporate or financial, which is minimization of volatility at reasonable costs. Using VaR to 

measure firm-wide currency risk allows corporate to understand, measure, control and 

communicate the risk in a manner that can be understood at all levels in the organization. 

Currency hedge decisions are always an exercise in cost-benefit analysis. Often, in times 

of financial market volatility, hedging activity could be hindered due to prohibitively high costs 

and lack of understanding of risk metrics to track. Taking a conservative approach and hedging 

the exposure completely could result in a very high cost for the organization. A mathematical 

framework that measures the risk as a single number (i.e. the impact of an adverse move to the 

organization) and looks at efficient ways of hedging the risk can help to resolve the dilemma to a 

large extent. We illustrate the case with the example of an Indian exporter firm that faces current 

account and capital account exposures in multiple currencies. A simple framework set at 

organization level can ensure that treasury professionals and senior management have clarity on 

the goals of hedging and the organization is protected from market volatility in a cost-efficient 

manner. 

  

REFERENCES 
Bauwens, L., Ben Omrane, W., & Rengifo, E. W. (2006). Intra-daily fx optimal portfolio 

allocation. Available at SSRN 912697. 

 

Chen, W., Kritzman, M., & Turkington, D. (2015). Alternative Currency Hedging Strategies 

with Known Covariances. Journal of Investment Management, 13(2), 6-24. 

 

Copeland, T., & Copeland, M. (1999). Managing Corporate FX Risk: A Value-Maximizing 

Approach. Financial Management, 28(3), 68-75. 

 

Dowd, K. (1999). A value at risk approach to risk-return analysis. The Journal of Portfolio 

Management, 25(4), 60-67. 

 

Dufey, G., & Srinivasulu, S. L. (1983). The case for corporate management of foreign exchange 

risk. Financial Management, 12(4), 54-62. 

 

Hendricks, D. (1996). Evaluation of value-at-risk models using historical data. Economic policy 

review, 2(1), 39-69.  

 



https://www.cribfb.com/journal/index.php/ijfb                               Indian Journal of Finance and Banking                    Vol. 5, No. 1; 2021 

37 

Huisman, R., Koedijk, K. G., & Pownall, R. (1998). VaR-x: Fat tails in financial risk 

management. Journal of risk, 1(1), 47-61. 

 

Morgan, J. P. (1996). Riskmetrics technical document. 

 

Marshall, C., & Siegel, M. (1996). Value-at-Risk: Implementing a risk measurement standard. 

 

Nain, A. (2004, March). The strategic motives for corporate risk management. In AFA 2005 

Philadelphia Meetings 

 

Rockafellar, R. T., & Uryasev, S. (2000). Optimization of conditional value-at-risk. Journal of 

risk, 2(3), 21-42. 

 

Smithson, C., & Simkins, B. J. (2005). Does risk management add value? A survey of the 

evidence. Journal of applied corporate finance, 17(3), 8-17. 

 

 

 

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