This work investigates the hedging performance of futures contracts in two asymmetric markets, peso/dollar traded at the Mexican derivatives market (MexDer); and dollar/ peso traded in the Chicago Mercantile Exchange (CME). Value at Risk and Expected Shortfall enhanced by GARCH (1,1) modeling was applied. The left and right tails of the futures return series are examined, for both short and long positions. The period analyzed comprises from October 2016 to June 2017, partitioned in three subperiods; the results obtained for each market are compared, and finally their statistical validity is tested applying Kupiec backtesting. Overall, hedging in the CME is more effective, albeit the MexDer outperforms that market several times. However, all metrics (with and without GARCH modeling added) show important weakness below the 99 percent confidence level.

Este trabajo investiga el desempeño de cobertura de contratos de futuros en dos mercados asimétricos, peso/dólar negociado en el mercado mexicano de derivados (MexDer); y dólar/peso negociado en el Chicago Mercantile Exchange (CME). Aplicamos valor en riesgo y déficit esperado mejorado por el modelado GARCH (1,1). Se examinan las colas izquierda y derecha de las series de rendimientos de futuros, tanto para posiciones cortas como largas. El período analizado comprende de octubre de 2016 a junio de 2017, dividido en tres subperíodos; los resultados obtenidos para cada mercado se comparan, y finalmente su validez estadística se prueba aplicando backtesting Kupiec. En general, la cobertura en el CME es más eficaz, aunque el MexDer supera a ese mercado varias veces. Sin embargo, todas las métricas (con y sin el modelado GARCH agregado) muestran una debilidad importante por debajo del nivel de confianza del 99 por ciento.

Globalization has led during the last five decades to a significant growth in trade, real and portfolio investments which in turn have been accompanied with a greater use of currency transactions, albeit dominated by the dollar vis-a vis other national currencies. Growth, however, has been characterized by volatility of exchange rates. To prevent negative results in their operations, corporations, policy makers, investors and traders hedge their holdings, among other alternatives, with future contracts.

Thus, currency hedge with future contracts has been reported widely in the financial literature.^{1}

Various techniques have been used in previous research, attempting to estimate the efficiency of futures markets. A great deal of the literature has dealt with the optimum hedge ratio. Another strand of research has concentrated in estimating tails’ risk attempting mainly to predict potential losses. Value at Risk analysis (VaR) models have been used for this purpose. However, few studies compare the efficiency of converse currency future contracts offered by two different markets. This work examines the performance of peso/dollar contracts offered by the Mexican Derivatives Market (MexDer) vs. the dollar/peso futures offered by the Chicago Mercantile Exchange (CME), which, while reflecting symmetries between the U.S. and Mexican economies, also present important asymmetries in size, volume of trade, and maturity. Value at Risk (VaR) and Expected Shortfall (ES) methodologies were used, enhancing them by incorporating GARCH modeling. Moreover, these methodologies integrate the trading position, distinguishing between downside and upward risk.

Concretely, the objective of this paper is to analyze, contrast and determine which of those metrics, applied to both markets, yield better and statistically robust estimates about the currency coverage with the futures pinpointed above. The hypothesis is that it is possible to obtain greater accuracy estimating potential losses by applying ES under a GARCH approach, with different levels of confidence (90%, 95%, 97.5% and 99%). The hypothesis also includes that hedging in the CME leads to a better hedging results than those obtained in the MexDer. The period of analysis considers from October 2016 to June 2017.

Historically, México has been associated with Canada and the United States conforming the North American Free Trade Agreement, NAFTA (1994-2020) and has now entered a renewed regional integration agreement again involving the United States, Mexico and Canada, (UMSCA), starting on July 1, 2020. However, it is important to underlie the fact that Mexico’s economy is less developed than its counterparts in the agreement, revealing severe economic and institutional differences among these countries.

COUNTRY
GDP
GDP PER CAPITA
"TOT STOCK MKT CAPITALIZATION"
TOTALSTOCK MKT CAPITAL GDP
United States
19,485. 394
53,336
31,774.59
163.01%
Mexico
1,150.89
10,292
417.021
36.24%
Mexico/US
5.53%
19.30%
1.31%

Source: World Bank National Accounts data, and OECD National Accounts data, 2020, and:

More striking is the difference regarding stock market capitalization. Total stock market capitalization in the U.S.^{2}

In this respect, our research contributes to the financial literature in two ways: 1) extending the financial literature by examining the performance of futures in two asymmetric economies characterized by markets, of different levels of development and offering a converse underlying asset; and, 2) analyzing practical alternative tools, sanctioned by regulating authorities, frequently used by market players in their decisions concerning estimations of currency coverage with futures of two economies linked by trade and financial activities facing significant economic-financial challenges. Moreover, it is important to recall that Mexico is the 15th world economy (

The paper is structured as follows. After the introduction, the second part presents a review of the literature. The third section describes the data and pre-estimation statistical analyses. The fourth section deals with the Value at Risk, Expected Short Fall, and GARCH econometric models. The fourth part corresponds to empirical application and analysis of results. The fifth and final section presents the conclusions.

As previously mentioned, foreign exchange risk has become more and more important. The financial markets have responded either enhancing traditional hedging instruments, or else creating new derivatives for this purpose. The volatility of markets, along with a search for tools to manage risk, have led to serious academic research and to the design of new financial instruments. In this section, some studies related to the use of VaR and Expected Short Fall applications adjusted by GARCH modeling are reviewed. GARCH modeling is important to overcome homoscedasticity assumption problems, which are ignored in many studies. It is important to acknowledge that VaR and ES have been endorsed by international and local regulation authorities. The complexity of other sophisticated models has limited their application, particularly in emerging markets.

Various studies confirm the benefits of hedging strategies with futures by applying VaR analyses extended with GARCH modeling

A more recent work by

In turn, Ben Raheb, Ben Salha, and

In another work,

A frequent research theme deals with the relationship between exchange rates and stock markets. This is the approach followed by

In a more recent work,

Following this trend of studies,

Also, related to recent trends in VaR/ES research,

Most recently,

Another research using intraday data is the work by

Concerning Latin America and Mexico the literature reports few studies, none is related with exchange rate coverage.

Similarly,

Finally,

Summing up, research on risk associated with exchange rate and hedging strategies is very important. The use of VaR and CVaR show the potential losses that the foreign exchange market can incur in. Applying GARCH modeling to those metrics, enhances their precision and applicability. Regarding currency hedging, academic research has concentrated on other risk issues such as the determination of the optimal hedge ratio. The use of VaR modeling has been rather limited, albeit highly sophisticated models have been designed for mature markets and developed economies.

VaR applications for emerging markets have mostly dealt with the impact of exchange rates on trade, and real and portfolio investments. Furthermore, research using high frequency intraday data is nonexistent in these markets due to the lack of information, as well as high costs. There are no concrete works about exchange rate hedging in Mexico. Therefore, this paper constitutes an important contribution on this matter. Moreover, this paper uses VaR metrics to compare hedging efficiency between two markets: one fully developed, and the other an emerging market; hedging is estimated in the dollar/peso offered by the CME of Chicago vis a vis the peso/dollar futures offered in the MexDer. The final econometric Var and ES include GARCH modeling to overcome erroneous homoscedasticity assumptions assumed in many studies.

A careful research strategy considering the big differentials between the MexDer and the CME was undertaken. Contract characteristics are similar. However, the CME is the largest futures market globally and its operations began in the nineteenth century. The MexDer, on the contrary, is a small market from an emerging economy; after some transitional issuing of some forward-warrant assets, the market finally began operations on December 15, 1998, trading peso/dollar futures.

Although trading contracts follow similar norms than other markets, besides the differences in size and maturation, the big difference so far is the size of each contract. In Mexico, each futures contract covers a lot of 10,000 U.S. dollars; in the CME each futures contract covers a lot of 500,000 Mexican pesos about 22,230 U.S. dollars. Futures in each market are subject to the volatility of both currencies, but the dollar is the dominant currency.

The period of analysis includes from October 2016 to June 2017. Data for the CME and the MexDer was gathered from Bloomberg; exchange rate was obtained from Banxico (Mexico’s Central Bank). For this research, it was considered a nine months cycle subdivided in three subperiods. The lapses between these partitions are: The first sub period (ex-ante) includes from October to December 2016, it analyzes the behavior of hedging prior a lapse of some stress; the second period examines the problem during a volatility sequence, from January to March 2017, impacted by tensions caused to the Mexican economy due to decreasing and unstable oil prices (Mexico’s second largest export), as well as a shaky exchange rate; the third (Ex-post period) comprises April to June 2017, which aims to examine post-stress futures behavior in both the Mexican and Chicago futures markets. This approach allows us to analyze in dept the performance of both markets.

Subperiods
Peso Futures in Chicago
FROM
TO
EXANTE_FMXP PERIOD
OCT¨-16
DEC-16
PERIOD PRIOR EXCHANGE PRESSURE
AMIDTS_FMXP PERIOD
JAN¨-17
MAR¨-17
PERIOD AMIDTS EXCHANGE PRESSURE
EXPOST_FMXP PERIOD
APR-17
JUN¨-17
PERIOD AFTER EXCHANGE PRESSURE
EXANTE_FDOLLAR PERIOD
OCT¨-16
DEC-16
PERIOD PRIOR EXCHANGE PRESSURE
AMIDTS_FDOLLAR PERIOD
JAN¨-17
MAR¨-17
PERIOD AMIDTS EXCHANGE PRESSURE
EXPOST_FDOLLAR PERIOD
APR-17
JUN¨-17
PERIOD AFTER EXCHANGE PRESSURE

Source: Prepared by authors with data from Blomberg and Bank of Mexico

Daily closing prices were used to calculate the logarithm of prices returns. All econometric analyses performed in this paper used these returns.

Where p_{i} > p_{j}

To ensure well-founded answers to the hypothesis, first the stationarity of the series was tested, applying the ADF test. The t-Student test was also carried out to reinforce the results of the stationarity of the series. Normality was tested employing the Jarque-Bera test

To the above described tests, the ARCH LM test for heteroscedasticity was added, for one, two, three and four lags. Akaike and Schwartz criterio were used to determine the minimum of lags that the model may include, which is expected to be a GARCH (1,1). The models ARCH and GARCH were applied with intercept and a moving average mean; the results were examined following the above-mentioned criteria.

In relation to the analysis and adjustment of volatility, the standard deviation in statistical terms is a measure of the rigor of random changes, generally unpredictable variations in the profitability or price of a title.

The asymmetrical and characteristic volatility clusters of the logarithmic returns series derive from the size of the impacts on prices and returns in certain periods. Particularly, market instabilities and bad news increase volatility. At first glance, it would appear that the series are non-stationary (the mean being a function of time and non-constant variance).

^{3}

Market
Futures
Mean
Std. Dev.
Skewness
Kurtosis
Jarque-Bera
ADF
MexDer
Dollar Futures
16.8449
2.4040
-0.2712
1.907
66.852
-13.166
Dollar Spot
16.8401
2.4094
-0.2654
1.898
67.274
-19.353
CME
MXP Futures
5.9999
1.0064
-0.4909
2.102
37.557
-23.394
MXP Spot
4.8992
0.3004
-0.1028
2.106
37.849
-31.623
Dollar Futures
0.00002
0.0083
-0.1363
3.657
22.739
-2.864
Dollar Spot
0.00003
0.0001
-0.0448
4.827
150.243
-2.864
CME
MXP Futures
0.00014
1.0984
-0.1291
8.064
1154.824
-2.864
MXP Spot
0.00014
1.0918
-0.1209
9.449
1870.436
-2.854
95% C.V.
5.99
-3.96

Source: Prepared by authors with futures and spot prices. Bank of Mexico and Bloomberg.

Finally, the Jarque Bera statistics confirms that all series are non- normal. The sharp differences in the statistical behavior of these market can be attributed to the fact that future lots are traded in currencies of different value, reflecting therefore the instability of the peso in the MexDer. However, this behavior also suggests the presence of market segmentation among these two neighboring countries; apparently, participants (hedgers) in these markets belong to well differentiated groups; most likely, few participants operate in both markets. The identified differences also unveil opportunities for price arbitrage; the dollar price in the MexDer and its equivalent in pesos in the CME most likely present temporary price disequilibria creating opportunities for spatial arbitrage.^{4}

The results of the Dickey Fuller Augmented Unit Root (ADF)^{5}

-8.7058
-8.7455
-6.7534
-6.9092
-8.6921
-8.7270
-6.7349
-6.8907
-8.7006
-8.7385
-6.7464
-6.9022
-8.7791
-8.8560
-6.7734
-6.7903
-8.7607
-8.8328
-6.7449
-6.9672
-8.7721
-8.8472
-6.7564
-6.9815
3.9088
3.9640
9.1179
6.7677
3.9180
3.9732
9.1271
6.7770
3.9123
3.9675
9.1214
6.7712

Source: Prepared by authors with futures and spot prices. Bank of Mexico and Bloomberg.

The tests ARCH 1, GARCH (1.1), and ARCHLM 1 were carried out. Models were selected according to the Akaike, Schwartz and Hannan, criteria. The decision rule indicates to choose the model with the lowest numerical values which in this case corresponds to the GARCH (1.1) model (

The VaR of a portfolio of financial futures contracts is defined as the maximum expected loss that an investor will face over a period of time given a confidence level α, (usually 95%, 97.5% and 99%), when investing, anchoring or liquidating positions in the portfolio due to unforeseen movements affecting market factors such as exchange rates, interest rates, prices of financial assets. Likewise, this metric is used by regulators to procure control of the operations carried out by financial institutions to establish standard capital requirements measures of financial institutions.

Statistically, VaR is defined as the probability that changes in the portfolio value will not exceed the maximum expected loss over a specified period of time for a given confidence level; Let

Where, ΔP represents changes or losses in the value of the portfolio. Another way to estimate the VaR of a portfolio is calculated by finding the inverse function of the cumulative distribution of risk factors. That is, a space of probability is fixed (Ω, F, P) where Ω represents the sample space or set of possible outcomes, F is a σ algebra representing measurable events, P is a measure of probability, and X is a random variable representing the investment portfolio losses and earnings during a given period of time.

Where F_{x}(

Additionally, let the set

This provides the return that is exceeded with a probability of (100 - ∝) per cent. However, two portfolios may have the same VaR value but with different potential losses. This is because the VaR does not calculate losses beyond the 100% percentile. This deficiency is mitigated by estimating an additional performance metric, that is, the Conditional Risk Value (CVaR) or Expected Shortfall (ES) described below. The Value at Risk is estimated by applying i, with αi, with i = 1%, 2.5%, 5%, and 10%. In our study the performance metric used corresponds to the percentage reduction in the VaR-GARCH (throughout this paper it will be called VaRG), which measures the percentage VaR-GARCH (applying the GARCH model) of a hedged portfolio compared to the VaR-GARCH of an uncovered portfolio, this applies to both VaR and ES; the

VarG = the percentage reduction in the VaRG of the hedged portfolio as compared to the unhedged portfolio. If future contracts fully eliminate risk VaRG = 1, whereas, if VaRG = 0 futures contracts do not reduce risk. Therefore, let x be a result of applying the metrics, then ,^{7}

Several criticisms have been generated towards the VaR model since it shows instability if there is no normal distribution of losses, as empirical evidence indicate. Thus, coherence is only based on the standard deviation of normal distributions on asset returns; under the assumptions of normal distribution the VaR is proportional to the standard deviation of the instrument returns (

The CVaR, or ES measures the average loss conditioned to the fact that VaR has been exceeded. Such metric provides, as mentioned, coverage with an estimator not only of the probability of loss, but also of the magnitude of a possible loss.

This means that managing risk using VaR can be inefficient to capture the effects of diversification which reduces portfolio risk

It is an alternative risk measure to partially amend the deficiencies presented by VaR. CVar is often referred to as the expected deficit or Expected Shortfall, ES.

For a X, let E(│X│)< ∞ and its distribution function , the Expected Shortfall of a given confidence α ϵ (0,1) can be defined as,

Where q_{u}(F_{X}) = F_{X}(u) is a quantile function F_{X}, thus, the relation between VaR and y ES is,

The expected excess measure is a coherent risk measure based on the expected value of potential losses that exceeds the VaR level. This robust risk measure has been studied independently and defined in different ways by several authors in recent years. The main names or variants adopted by this risk measure are as follows: Tail Conditional Expectation (TCE), Worst Conditional Expectation (WCE), Tail Mean CVaR, Mathematical Conditional Expectation of VaR Losses, Expected Shortfall (ES), Conditional Value at Risk (CVaR) (

In statistical terms, the ES is based on a continuous distribution whose random variable measuring changes in portfolio value losses can be defined as: the mathematical conditional expectation of losses that have exceeded the VaR level,

As in the performance metric presented in eq. (7) to evaluate coverage performance in the VaRG model, the coefficient to include GARCH assessment was modified. In this model, the coefficient corresponds to the percentage reduction in the ES, under the alphas considered in the VaRG; the modified ^{8}

So, if a position in CME is found to have a higher VaRG but a lower ESG than MexDer futures, that indicates that the volatility of futures in CME is higher in normal market situations, but in extreme situations the MexDer futures have higher volatility.

The use of GARCH (p,q) models has become widespread to explain the variance in time. In general, GARCH models assume that conditional variance is affected by their past events. The advantage of these models over the original ARCH models (p) is that GARCH models allow to capture persistence of volatility (presence of volatility clusters). In fact, regarding exchange rates, several papers in the financial literature deal with the issue of optimal coverage using multivariate GARCH models to generate optimal hedge ratio (

The GARCH model we employ is the Vector GARCH model (1,1) proposed by

where,s

r_{st} y r_{ft} = spot and futures’ returns, respectively,

ε_{st} y ε_{ft} = residuals representing innovations in the spot and futures prices, respectively,

Ω_{t-1} = the information set at time t-1,

σ2_{st} and σ2_{ft}, = variance of spot and futures, respectively, and

σ_{sft} = ε_{st} and ε_{ft} covariance.

However, this model is restricted to the diagonal arrays α and β, so only the upper triangular portion of the variance-covariance matrix is used. This means that the conditional variance depends on past values themselves and the past values of square innovations in returns. This reduces the number of parameters to nine (each of the α and β has three elements). This is subject to the requirement that the variance-covariance matrix be positively defined to generate positive elements of coverage. Let

where, j,k = 1 for the GARCH (1,1) model; 𝛾, 𝛼 and 𝛽 are positive, and α_{i} + β_{1} ≤ 1, for i = 𝑠, 𝑓 . The conditional mean follows an autoregressive process. The correlation coefficient 𝜌𝜌 equation (22) is a constant. One advantage of this model is that it consists of a positive semi-defined matrix, subject to positive conditional variances, which means that the variance- covariance matrix is positive or non-negative. When using this method, the results are used to build hedging portfolios where +𝑟_{𝑠} − ℎ ∗ 𝑟_{𝑓} is the short hedge, y is the long hedge, 𝑟_{𝑠} and 𝑟_{𝑗} are the spot and futures returns respectively, and, ℎ ∗ is the estimated hedge.

The probability of failure (𝑝∗) of the VaR metrics is estimated applying a maximum likelihood process, a likelihood ratio (LR). Finally, logarithms of a binomial distribution are gathered, and this function is maximized with respect to the estimated probability (𝑝^{∗}) . Once the LR estimator is obtained, a statistical contrast is established between the theoretical and estimated probabilities (ECUACION respectively). The assessment of significance is carried out with the maximum likelihood ratio, from the logarithm of the probability distribution applied for each of these probabilities; the likelihood ratio defined as:

The LR test represents a Chi- square distribution with one degree of freedom.

Hitherto we have established the statistical characteristics of the price and return series and determined the GARCH (1,1) model appropriate to estimate the volatility of the logarithmic returns of spot and futures series of the MexDer and the CME. The econometric models for estimating the VaRG and ESG models are presented. Aiming at the greatest precision, in this section we report and compare the evidence obtained using confidence levels of 90%, 95%, 97%, and 99%.

VaRG = 90%,
VaRG 95%,
VaRG 97.5%
VaRG 99%
"VaRG90%
VaRG95%
VaRG 97.5%
VaRG 99%
MexDer Dollar
futures
EX ANTE
71.19
74.39
84.59
90.43
86.66
97.78
91.57
92.43
Short AMIDTS
70.25
76.73
79.73
86.82
85.23
95.48
89.25
91.82
EX POST
68.49
77.27
90.03
80.87
78.34
97.28
90.27
82.87
DEUA EX ANTE
74.12
77.33
71.19
78.43
88.72
88.43
93.72
94.43
Long AMIDTS
69.84
71.19
74.91
81.82
85.28
92.82
91.23
97.28
EX POST
69.69
80.91
73.96
77.87
77.36
92.87
89.24
95.87
CME Peso
Futures
MXP EX ANTE
79.53
90.96
75.91
85.52
91.27
93.79
93.41
95.89
Short AMIDTS
76.26
75.91
68.59
80.37
86.29
91.26
89.35
93.26
EX POST
71.87
86.01
75.76
90.54
87.19
88.67
96.73
89.87
MXP EX ANTE
69.91
78.56
72.09
83.88
80.19
86.88
96.47
89.88
Long AMIDTS
71.64
75.76
74.59
80.29
76.28
95.95
94.31
95.29
EX POST
68.89
78.09
70.28
80.97
84.21
86.19
86.71
91.97

Source: Prepared by authors with data from Bloomberg and Banco de México. Applying the E-Views 9 package

First, it is important to stress that both the hypotheses assumed are confirmed. In all situations the ES-GARCH model outperforms the VarGARCH model. Its estimates are more precise at all confidence levels, for both the Mexican Market and the CME, again, for both the short and long positions. Similarly, the Chicago market shows a better performance than the Mexican market in 28 out of 48 total hedging alternatives.

Another interesting outcome is the practically nil efficiency of both methodologies in both markets for confidence levels of 97.5% and below applying the VaR-GARCH method; very frequently hedging is in the 70.0% and even lower mark. This problem is almost inexistent applying the ES- GARCH alternative; in fact, hedging effectiveness improves a lot at the 97.75% confidence level and at the 99.0% confidence level the best results are obtained.

Interestingly, for the short position in the MexDer, the more rigorous estimation is at a 95% level of confidence; but for the long position the best hedging strategy can be attained at a 99% level of confidence. In the case of the CME, for the short position the best metrics are at the 99%, but for the long position the best metrics are shared among the 95%, 97.5% and 99% levels of confidence.

The greatest protection for the short position during the turbulence period is attained with ESG at 95% confidence level; 95.48 represents the percentage reduction of the expected shortfall in the covered position compared to the uncovered position; when the coefficient approaches one (100% in our analyses to ease the interpretation of the results), there is a total decrease in risk; on the contrary, if it tends to zero, it implies that there is no reduction of risk in the MexDer; this can be attributed to futures volatility in the CME in normal market situations, while in tense situations the MexDer futures seemingly have lower volatility.

Finally, looking at the differences in performance between metrics, the best sample performance metric in the MexDer (and the entire sample) is that of the 95% ESG confidence level resulting in a 97.78, while the worst coverage performance corresponds to the VaRG with 68.49 (both in the short position); this represents a performance differential of 31 percent. In the case of the CME, the best hedging is obtained during the ex post period (96.73) for the short position (ES at 97.5%), whereas the worst coverage is achieved during the same subperiod 68.89 per cent (VaRG at 90%).

Summing up, exchange rate hedging in the Chicago Mercantile Exchange is more efficient applying ESG. The empirical evidence depends on the alphas (α) under consideration and the market to determine which of the two coverages should be used. Chicago is more convenient than hedging exchange rate in the Mexican Market. However, to ensure solid predictions ES-GARCH should be estimated at a 99.00% confidence level. Differences in the hedging strategies between the two markets are noteworthy. These differences can partially be attributed to market depth, traded volume, contract size, and market performance.^{9}

Complementing

7,100,313
172,175,518,270
278,790 (667,896)
0.0485
310,000
8,246,654,784
298,003 (779,388)
00.54.96
1,759,000
48,691,771,949
328,640 (831,460)
0.05536
9,169,313
229,113,945,003
905,433 [2,278,744]
2,600,554
25,538,937,760
2,896,296
20.6194
2,498,514
26,997,745,531
2,560,339
18.7955
2,787,224
29,029,681,662
2,874,961
18.0626
7,886,292
81,566,364,953
8,331,596
1.63X
2.81X
0.1087 [27.35]

Source: Prepared by authors from Bloomberg and Baxmex data.

At any rate, the differences could be larger. While volume remains rather stable in the Mexican market, in the Chicago market there was a big drop after the first subperiod, particularly from the first to the second subperiod, the period of higher volatility. This can probably be attributed to investors’ attitudes and institutional factors. As previously mentioned, the CME is a long large and well established market while the MexDer is a market still in the process of consolidation and growth. Feeling the upcoming of a period of turbulences derived from unfavorable economic conditions in Mexico, experienced hedgers in Chicago probably adjusted their holdings of dollar/ peso futures migrating to other currencies. Finally, migration probably took place to the dollar/peso options market created by the CME in 2017. The differences also show the presence of segmentation among these markets and the possible existence of arbitrage opportunities.

This test was carried out for each partition from the sample series. The shaded areas in

Number of failures
Zone
Dollar Futures
Dollar USEx Ante
2
Short Amidts
1
Ex Post
2
Dollar US
Ex Ante
3
Long
Amidts
3
Ex Post
2
Peso Futures
MXP
Ex Ante
4
Short
Amidts
3
Ex Post
2
MXP
Ex Ante
3
Long
Amidts
3
Ex Post
2

Source: Prepared by authors from calculations made in excel with sample data

Number of failures
Zone
Dollar Futures
Dollar US
Ex Ante
4
Short
Amidts
6
Ex Post
7
Dollar US
Ex Ante
5
Long
Amidts
3
Ex Post
7
Peso Futures
MXP
Ex Ante
4
Short
Amidts
3
Ex Post
5
MXP
Ex Ante
5
Long
Amidts
7
Ex Post
7

Source: Prepared by authors from calculations made in excel with sample data

The number of failures of the estimates are well below the expected number of failures according to the parameters set out by the Kupiec test

"Significance level (Gray Zone)"
Days
T≤255
T≥510
T≥1000
0.001
1%
N < 7
1 < N < 11
4 < N < 17
0.05
5%
6 < N < 21
16 < N < 36
37 < N < 65
0.1
10%
16 < N < 28
38 < N < 65
81 < N < 120

Source: Prepared by authors from Kupiec information

This article contrasts the effectiveness of hedging exchange rate risk using two metrics most often applied in finance for the case of the peso/dollar traded in Mexico, and the dollar/peso traded in Chicago. The metrics used are VaRG and ESG applying a heteroscedasticity autoregressive GARCH (1,1) model.

The VaRG as a performance measure provides lower results in terms of better hedging performance than the results obtained with the ESG metric. This suggests that the magnitude of coverage performance effectiveness is related to the result that is intended to be achieved, since the results are based on the choice of a performance metric. ESG, as a metric for assessing coverage performance is statistically adequate; results obtained at a 99.0% confidence level are very rigorous. A caveat to its application must be added: the results are based on a specific period; ESG should be employed, like any other model, with caution and the support of continuing research.

Finally, this research underlines the importance of quantifying risk exposure; it is very important for all risk-return decisions concerning trade, investments corporate activity, and policy making, as well as for the choice of hedging alternatives. Further research is needed, particularly for the case of emerging markets and currencies subject to sharp volatility patterns. In the case of the U.S. and Mexican derivative markets further research is necessary to identify their differences and above all as a means to foster its integration with global markets as well as to the development and contribution to the advancement of the financial sector in Mexico and its potential to favor this nation’s economic development.

The authors wish to express their appreciation to Jaime Díaz Tinoco, CEO, Processar, Inc., Rodolfo Liaño Gabilondo, CEO, Pied a Terre, Inc., and two unknown referees for their valuable observations and suggestions.

Hedging (also known as covering) refers to any strategy employed to reduce the risk of undesirable price movements on holdings of any asset; the goal is securing a predetermined price (for the covered asset). Derivatives like futures, options and swaps are available for this purpose. Currency Futures examined in this paper are contracts to buy/sell a given currency for a specific price at a predetermined period in the future.

It includes market capitalization of all U.S. based public companies listed in the New York Stock Exchange, Nasdaq, and OTCQX U.S. Market:

Econometric results reported in Tables 3 and 4 were obtained employing E-View 10.0.

Taking advantage of the lower price in one market to sell at the higher price in the other market.

It is fair to acknowledge that although this metric has a long-standing background, a formal practical model was advanced by JP Morgan in the 1990’s. The metric has also become very popular in teaching and research to a great extent due to a text published by

The formula generalizes for portfolios of n assets. Our portfolio comprises only one asset in each market: the dollar in the MexDer and the Peso in the CME. The hedged portfolio refers to the asset protected with a futures contract; the un- hedged portfolio simply holds the original asset unhedged.

See supranote 4.

See also analysis of basic statistics, Table 3, page 12.