H O S T E D BY Available online at www.sciencedirect.com ScienceDirect Wine Economics and Policy 8 (2019) 114e126 www.elsevier.com/locate/wep Weather index-based insurance as a meteorological risk management alternative in viticulture Andrea Martínez Salgueiro Department of Business, Universitat Autonoma de Barcelona (UAB), Building B, Campus UAB, Bellaterra, Cerdanyola del Valles, Barcelona, 08193, Spain Received 28 November 2018; revised 12 June 2019; accepted 21 July 2019 Available online 26 July 2019 Abstract This article explores the hedging potential of two weather index-based insurance programmes designed for the Rias Baixas Protected Designation of Origin (Spain). The first alternative insures both extreme and non-extreme weather events, while the second instrument covers exclusively extreme meteorological states. Two bioclimatic indicators computed for the period most correlated to grape yields are proposed as underlyings: the Branas, Bernon and Levadoux (BBL) and the Ribereau-Gayon and Peynaud hydrothermal scale (RGP). Yield-weather dependence is then modelled with two different methodological approaches: copulas and linear regression. To asses the risk reducing poten- tial, a hedging effectiveness analysis based on real and simulated data is carried out. The model uses variance and expected shortfall as risk measures. The results attained point out the high hedging ability of both insurance programmes, especially of the first of them based on RGP. This appraisal also reveals that the copula technique outperforms linear regression. Overall, the study results suggest that the implementation of policies geared to bioclimatic indices able to signal adverse weather events can significantly mitigate weather-related yield variations in viti- culture. © 2019 UniCeSV University of Florence. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Keywords: Weather index-based insurance; Viticulture; Meteorological risk; Hedging effectiveness; Copula approach 1. Introduction Different adaptation measures have been suggested and occasionally adopted by wine producers to mitigate the in- Fine wine making is extremely sensitive to weather con- come volatility derived from weather risk exposure and other ditions (Cyr and Kusy, 2007, p.146; Zara, 2010, p.222; sources of uncertainty. Some of them are supported by the Ashenfelter and Storchmann, 2016, p.25). Meteorological risk European Union's and member states' agricultural policies does not only adversely impact the quantity (Lobell et al., (Casta~neda-Vera and Garrido, 2017, p.3). These alternatives 2007; Chevet et al., 2011; Lorenzo et al., 2012) but also the are classified into two main groups. The first of them are the quality (Jones et al., 2005; Storchmann, 2005; Alston et al., so-called self-coping strategies, which involve the use of on- 2011; Lorenzo et al., 2012) of the grapes used for wine farm resources to change the production strategy (diversifi- production. cation, input intensification, variation in harvest times, geographical shifts in areas planted, substitution of grape cultivars and acquisition of new technologies), the commercial Abbreviations: PDO, Protected Designation of Origin; CAP, Common strategy (vertical integration) or the use of business benefits Agricultural Policy; IST, Income Stabilisation Tool; WI, Winkler Index; HI, (stabilisation accounts) (Ashenfelter and Storchmann, 2016, Huglin Index; BBL, Branas Bernon and Levadoux; RGP, Ribereau-Gayon and p.25; Casta~neda-Vera and Garrido, 2017, p.5). The second Peynaud hydrothermal scale; ENESA, State Agricultural Insurance Entity; group comprises those measures that transfer the risk to a third AEMET, Spanish National Meteorological Agency; ES, Expected shortfall. E-mail address: andrea.martinez@uab.cat. party in return for a fee, such as insurance or mutual funds Peer review under responsibility of UniCeSV, University of Florence. (Zara, 2010, p.223; Ashenfelter and Storchmann, 2016, p.25; https://doi.org/10.1016/j.wep.2019.07.002 2212-9774/© 2019 UniCeSV University of Florence. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). A. Martínez Salgueiro / Wine Economics and Policy 8 (2019) 114e126 115 Casta~neda-Vera and Garrido, 2017, p.5). Concerning insur- volatility of this meteorological variable as a determinant for ance, two main modalities are usually implemented: specific the use of weather derivatives in viticulture. Following a weather risk policies and multi-peril crop insurance.1 Both different approach, Zara (2010) designed a temperature risk yield indemnities that are not based on transparent criteria but hedging strategy for the Bourgogne C^ote de Nuits Pinot Noir on the subjective assessment and estimation made by the in- PDO (Protected Designation of Origin) and evaluated its risk surance firm's loss assessor (Skees and Reed, 1986, p.658; reducing potential based on the comparison of the crop's Smith and Goodwin, 1996, p.437; Coble et al., 1997, p.225; economic value with and without insurance. Hess et al., 2002, p.297; Zara, 2010, p.223). This paper aims to contribute to the literature by exploring Although less commonly adopted in this sector, there is the hedging ability of different weather index-based insurance another insurance alternative, the so-called weather index- programmes designed for the Rias Baixas PDO. This is a small based insurance. In contrast to the other two policies, this wine-growing area located in the northwest region of the instrument is based on a weather index instead of on actual Iberian Peninsula, Galicia (Spain). Despite having a long yields. Thus, this option not only significantly reduces tradition, it was not until 1988, after the Rias Baixas wine administrative costs and insurance premiums (Bokusheva Regulating Council was set up, that this activity began playing et al., 2016, p.200) but also encourages best management a significant role in the regional economy. Nowadays, the Rias practices as there are no asymmetric information and moral Baixas wine-growing industry generates 7600 full-time jobs hazard issues (Skees and Reed, 1986, p.658; Quiggin et al., and 5200 temporary positions, which represent between 7% 1993, p.95; Smith and Goodwin, 1996, p.437; Coble et al., and 12% of the total area's employment (Denominaci on de 1997, p.225; Hess et al., 2002, p.297; Turvey and Kong, Origen Rías Baixas, n.d.-a). 2010, p.18). Despite these advantages, this tool presents Spain, as a member state, is subject to the Common Agri- some design challenges, such as the selection of a suitable cultural Policy (CAP) of the European Union, which has underlying that adequately captures production risk and the traditionally supported two main alternatives to reduce income availability of reliable historical weather data (Cyr and Kusy, volatility: insurance and mutual funds. However, its last re- 2007, p.146). form (2014e2020) has enlarged the available battery of The usual predominance of small farms increases the bu- measures with the introduction of the Income Stabilisation reaucracy implied by the specific weather risk and multi-peril Tool (IST) (El Benni et al., 2015, p.2; Casta~neda-Vera and crop insurances, which are the most commonly used financial Garrido, 2017, p.4; Trestini et al., 2017a, p.25; Trestini instruments. This often leads to public intervention (Turvey et al., 2017b, p.461). Mutual funds refer to private initiatives and Kong, 2010, p.18). For instance, in Spain, the Ministry that allow farmers or groups of farmers to self-manage their of Agriculture and Fisheries, Food and Environment, through risks by contributing to a common financial reserve. When the State Agricultural Insurance Entity (ENESA), subsidises a losses occur, the farmers whose income has been negatively percentage of the insurance costs faced by farmers. Weather affected are compensated (European Commission, 2017). The index-based insurance, which carries less management ex- new instrument of IST is directly related to the concept of penses, has consequently arisen as a more effective option, as mutual funds, as it covers part of their paid indemnities. shown by the increasing interest towards its application in the Indeed, Article 39 of the EU Regulation No 1305/2013 settles agricultural sector. In fact, over the last years, several authors a maximum reimbursement by the IST of 65% of the have addressed its implementation in viticulture. Such is the compensation previously paid by the mutual fund, which can case of Turvey et al. (2006) and Cortina and Sanchez (2013), amount up to 70% of the income loss (Trestini et al., 2017a, who focused on the relevance of the accurate valuation of this p.25). Despite promising, this measure presents some chal- insurance typology. The first of them developed and applied a lenges, such as the precise definition of income trigger levels pricing procedure for situations where returns depend on both per year, farm type and country, which may be refraining its the occurrence and timing of the weather event. For their part, application at European and, specifically, at Spanish level Cortina and Sanchez (2013) modelled and valued a tempera- (Meuwissen et al., 2011, p.8). In fact, Castilla y Leon has been ture weather contract to mitigate late frost risk. Other authors, the only Spanish region supporting IST within its Rural despite still being interested in the valuation methodology, Development Programmes (2014e2020) (Casta~neda-Vera and devoted more attention to the hedging effectiveness issue, such Garrido, 2017, p.6; Trestini et al., 2017a, p.25; Trestini et al., as Cyr and Kusy (2007) and Cyr et al. (2008). These authors 2017b, p.461). Regulation No 1305/2013 also considers in its concluded on the high risk reducing ability of this insurance article 36 the possibility of covering part of the premium of modality based on the analysis of the meteorological volatility different insurance typologies, mutual funds and IST. How- in the Ontario ice-wine producing region. Some years later, ever, this measure has already been implemented in several Cyr et al. (2010) designed a rainfall-based weather contract for EU countries through State aids. Such is the case of Spain the Niagara region of Canada. They highlighted the increasing (Casta~neda-Vera and Garrido, 2017, p.6), where the Spanish System of Combined Agricultural Insurance, founded in 1978, provides a financially feasible alternative that allows the 1 The first type of policies is mainly used in Europe, whereas the second agricultural sector to cope with the damages caused by non- modality, which insures grape yields against a fixed package of risks, is controllable and unexpected risks. Nowadays, there are pol- commonly applied in US (Zara, 2010, p.223). icies available for all agricultural products that provide 116 A. Martínez Salgueiro / Wine Economics and Policy 8 (2019) 114e126 coverage against almost all natural disasters, such as frost, meteorological states is considered. Two different hydrother- hail, rain and wind among others. The system is based on the mal bioclimatic indices are suggested as underlyings. joint participation of private and public institutions: the The remainder of the paper is organised as follows. Section Spanish national and regional governments, which provide 2 reviews the materials and methods applied to design and grants that cover part of the insurance premiums; the Profes- value the suggested insurance plans. Then, Section 3 presents sional Agricultural Associations, representative of farmers and the calculations. After that, Section 4 displays the hedging ranchers; and the insurance entities, grouped in Agroseguro effectiveness analysis and discusses the results attained. (Agroseguro, n.d.). Finally, Section 5 summarises the main conclusions of the This insurance structure has enjoyed considerable demand research. since its launch. In 2017, the number of agreed policies amounted to 240186. Although the public budget devoted to 2. Materials and methods insurance has decreased in comparison to pre-financial crisis times, it has started to rise again since 2014. In fact, in 2017, With a current coverage of 4061 ha spread over different the grants supplied by the national and regional governments locations of the province of Pontevedra and a small part of A added up to the significant amount of 314.11 million euros. Coru~na county, the Rias Baixas PDO produces wines of The highest number of agreed policies was registered for worldwide renown that share common and unique character- arable crops, with 131082 contracts, followed by winery, with istics derived from the climate, landscape and soil features of 29428 agreements (Agroseguro, 2017). These figures empha- this wine-growing area. Regarding meteorology, this Atlantic sise the need of hedging meteorological risk in viticulture and region is characterised by heavy rainfall in winter. Pre- indicate that the launch of weather index-based insurance may cipitations are also common in spring and autumn, while actually succeed in Spain. This idea is further reinforced by infrequent and light during summertime. Temperatures are the positive results of different studies which have analysed mild in winter and warm in summer. Concerning the land- the farmers’ willingness to pay for weather index-based pol- scape, the sub-zone of Val do Salnes, which accounts for more icies (McCarthy, 2003; Sarris et al., 2006; Turvey and Kong, than 60% of the total yearly production, is mainly charac- 2010; Ali, 2013). However, the implementation of this alter- terised by the predominance of low-lying land and the pres- native would be subject to a thorough programme design. For ence of coastal plains. For their part, Condado do Tea and O instance, given that wine producers generally have a “lack of Rosal sub-zones are better described by the alternation of knowledge about the consequences of climate risk on their inter-river areas. In respect of the soil characteristics, granite is financial results and the way to hedge them”, the most the most commonly type of rock found in the Rias Baixas appropriate distribution vehicle may not be individual firms. production region (Denominacion de Origen Rías Baixas, n.d.- Instead, associations of producers able to offer the product in a b). more understandable way may be required (Zara, 2010, Concerning the life cycle of the vineyards of this PDO, p.234). three different stages are clearly distinguished and temporally Most authors who have addressed the application of this allocated (Lorenzo et al., 2012, p.888): the bud-break, which type of insurance in the agricultural sector have used linear takes place between April and June; the bloom, which occurs regression to model the relationship between yields and between June and mid-August; and the veraison, which ma- weather, assuming thus linear correlation (Vedenov and terialises between mid-August and September. Barnett, 2004; Breustedt et al., 2008; Pelka and Musshoff, Data on daily weather conditions for the period 2013) and treating the yield-index distribution as a multivar- 1990e2017, which were used for the construction of the un- iate normal (Embrechts et al., 2003, p.342; Bokusheva, 2018, derlying indices, were extracted from the Spanish National p.3). This assumption is not valid for non-elliptical distributed Meteorological Agency (AEMET) and the regional meteoro- risks (Embrechts et al., 2003, p.342) and may lead therefore to logical agency of Galicia, MeteoGalicia. Pontevedra station inaccurate conclusions. Consequently, in the present research, was chosen for the analysis as weather data at this location dependence is modelled using copulas and the results are correlate significantly to those from the main regions of pro- compared to those derived from the linear regression duction of the Rias Baixas PDO: O Rosal (As Eiras station), approach. The copula technique has been suggested in some Ponteareas (A Granxa station) and Vilanova de Arousa agricultural studies. Goodwin and Hungerford (2015) applied (Tremoedo station). Concretely, Spearman correlation values it to price and rate insurance schemes that covered several over 0.97 (p < .01) and 0.86 (p < .01) were found regarding sources of risk-either low prices, low yields or a combination temperature and rainfall respectively. Fig. 1 shows the location of these-. Focusing on weather index-based insurance, of these meteorological stations in the region of Galicia and of Bokusheva (2011) proposed this methodology to capture the Rias Baixas PDO in Europe. The shaded areas correspond temporal changes in the weather-yield joint distribution, while to the production sub-zones. Bokusheva et al. (2016) and Bokusheva (2018) used copulas to Grape yield data (in kg/ha) for the timespan 1990e2017 design and rate contracts that provided a hedge against were provided by the Regulating Council of the Rias Baixas extreme weather events. In this article, this last insurance ty- PDO. pology is also addressed and additionally, a hedging modality In order to evaluate the hedging effectiveness of the that covers both extreme and non-extreme adverse weather index-based insurance programmes suggested, a A. Martínez Salgueiro / Wine Economics and Policy 8 (2019) 114e126 117 Fig. 1. Location of the Rias Baixas PDO production area and of the meteorological stations considered in the analysis. stepwise process was followed. First, indices that are strongly X J and significantly correlated to grape yields were chosen. Then, BBL ¼ Tj Rj ð1Þ j¼1 the relationship between yields and the weather indicators selected was examined. After that, and before the hedging where j denotes the month, which ranges between April and effectiveness could be quantified, the insurance policies were August; Tj is the mean monthly temperature on month j; and priced based on the results derived from the previous step. The Rj is the cumulative monthly rainfall on month j. elements of this analysis are summarised in Fig. 2. The RGP index is calculated as: 2.1. On the selection of weather indices X I RGP ¼ maxfTi  10; 0g  Ri ð2Þ i¼1 Bioclimatic indicators have been generally used for viti- culture zoning. Some of them include only one factor, such as where i denotes the day and is comprised between April 1 and the Winkler (WI) and Huglin (HI) indices, which account for October 30; Ti is the mean daily temperature on day i, which is the accumulated heat over the growing period. Other available T þT given by i ðminÞ 2 i ðmaxÞ ; and Ri is the cumulative daily rainfall on indicators compile both temperature and rainfall factors, such day i. as the Branas, Bernon and Levadoux (BBL) and the Ribereau- The design of an effective weather index-based insurance Gayon and Peynaud hydrothermal scale (RGP). programme relies on the selection of a measure as correlated The WI and HI may be suitable underlying variables for as possible to the yield. Thus, both hydrothermal indicators weather index-based insurance when there is a substantial were not only calculated for their standard periods but also for level of basis risk for rainfall (Zara, 2010, p.235). However, different timespans. Regarding BBL, the Kendall rank corre- given the high correlation in terms of precipitation between lation coefficient increased from 0.40 (p < .01)) to 0.56 the main Rias Baixas PDO producing areas and the meteo- (p < .01) when the calculation period was AprileJune instead rological station of Pontevedra, the BBL and RGP indicators of AprileAugust. Concerning RGP, this correlation coefficient were selected as underlyings. Indeed, they showed higher raised from 0.41 (p < .01) to 0.63 (p < .01) when the levels of correlation to grape yields. computation timespan was AprileAugust instead of The BBL index is computed as: AprileOctober. Therefore, these modified indicators were used as underlyings. Fig. 2. Steps of the hedging effectiveness analysis of weather index-based insurance. 118 A. Martínez Salgueiro / Wine Economics and Policy 8 (2019) 114e126 Figs. 3 and 4 depict the evolution of the grape yield and estimated with the algorithm introduced in Bai and Perron meteorological indices data over the period 1990e2017. (2003) and their optimal number was computed following Summary statistics of these three variables can be found in the Bellman principle. This assessment did not reveal the Table A1 of the Appendix. presence of any structural break. Fig. 3 shows a clear increasing trend for grape yields, which At the light of these results, there is no evidence that the is verified by the results of the non-parametric Mann-Kendall increasing trend in grape yields is related to the effect of test (p < .01). This may be explained by the technological climate change or any particular behaviour of the bioclimatic development that winery has experienced over the last de- indices. Thus, this study considers that the upward trend is cades. However, before concluding this, the evolution of the mainly explained by technological development. Accordingly, meteorological indices needs to be considered, as climate the relationship between yield and weather evaluated in the change could have also had some effect on their development. next section was estimated using detrended yield data. In that case, this phenomenon might be related to a certain extent to the grape yields’ upward trend. 2.2. On the estimation of the relationship between yield The analysis of the evolution of the bioclimatic indices and weather displayed in Fig. 4 shows that neither BBL nor RGP seem to follow a trend. This was further explored by applying the The computation of insurance payoffs requires the accurate Mann-Kendall test, whose outcomes supported the graphical characterisation of the relationship between the detrended findings for both indices (p > .05). For their part, the yield and weather. This allows the estimation of the expected Augmented Dickey-Fuller (ADF) and the Kwiatkowskie- detrended yield conditioned on the occurrence of adverse PhillipseSchmidteShin (KPSS) tests were used to analyse the weather events. In this article, two insurance modalities were presence of a unit root and stationarity. For both series, results suggested. led to rejection of the existence of a unit-root (p < .01) and The Insurance Type I covers both extreme and non-extreme non-rejection of stationarity (p > .05). Autocorrelation was weather conditions and was designed to provide a different also assessed graphically through the autocorrelation function indemnity for certain ranges of the bioclimatic index. The (ACF) and the partial autocorrelation function (PACF). Figs.  p;pþ0:1 ) is expressed as follows for expected detrended yield (m* A1 and A2 of the Appendix display the correlograms for each of the ranges considered:    m*  p;pþ0:1jq ðWÞW < q ðWÞ ¼ E Qdet qp ðWÞ  W < qpþ0:1 ðWÞ  p;pþ0:1 ¼ m ð3Þ p pþ0:1 BBL and RGP respectively, which indicate that no autore- where Qdet denotes detrended yield, W is the weather index, E gressive or moving average terms are needed. Finally, the corresponds to the expectation operator and qp denotes the p- presence of structural breaks was also tested. The breaks were quantile, with 0  p  1. The Insurance Type II offers hedge against extreme mete- orological events. Thus, it makes necessary the computation of the expected detrended yield when extreme weather states are recorded. If the correlation between the detrended yield and weather is positive, this measure is derived as:  det    0;p ¼ m m*  ¼ E Q W  qp ðWÞ ð4Þ 0;pjWqp ðWÞ On the contrary, if the correlation is negative, it is computed as:  det    p;1 ¼ m m*  W  qp ðWÞ p;1jWqp ðWÞ ¼ E Q ð5Þ As mentioned in Section 1, two methodologies were applied to capture yield-weather dependence and conse- quently, to derive the expected detrended yields of the insur- ance modalities proposed: copulas and linear regression. The application of copulas has been extensively contem- plated in Integrated Risk Management as a method to deal with deviations from the normal distribution behaviour and the existence of heavy tails (Embrechts et al., 2003, p.331). Fig. 3. Yield evolution (1990e2017). Recently, this methodology has been considered in some A. Martínez Salgueiro / Wine Economics and Policy 8 (2019) 114e126 119 Fig. 4. BBL (left-hand side) and RGP (right-hand side) evolution (1990e2017). agricultural applications (Bokusheva, 2011, 2018; Goodwin According to the copula approach, the joint distribution of and Hungerford, 2015; Bokusheva et al., 2016). Qdet and W can be described by a parametric copula Cðu; v; qÞ, Copula theory dates back to Sklar (1959), who demon- where u ¼ FQdet ðqdet Þ, v ¼ FW ðwÞ and q is the copula strated that a n-dimensional distribution function can be parameter. This definition allows the computation of m* p;pþ0:1 , decomposed into two parts: the marginal distributions and a   and m* 0;p m* p;1 , which were derived in this article from the dependence function. Thus, according to Sklar's theorem, marginal expected shortfall expression introduced in Jiang considering two random variables X and Y with marginals (2012, p.13) and Eckernkemper (2018, p.91). FX ðxÞ and FY ðyÞ, the join distribution FXY ðx; yÞ is: The results obtained from this method were compared to those generated using simple linear regression. The payoffs FXY ðx; yÞ ¼ CðFX ðxÞ; FY ðyÞÞ ð6Þ were conditioned on the same thresholds of the hydrothermal indices as in the copula approach. where CðFX ðxÞ; FY ðyÞÞ is a copula that captures the depen- dence between X and Y (Reboredo, 2011, p.949). There are several advantages to using copulas to analyse yield- 2.3. On the valuation of weather index-based insurance weather dependence (Reboredo, 2011, p.949). First, they model The methodology introduced in Section 2.2 allows the the marginal behaviour of the random variables separately and estimation of the expected detrended yield value conditioned thus, allow for flexibility in the description and estimation of on a hydrothermal index and thus, the calculation of the in- margins. Second, the copula function not only captures the level surance payoff. but also the structure of dependence. Therefore, this methodology The indemnity of the Insurance Type I based on BBL was is expected to improve the results attained using simple linear computed as: correlation, which analyses how random variables “move together on average across marginal distributions assuming 8 > >  0:9;1t multivariate normality” (Reboredo, 2011, p.949). < K  m* if BBLt  q0:9 ðBBLÞ In this study, parametric copulas were examined, which I t; BBL ¼ K  m* I  p;pþ0:1t if qp ðBBLÞ  BBLt < qpþ0:1 ðBBLÞ > > consist of elliptical and Archimedean classes. Elliptical cop- : 0 otherwise ulas, such as the Gaussian and t-copulas, do not have a closed ð7Þ form and are restricted to have radial symmetry, whereas Archimedean copulas have a close form and allow for a where t denotes the year and p takes the values 0.5, 0.6, 0.7 number of different dependent structures (Embrechts et al., and 0.8. 2003, p.2, p.365). This last typology comprises families such Equivalently, the indemnity of this insurance typology as Frank, Joe, Clayton and Gumbel. based on RGP was derived as follows: 8 > >  0;0:1t > > K  m* if RGPt < q0:1 ðRGPÞ > > < K  m*  p;pþ0:1t if qp ðRGPÞ  RGPt < qpþ0:1 ðRGPÞ I It; RGP ¼ ð8Þ > >  0:4;0:5t K  m* if q0:4 ðRGPÞ  RGPt  q0:5 ðRGPÞ > > > > :0 otherwise 120 A. Martínez Salgueiro / Wine Economics and Policy 8 (2019) 114e126 rotated versions were considered to capture dependence be- where p takes the values 0.1, 0.2 and 0.3. tween the detrended yield and BBL, while non-rotated and The payoff of the Insurance Type II based on BBL was survival copulas were tested to describe the relationship be- calculated in the following form: tween the detrended yield and RGP. The marginals were 8 modelled using empirical distributions, thus following a non- <  p;1t if BBLt  qp ðBBLÞ parametric approach. K  m* I IIt; BBL ¼ ð9Þ The copula parameter was estimated through the inversion :0 otherwise of Kendall's tau technique and the most appropriate copula was then selected using the Cramer-von-Mises criterion. As where p takes the value 0.7. explained in Genest et al. (1995), the Kendall's tau inference While the indemnity of the insurance based on RGP was procedure requires significantly lower computational effort derived as: than the maximum likelihood technique and produces 8 < consistent results in the bivariate case. The specific assump-  0; pt if RGPt  qd ðRGPÞ K  m* tions under which it can be applied hold here (Brahimi and I IIt; RGP ¼ ð10Þ :0 otherwise Necir, 2012, pp.476e477). Table 1 displays the estimated dependence parameters of where p takes the value 0.3. the copula models considered as well as the p-values of the The fair premium (p) was calculated as the expected value Cramer-von-Misses test statistic. The results indicate the of the insurance payoff. Frank as the most suitable copula to capture dependence be- tween the detrended yield and each of the bioclimatic indices 2.4. On the estimation of the hedging effectiveness under study. Figs. 5 and 6 show the densities and contour plots of the The risk-reducing effectiveness of both insurance modal- Frank copulas modelling dependence between the detrended ities was evaluated based on two different criteria: variance yield and the BBL and RGP indices respectively. and expected shortfall (ES). These measures were computed Regarding the linear regression methodology, the relation- for the insured and uninsured detrended yield. The price effect ship between the detrended yield and weather was captured was not considered as it might distort results. Thus, this through the following model: research examined the risk reducing ability purely derived from the implementation of weather index-based insurance. t ¼ c þ bWt þ et Qdet ð13Þ 0 The insured detrended yield (Qdett ) for each year t was where W is the bioclimatic index and t denotes the year. calculated by adding the indemnity to the uninsured detrended Table 2 shows the parameter estimates and the explanatory yield and subtracting the insurance premium. power of model (13) when W takes the form of BBL and RGP. The expected shortfall was calculated in the following form Hedging effectiveness was evaluated based on both real for the insured and uninsured detrended yield: and simulated detrended yield data. Concerning the copula Za approach, random values of u and v were first generated from  '  1  ' ESa Qdet ¼ qp Qdet dp ð11Þ the selected copula (in this case the Frank) and its estimate, t a using the R command rCopula() of the package “copula”. 0 Za Next, it was checked that the correlation between the simu-   1   lated values was preserved. Finally, they were transformed as ESa Qdet ¼ qp Qdet dp ð12Þ t a F 1 1 Qdet ðuÞ and F w ðvÞ, applying the R command qemp() of the 0 package “EnvStats”. where 0  a  1 and qp is the p-quantile. Regarding linear regression, random paths were drawn from The hedging effectiveness analysis was applied to the real (13). Values of both hydrothermal indices were first generated detrended yield samples. Additionally, 10000 simulated values based on their empirical distributions, using the R command of the detrended yield were generated from the copula and remp(). The driving noise process was then modelled with nor- linear regression approaches. mally distributed random variables, applying the Excel command INV.NORM() with the mean and standard deviation of the re- 3. Empirical procedure siduals and a random generated probability. The Jarque-Bera test results of the residuals are displayed in Table A2 of the Appendix. Five different copula models were employed to estimate yield-weather dependence: Gaussian, Frank, Joe, Gumbel and 4. Results and discussion Clayton.2 Regarding the Archimedean classes, 90 and 270 This section compares the hedging effectiveness ability of the insurance modalities suggested based on real and simu- 2 Gaussian and Frank classes require the same degree of dependence in both lated data. corners of the copula, meanwhile Joe, Gumbel and Clayton are used to model asymmetric joint distributions. A. Martínez Salgueiro / Wine Economics and Policy 8 (2019) 114e126 121 Table 1 Copula dependence parameter estimates. Detrended yield-BBL Normal Frank Clayton (r90) Clayton (r270) Gumbel (r90) Gumbel (r270) Joe (r90) Joe (r270) Param. 0.77 (0.29020) 6.97 (0.43407) 2.55 (0.23626) 2.55 (0.01349) 2.28 (0.33217) 2.28 (0.32617) 3.39 (0.09241) 3.39 (0.4001) Detrended yield-RGP Normal Frank Clayton Clayton (surv.) Gumbel Gumbel (surv.) Joe Joe (surv.) Param. 0.84 (0.34316) 8.78 (0.58791) 3.4 (0.08541) 3.4 (0.02647) 2.7 (0.34416) 2.7 (0.34715) 4.22 (0.16434) 4.22 (0.36713) Notes: Param. stands for the copula dependence parameter, surv. for survival and r for rotated. P-values of the Cramer-Von-Misses test are given in parenthesis. Fig. 5. Density (left-hand side) and contour plot (right-hand side) of the Frank copula modelling detrended yield-BBL dependence. Fig. 6. Density (left-hand side) and contour plot (right-hand side) of the Frank copula modelling detrended yield-RGP dependence. Table 3 displays the risk reducing effects as measured by based policies and of up to 43% and 35% for RGP-based variance as well as the p-values of the Fligner-Killeen test for contracts regarding the Insurance Types I and II respectively. homogeneity of variances. Our results suggest the high These positive conclusions in terms of hedging potential are hedging effectiveness potential of both insurance modalities, somewhat impaired by the test results, as only the RGP-based especially when the copula approach is used to model yield- Insurance Type I leads to significant non-homogeneous vari- weather dependence. Based on the real sample, this method- ances (p < .05). The other typologies, modelled with the ology provides risk reductions of up to 34% and 38% for BBL- copula technique, yield significant results at the 10% level. 122 A. Martínez Salgueiro / Wine Economics and Policy 8 (2019) 114e126 Table 2 The outcomes of Tables 3e5 point unequivocally at the Values of the coefficients and statistical results of the regression models. Insurance Type I based on the RGP indicator and dependence BBL RGP modelled with the copula approach as the most suitable C 6328.473 (0.00000) 947.8221 (0.2585) alternative. The RGP, computed for the period AprileAugust, B 0.644600 (0.00000) 5.377860 (0.00000) is actually the index most strongly and significantly correlated Adjusted R2 0.470128 0.511023 to the detrended yield of those considered. Our results high- Prob (F-statistic) 0.000034 0.000012 light thus the importance of choosing the right underlying to Notes: P-values are given in parenthesis. The constant term of the yield-RGP accurately mitigate basis risk,3 which is one of the main model is not significant, which can be explained by the fact that the yield cannot be negative. However, it was not removed as it is helps checking the concerns refraining the development of a market for weather sensitivity to RGP. index-based insurance. This article demonstrates that the use of the relative recent methodology of copulas in agricultural insurance practises The test outcomes might be affected by the sample size as may outperform linear regression. Specifically, our outcomes observations are only available for the period 1990e2017. The show that the application of the insurance policies proposed reliability of the hedging potential and the test results are thus with dependence modelled through this approach may be expected to improve with the simulated samples, which are highly beneficial for the Rias Baixas PDO wine-growing in- based on 10000 values. Indeed, more favourable hedging ef- dustry. These results become even more favourable taking into fects are attained with simulated data, as measured by the risk account that the indices proposed as underlyings are simple reducing extent and its significance. With the copula tech- and effortless to construct. In fact, both BBL and RGP have nique, figures of up to 41% and 34% are derived regarding been generally used for viticulture zoning. Furthermore, this BBL-based policies (p < .01 and p < .05) for the Insurance research overcomes one of the main difficulties of the hedging Types I and II respectively, while values of up to 47% and 40% strategy building process suggested by other authors, which is (p < .01) are reached for RGP-geared contracts. the need of selecting the optimal number of contracts, which In line with the previous findings, Table 4 shows the high may even render these instruments unfeasible. In fact, the hedging ability of the insurance modalities suggested. programmes designed in this study are significantly simpler Concretely, it demonstrates their strong downside risk and only require the acquisition of the policies that cover the reducing potential as evaluated by expected shortfall, espe- most sensitive production period. cially the lower the value of a. As with the variance criterion, Despite the positive results here attained, it should be noted this measure indicates the copula as a superior method to that this study has not been based on individual farms data but capture and model dependence. Based on the simulated sam- on the whole Rias Baixas PDO average yield. Thus, the actual ple and on this methodology, the Insurance Type I is favoured risk reducing ability may vary as the risk exposure at an in- for both BBL and RGP-based contracts, with expected short- dividual firm might differ from the effect experienced at the fall increases over 300 and 500 units respectively based on real county level. Accordingly, further research based on dis- data and over 450 and 550 regarding simulated data. aggregated data would be needed before stating policy im- The analysis of the risk reducing potential of both insurance plications for the insurance sector and concluding about the typologies, displayed in Tables 3 and 4, points at the Insurance risk hedging ability of the suggested insurance modalities. Type I as the most suitable option. The appropriateness of this This research validates two relevant methodological ap- modality is further explored through its loss-indemnity cor- proaches, linear regression and copulas, and makes special relation in Table 5. Significant and strong Spearman's rank emphasis on the high value of the second technique. In fact, it coefficients are derived for both BBL and RGP-geared pol- is shown that copulas allow for greater flexibility and capture icies, either based on real or simulated data. However, the yield-weather dependence more precisely. Thus, this article RGP-based typology, for which correlation decreases with the represents a valuable example on their promising potential for simulated sample but still remains at the substantial level of insurance design and valuation applications in viticulture. 0.77, is revealed as superior. 5. Conclusion Table 3 Downside risk reduction estimates of weather index-based insurance as This article explored the applicability of two weather measured by variance. index-based insurance modalities to cover grape yield losses Index Insurance Type I Insurance Type II of the Rias Baixas PDO. The first alternative was designed to Copula LR Copula LR provide a hedge against both extreme and non-extreme Real data adverse meteorological states, while the second instrument BBL 34% (0.08305) 24% (0.24048) 38% (0.07789) 36% (0.08451) was planned to insure exclusively extreme weather events. RGP 43% (0.03529) 38% (0.06509) 35% (0.09484) 30% (0.13345) Simulated data BBL 41% (0.00911) 30% (0.08338) 34% (0.03035) 30% (0.10074) RGP 47% (0.00132) 33% (0.0671) 40% (0.00728) 26% (0.17228) 3 Basis risk can be defined as “the risk that payoffs of a given hedging in- Notes: LR stands for linear regression. P-values of the Fligner-Killeen test are strument do not correspond to shortfalls in the underlying exposure” (Woodard given in parenthesis. and García, 2008, p.99). A. Martínez Salgueiro / Wine Economics and Policy 8 (2019) 114e126 123 Table 4 Downside risk reduction estimates of weather index-based insurance as measured by Expected shortfall (ES). Index No insurance Insurance Type I Insurance Type II Copula Change LR Change Copula Change LR Change Real data ES0.3 BBL 1386.17 1726.99 340.83 1587.97 201.81 1781.00 394.83 1768.26 382.10 RGP 1386.17 1921.86 535.70 1890.68 504.519 1813.52 427.36 1801.46 415.30 ES0.2 BBL 1032.13 1354.25 322.13 1165.69 133.56 1403.90 371.77 1398.29 366.16 RGP 1032.13 1575.54 543.41 1536.27 504.15 1471.99 439.86 1448.99 416.86 ES0.1 BBL 386.46 687.37 300.91 392.68 6.22 973.86 587.40 926.75 540.29 RGP 386.46 982.30 595.84 927.61 541.15 1008.99 622.54 891.95 505.50 Simulated data ES0.3 BBL 1386.17 1842.97 456.81 1692.92 306.75 1734.74 348.57 1756.04 369.87 RGP 1386.17 1954.24 568.08 1793.07 406.90 1821.07 434.90 1693.54 307.37 ES0.2 BBL 1032.13 1539.01 506.88 1374.93 342.80 1392.05 359.92 1430.86 398.73 RGP 1032.13 1685.12 652.99 1493.02 460.90 1517.37 485.25 1377.65 345.52 ES0.1 BBL 386.46 1093.16 706.71 911.40 524.94 963.85 577.39 960.16 573.70 RGP 386.46 1272.96 886.50 1060.27 673.81 1095.35 708.90 917.32 530.86 Notes: LR stands for linear regression. Higher (lower) ES corresponds to lower (higher) risk exposure. Table 5 In conclusion, the results of this article suggest the high Loss-indemnity correlation of the Insurance Type I as measured by the potential for the use of weather index-based insurance in Spearman's rank coefficient. winery through an empirical application to the Rias Baixas Index Real data Simulated data PDO. Before its implementation, the institutional framework BBL 0.7545866 0.7158559 as well as other design issues, such as the most appropriate (0.00000) (0.00000) distribution vehicle, should be thoroughly considered. Future RGP 0.8136685 0.7689534 (0.00000) (0.00000) lines of research may explore farmers’ willingness to pay as well as attitudes and impressions towards this insurance in- Notes: P-values of the correlation test are given in parenthesis. strument. It would also be interesting that the copula Two hydrothermal indices, the BBL and RGP, were suggested approach, as a method to design and rate policies, was further as underlyings and computed for the periods with higher yield explored by applying it to other regions and appellations of dependence. origin. Two different methodologies were applied and compared to estimate the relationship between weather indices and yield: Conflict of interest linear regression, which has been the most commonly used in the related agricultural literature; and the most recent tech- This research is funded by a grant awarded to Andrea nique of copulas, which allows the accurate modelling of the Martínez Salgueiro by “la Caixa” Foundation in its “Doctoral degree and structure of dependence. Regarding this last Scholarship Programme 2016”. This institution, which en- approach, the Frank copula was selected as the alternative that courages the publication of research results, had no other better captured both the BBL and RGP-yield dependencies. involvement in the development of this study. The hedging effectiveness was then evaluated based on real and simulated data. Acknowledgements Our analysis revealed that the application of weather index- based insurance policies in the Rias Baixas PDO wine- The project that gave rise to these results received the growing area may be very beneficial and efficiently reduce support of a grant from “la Caixa” Foundation (ID weather risk exposure, as measured by grape yield variance 100010434). The grant code is LCF/BQ/DE16/11570002. The and expected shortfall. The insurance modality designed to author is thankful to Maria-Antonia Tarrazon-Rodon (UAB) cover both extreme and non-extreme adverse weather states and Juan Carlos Reboredo (USC) for interesting insights on based on the RGP indicator yielded better results in terms of previous stages of this research. She also thanks the two risk reducing ability. Furthermore, the copula approach out- anonymous reviewers whose comments helped improve and performed linear regression. clarify the manuscript. 124 A. Martínez Salgueiro / Wine Economics and Policy 8 (2019) 114e126 Appendix. Table A1 Summary statistics of detrended grape yields, BBL (AprileJune) and RGP (AprileAugust). Yield BBL (AprileJune) RGP (AprileAugust) Mean 3329.516 4652.433 795.3607 Median 3391.726 4598.025 755.7500 Std. Dev 1638.803 1779.202 221.6664 Skewness 0.120353 0.279695 0.273775 Kurtosis 0.518633 2.281322 2.282065 Table A2 Jarque-Bera test results of the regression models residuals. 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