Wine price risk management: International diversification and derivative instruments

International Review of Financial Analysis 22 (2012) 30–37

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International Review of Financial Analysis

Wine price risk management: International diversification and derivative instruments☆ Apostolos Kourtis a, Raphael N. Markellos a,⁎, Dimitris Psychoyios b, c a b c

Norwich Business School, University of East Anglia, UK Dept. of Industrial Management, University of Piraeus, Greece Manchester Business School, University of Manchester, UK

a r t i c l e

i n f o

Article history: Received 7 December 2010 Received in revised form 20 January 2012 Accepted 11 February 2012 Available online 7 March 2012 JEL classification: G1 F3 Q1

a b s t r a c t Variations in fine wine prices can be prominent and have widespread economic and financial implications. Although fine wine investments are dominated by French wines, we demonstrate that significant international diversification benefits exist for investors in Italian, Australian and Portuguese fine wines. This is important since we also find that diversification across varieties of French wine is not likely to be that effective. We propose the development of futures and options contracts on standardized wine price indices in order to enhance market completeness and to address the risk management needs of all market participants. Several popular continuous time processes are used to approximate empirically the dynamics of four fine wine price indices. On the basis of our results, we recommend appropriate equilibrium models for pricing fine wine futures and option contracts. © 2012 Elsevier Inc. All rights reserved.

Keywords: Fine wine International diversification Derivatives Option pricing

1. Introduction The international wine industry and trade is built around one of the most ancient agricultural commodities which has been produced for over 8000 years (Pellechia, 2006). In the US alone, which now consumes the largest proportion of the total volume of table and fine wine internationally, retail sales exceed $30 billion (Press release, March 11, 2011, Wine Institute). To gain perspective, the value of the entire US wheat production for the 2009 crop was estimated by the US Department of Agriculture at $10.6 billion. In the present paper we will focus on fine wines which can be broadly defined as the product of particularly good vintages from the best vineyards. They often command prices in excess of hundreds of thousands of dollars and sometimes attain the rare “Veblen good” status. Although fine wines have been produced, collected, consumed and traded at an international level for millennia, a new and interesting development is that they have attracted over recent years increasing interest from individual and institutional investors. Although the fine wine (so-called “alternative”) investment market is

☆ The authors are grateful for useful feedback received by the participants of the Enometrics XVII conference organized by the Vineyard Data Quantification Society (VDQS) in Palermo, Italy in June 2010. ⁎ Corresponding author. Tel.: + 44 1603 597395; fax: + 44 1603 593343. E-mail addresses: [email protected] (A. Kourtis), [email protected] (R.N. Markellos), [email protected] (D. Psychoyios). 1057-5219/$ – see front matter © 2012 Elsevier Inc. All rights reserved. doi:10.1016/j.irfa.2012.02.001

still relatively small with an estimated value of around $3 billion per year, it is rapidly growing (Reuters, 12 January, 2010, Wine investment funds grown into global business). The two main reasons for investing in fine wines is that they are favorably taxed and that their prices are not considered to be closely linked to those of conventional investments. Interest has been fueled recently by: the significant returns of some fine wine investments over the financial crisis period, the rapidly expanding demand from China and the development of specialized markets, dealers and comprehensive databases. Despite the apparent interest, the risk profile of fine wine as an alternative investment remains largely unknown. As with all agricultural markets, the wine market is subject to a variety of systematic and unsystematic risks including, for example, human or personal farmer risk, weather risk, production factor risk, yield risk, price risk, institutional/policy framework risk and economic/financial risks (see European Commission, 2001; Kimura, Antón, & LeThi, 2010; Moschini & Hennessy, 2001). Empirical studies show that the price of wine depends particularly on a number of factors which include, weather, reputation, natural endowments, production technology, year of vintage, grape composition (see Hadj Ali, Lecocq, & Visser, 2008, inter alia) and prevailing economic conditions (see Masset & Weisskopf, 2010). In the present paper we focus on the risk which is related to the variation in fine wine prices. This results mainly from the fact that output prices cannot be determined accurately prior to production since inelastic demand translates into high price uncertainty. Our focus on fine wine price risk is justified

A. Kourtis et al. / International Review of Financial Analysis 22 (2012) 30–37

on the basis of several reasons. First, agricultural risks in general are a growing problem nowadays since there is widespread evidence that they have risen considerably over the recent past (see OECD, 2009). Second, although in the past these risks concerned mostly farmers and governments, it is more evident now that they affect a wide spectrum of stakeholders which includes consumers, insurers, lenders, retailers, collectors, investors, governments and policy makers. Third, although most agricultural risks were traditionally assumed to a large extent by the government, the trend is to introduce effective risksharing without subsidies (see, for example, Skees, 1999). Fourth, price uncertainty has considerably increased in the last years and is expected to continue to increase in the future due to changes in EU agricultural policies and the globalisation of the market. In particular, we know since the seminal work of Krasker (1979) and Jaeger (1981) (for more recent studies see Burton & Jacobsen, 1999, 2001) that wine price returns vary considerably. Fifth, despite the apparent need for efficient price risk management, the tools available to producers are limited to ineffective or costly approaches that include diversification in agricultural production, insurance policies, forward contracts, cash reserves, underleverage and wine reserves (Baquet, Hambleton, & Jose, 1997; Boehlje & Lins, 1998; European Commission, 2001; Viviani, 2006). Sixth, fine wine price risk is of particular interest to private or institutional investors who specialize in wine or are interested in including wine assets in their portfolios. The present study attempts to shed more light on fine wine investment risk by looking into the benefits of diversification across countries and wine varieties. We also examine the intertemporal behavior of fine wine price returns in relation to other benchmark investments. Although a longstanding literature has demonstrated the benefits of international diversification for portfolio risk reduction (see, for example, Kearney & Lucey, 2004; Olibe, Michello, & Thorne, 2008), the effectiveness of this approach is unknown for fine wine investments. This is probably due to the fact that the fine wine investment market is dominated by French wines. Diversification across wine producing countries is particularly relevant since this is a truly international market and prices are sensitive to climate variations at a country level. Also, although the consensus in the literature favors the inclusion of commodities in investment portfolios (eg., Puri, 1996), relevant studies on wine are still limited (a recent exception is Masset & Weisskopf, 2010). In order to deal with price risk and address the needs of all market participants, we propose in this paper the development of specialised wine derivatives. Even though financial derivatives, such as options, futures and swaps, provide state-of-the-art tools for risk management in most major financial and commodity markets, derivatives on wine are not available at present. This is a significant setback since, as with all commodity markets, the development of the wine market depends critically on the ability it has to satisfy the risk management requirements of all stakeholders. The first and only tradable wine futures contract was Winefex which was developed by Euronext in Paris back in 2001 using en primeur (forward) fine Bordeaux red wine prices to form the underlying (for a description of en primeur contracts, see Hadj Ali & Nauges, 2007). Unfortunately, this contract was very short-lived and lasted only for four months (the reasons for this failure are discussed by Pichet, 2010). The underdevelopment of wine derivatives is further discussed by Viviani (2006) who highlights product differentiation as a major limiting factor. A real rather than financial option mechanism in the protection provided by the federation of Côte du Rhône (Inter-Rhône) wine producers to its members has been identified by Viviani (2007). Financial options for the management of weather risk are discussed in the wine economics literature (Cyr & Kusy, 2007). In order to overcome potential problems that could be caused by the inherent heterogeneity between different wines, in the present paper we adopt wine price indices as the underlying assets. In our analysis, we compare several continuous time processes with respect to their ability to approximate the behavior of wine

31

price indices. The results are then used to develop a framework of models for pricing futures and options on a wine price index. The rest of the paper is organised as follows. Section 2 provides a description of the data along with a preliminary statistical analysis. Particular attention is devoted on studying the relationships between alternative wine classes across countries and varieties in order to explore the diversification benefits that are available to wine investors. An analysis of risk factors is also undertaken by examining the sensitivity of wine price indices to various economic and financial variables. Section 3 evaluates the ability of several popular stochastic processes to model the dynamics of wine price indices and on the basis of the results, Section 4 outlines a methodological framework for pricing futures and options written on a wine index. The final section concludes the paper.

2. Empirical application We draw our time series of wine price indices from WinePrices.com and the London International Vintners Exchange (Liv-ex). Data from the first source allow us to study wine price diversification across various countries and wine varieties. Data obtained from the second source do not allow an international analysis but go much further back in time and thus are used to meet the high data-requirements of the continuous time process estimation used. WinePrices.com is an online resource for wine auction and retail price information from which we obtain monthly observations for the period 1/2005 to 1/2010 on nine different fine wine price indices. As claimed by WinePrices.com, the indices are comprised of the most representative and actively traded wines worldwide using an extensive database which includes over 530,000 auction prices from the last eight years and over 1 million US retail prices on nearly 200,000 unique wines. The WinePrices indices analysed are: the Fine Wine 100 Index (FW100, the most representative price index with a global composition), the Fine Wine 250 Index (FW250, the most widely diversified index globally), the Bordeaux First-Growth 100 Index (BRD100, consists of First-Growth wines), the California 100 Index (CLF100, consists of California wines), the Rhone 50 Index (consists of Rhone valley wines), the Burgundy 50 Index (BRG50, consists of Burgundy region wines), the Italy 25 Index (ITL25, consists of Italian wines), the Australia 20 Index (AUS20, consists of Australian wines) and the Port 10 Index (PRT10, consists of Portuguese port wines). The wines in each index are chosen on the basis of their sales consistency since 2005. This means that that the number of wines in any particular index will depend on the availability of actively traded labels. The percentage price movement of each wine is weighted equally with any other in the same index. A volume-weighted average price is determined by dividing the total value of all 750 ml transactions (inclusive of the buyer's premium) by the total number of bottles purchased. Prices are calculated in US dollars and all series

5.8 5.6 5.4 5.2 5.0 4.8 4.6 4.4 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 Fig. 1. Logarithmic price levels for the Liv-ex 100 fine wine index.

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A. Kourtis et al. / International Review of Financial Analysis 22 (2012) 30–37

Table 1 Descriptive statistics of Wine Indices returns.

Obs. Mean Median Maximum Minimum Std. Dev. Skewness Kurtosis JB

FW100

FW250

BRD100

RH50

BRG50

CLF100

ITL25

AUS20

PRT10

60 0.0134 0.0051 0.1892 − 0.2268 0.0704 − 0.0810 4.4210 5.1135

60 0.0113 0.0049 0.1655 − 0.1885 0.0652 0.0906 3.7787 1.5980

60 0.0150 0.0066 0.2356 − 0.2395 0.0820 − 0.0287 4.0962 3.0124

60 0.0059 0.0000 0.3173 − 0.2197 0.0813 0.5321 6.7031 37.1130**

60 0.0127 0.0079 0.1802 − 0.1408 0.0666 0.2207 3.0777 0.5020

60 0.0032 0.0000 0.1165 − 0.1478 0.0506 − 0.2566 3.5664 1.4601

60 0.0054 0.0000 0.1611 − 0.1527 0.0597 0.4655 3.7532 3.5849

60 0.0020 0.0000 0.1413 − 0.1862 0.0610 − 0.1909 3.8476 2.1603

60 0.0052 0.0055 0.2933 − 0.1826 0.1064 0.3445 2.9037 1.2098

Obs. Mean Median Maximum Minimum Std. Dev. Skewness Kurtosis JB

Liv-ex 50

Liv-ex 100

Liv-ex 500

Liv-ex INV

108 0.0116 0.0096 0.1219 − 0.1726 0.0334 − 0.7700 11.8037 356.1192**

108 0.0110 0.0086 0.1084 − 0.1677 0.0307 − 1.2948 13.5621 527.2582**

108 0.0086 0.0060 0.0450 − 0.0292 0.0141 0.2461 3.2977 1.4750

108 0.0103 0.0085 0.0857 − 0.1373 0.0260 − 1.1003 12.1452 394.4610**

One (two) stars denote significance at the 5% (1%) level. JB is the Jarque–Bera test of normality test statistic.

are freely available over the web from the site http://wineprices. vinfolio.com. The second dataset compiled by the Liv-ex consists of four time series of price indices reported at a monthly frequency from July 2001 to July 2010. This is an exchange market for an estimated 300 major merchants of fine wine from 26 countries across Europe, Asia, North America and Australasia. According to the exchange, these merchants combined account for about 80% of the global turnover in fine wine. Liv-ex advertises comprehensive price data on almost 100,000 fine wines. Our first series comprises of monthly observations on the Liv-ex 100 Fine Wine Index. This has been reported in the financial

Liv-ex100

.15

industry “as wine industry's leading benchmark” (Reuters, 4th November 2008). The index reflects prices of the 100 of the most soughtafter fine wines for which an active secondary market exists. Most of the index depends on Bordeaux wines, as is the overall market, but the index also covers labels from Burgundy, the Rhone, Champagne and Italy. In order to better represent the actual impact on the market of each wine, the index is weighted to account for original production levels along with the increasing scarcity as the wine ages. In order to get a better understanding of wine price baskets and possibly more robust results, we analyse three more indices compiled in a similar manner by Liv-ex: the Fine Wine Investables Index (Liv-ex INV), the

Liv-exINV

.10

.10

.05

.05 .00

.00

-.05

-.05

-.10 -.10 -.15 -.15

-.20 2002

2004

2006

2008

2010

Liv-ex 50

.15

2002

2004

2008

2010

2008

2010

Liv-ex 500

.06

.10

2006

.04

.05 .00

.02

-.05

.00

-.10 -.02 -.15 -.04

-.20 2002

2004

2006

2008

2010

2002

Fig. 2. Fine wine index returns.

2004

2006

A. Kourtis et al. / International Review of Financial Analysis 22 (2012) 30–37

24 Kernel Normal Student's t

20

Density

16 12 8 4 0 -.2

-.1

.0

.1

.2

.3

Fig. 3. Epanechnikov density of Liv-ex 100 returns.

Fine Wine 50 Index (Liv-ex 50) and the Fine Wine 500 Index (Liv-ex 500). The Liv-ex INV tracks Bordeaux red wines from 24 leading chateaux which are typical ingredients of a wine investment portfolio. The choice of wines is based on Robert Parker scores. The Liv-ex 50 follows the prices movements of the Bordeaux First Growths (Haut Brion, Lafite, Latour, Margaux and Mouton Rothschild) which are the most widely traded fine wines. The only qualifying criterion is production from the ten most recent vintages (excluding futures, currently 1998– 2007). Finally, the Liv-ex 500 is the broadest index of all and comprises of any commonly traded fine wine and reflects the stock a general merchant would be holding. As with the Liv-ex 100, the Liv-ex 500 is based mostly on Bordeaux wines but also includes wines from Burgundy, the Rhone, Champagne, Port, Italy and the New World. All indices are price weighted and are based on mid prices rather than transaction prices. Mid prices are determined as the mid-point between the current highest bid price and lowest offer price on the Liv-ex trading platform. Each price is also verified by a valuation committee to ensure data robustness. The Liv-ex 100 can be downloaded from Reuters but all indices are freely available over the web from www.Liv-ex.com. The time series plot of the Liv-ex 100 index logarithmic price levels in Fig. 1 indicates that wine prices exhibit persistent variations along an upward slope and decrease sharply during the credit crisis in 2008. The plots of the remaining series analysed allow similar conclusions to be drawn and are omitted in order to preserve space. Descriptive statistics for the logarithmic returns (referred to simply as returns hereafter) of the indices under study are presented in Table 1. The shorter WinePrice indices are normally distributed, with the exception of the RH50. For the Liv-ex data, in all cases except for the most widely diversified Liv-ex 500 index, returns have abrupt upward and downward variations as indicated by the significant Jarque-Bera test statistics. This is also evident from the negative skewness, the excess kurtosis and the violent jumps that exceed 17% (or about 5.5 standard deviations) in magnitude. The plot of

33

Liv-ex series returns in Fig. 2 confirms the existence of extreme variations. The nonnormality of the returns is depicted by the density of Liv-ex 100 returns which is presented in Fig. 3. This graph gives the Epanechnikov density of returns along with superimpositions of the normal and t-student distribution, respectively. Clearly, the t-student offers a better fit to the leptokurtotic density of the Liv-ex 100 returns. In order to evaluate the potential for diversification of wine price risk across different countries and wine varieties we undertake a correlation and principal component analysis of the WinePrice index return series. The results of the correlation analysis in Table 2 allow us to draw two major conclusions. First, the benefits of international diversification are potentially significant since the correlation coefficients with wines from Italy, Australia and Portugal are relatively small with average values at 28.1%, 32.7% and 29%, respectively. Californian wines offer the smaller diversification benefits with correlations ranging between 36% and 77.7% (avg. correlation is 55.7%). Second, the diversification benefits across the major French wines are limited and are smallest for the Bordeaux First-Growth wines (avg. correlation is 60.3%). The Burgundy region wines offer the best diversification opportunities (avg. correlation is 44.1%) and are followed by the Rhone valley wines (avg. correlation is 49.2%). The results from the correlation analysis are further confirmed through a principal component analysis. This shows that the two factors with an eigenvalue above unity are able to explain 65.9% of the variation in the series. The factor loadings of these first two components, as shown in Table 3, indicate that Italian, Australian and Portuguese wines form a distinct group which has a different behavior than the remaining wines. In order to assess the risk factors that potentially affect wine prices we now examine how wine index returns are related to stock market performance (S&P 500, FTSE100, DAX30, CAC40, MSCI-World, MSCI-Europe index returns), interest rates (1-month Euribor and US Treasury Bill rates) and the overall performance in the various components of the agriculture and food industries (MSCI Agriculture & Food Chain/AFC Index for the world and Europe). The Liv-ex dataset is now used in order to increase the sample sizes available and gain degrees of freedom. The correlation analysis results summarised in Table 4 indicate that wine price returns are closely related to the performance of the stock market (Corr Liv-ex 100, MSCI-World =29.7%) and of the agriculture and food industries at an international level (Corr Liv-ex 100, MSCI AFC World =23.8%). Interest rates appear to have a mixed effect on wine prices which is negative for the 1-month Euribor and positive for the 1-month US Treasury Bill rates, respectively. Although stock markets seem to be a significant systematic risk factor, the CAPM beta coefficients suggest that investments in wine are passive. For example, assuming a US investor, a market model regression of Liv-ex 100 against S&P 500 returns gives a beta coefficient of only 0.17. Moreover, the R-squared of the regression suggests that most of the wine risk is unsystematic and hence diversifiable since only 6.89% of the variations in the Liv-ex 100 returns can be explained by market returns. Similar results are obtained for other specifications of the market model with alternative wine indices and stock

Table 2 Diversification benefits across countries and regions using WinePrice Index returns. FW100 FW100 FW250 BRD100 RH50 BRG50 CLF100 ITL25 AUS20 PRT10

95.1%** 90.2%** 54.0%** 57.0%** 73.9%** 33.5%** 42.8%** 27.7%*

FW250

BRD100

RH50

BRG50

CLF100

ITL25

AUS20

Mean

95.1%**

90.2%** 93.3%**

54.0%** 61.8%** 52.3%**

57.0%** 65.9%** 51.8%** 59.1%**

73.9%** 77.7%** 67.6%** 55.0%** 36.0%**

33.5%** 32.6%** 28.8%* 37.5%** 14.4% 37.7%**

42.8%** 43.5%** 38.3%** 24.6% 24.7% 42.4%** 12.3%

63.8% 67.1% 60.3% 49.2% 44.1% 55.7% 28.1% 32.7% 29.0%

93.3%** 61.8%** 65.9%** 77.7%** 32.6%** 43.5%** 33.4%**

One (two) stars denote significance at the 5% (1%) level.

52.3%** 51.8%** 67.6%** 28.8%* 38.3%** 26.4%*

59.1%** 55.0%** 37.5%** 24.6% 25.5%*

36.0%** 14.4% 24.7% 33.5%**

37.7%** 42.4%** 19.3%

12.3% 28.2%*

37.9%**

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A. Kourtis et al. / International Review of Financial Analysis 22 (2012) 30–37

Table 3 Factor loadings of first two principal components (PC) using WinePrice Index returns.

FW100 FW250 BRD100 RH50 BRG50 CLF100 ITL25 AUS20 PRT10

PC1

PC2

0.4170 0.4358 0.4013 0.3271 0.3110 0.3657 0.2023 0.2397 0.1984

− 0.1893 − 0.1634 − 0.2202 − 0.0385 − 0.0296 − 0.1502 0.3218 0.4038 0.7729

Table 4 Correlation of the Liv-ex Index returns with other key economic variables.

Liv-ex INV Liv-ex 50 Liv-ex 500 S&P 500 FTSE100 DAX30 CAC40 MSCI-World MSCI-Europe Euribor (1 month) US T-Bill (1 month) MSCI AFC World MSCI AFC Europe

Liv-ex 50

Liv-ex 100

Liv-ex 500

92.9%**

94.2%** 92.0%** 60.6%** 26.3%** 27.9%** 23.2%* 23.1%* 29.7%** 30.5%** − 19.9%* 32.0%** 23.8%* 17.1%

67.1%** 56.8%**

56.8%** 24.7% 21.6%* 20.5%* 20.4%* 28.0%** 28.5%** − 21.0%* 29.8%** 25.2%** 15.9%

22.8% 8.5% 17.7%* 17.5%* 23.4%* 19.1%* 3.1% 47.8%** 18.5%* 13.0%

Liv-ex INV 92.9%** 67.1%** 28.2% 21.2%* 21.8%* 21.9%* 31.3%** 30.5%** − 22.3%* 33.6%** 27.9%** 19.7%*

One (two) stars denote significance at the 5% (1%) level.

Table 6 Parameter estimates of diffusion and jump-diffusion processes for the Liv-ex 100 index. Diffusion

Jump diffusion

Parameter

GBMP

MRGP

MRSRP

MRLP

GBMPJ

MRLPJ

μ

–

–

–

Θ

–

σ λ

0.1057 (14.6545) –

0.1386 (1.3019) 6.8516 (0.0497) 21.5076 (14.6617) –

0.1803 (1.8308) 31.5348 (0.4889) 1.4720 (14.6648) –

0.0724 (0.8393) 3.1882 (1.4525) 0.1050 (14.6355) –

0.0992 (3.7692) –

–

k

0.1355 (3.8433) –

μj

–

–

–

–

σj

–

–

–

–

η

–

–

–

–

0.0493 (8.0761) 5.4562 (2.3466) 0.0063 (0.8613) 0.0397 (6.3021) –

ℑ BIC

− 320 649

− 351 716

− 331 675

− 315 644

− 299 617

–

0.0772 (1.6486) 3.4436 (3.6015) 0.0459 (8.6447) 4.9870 (1.9661) – – 45.0665 (5.5431) − 297 613

Numbers in brackets denote t-statistics. The table also gives the Log-Likelihood value (ℑ) and the Bayes Information Criterion (BIC). The data are sampled at a monthly frequency between July 2001 and July 2010.

Mean Reverting Gaussian processðMRGPÞ

ð2Þ

dSt ¼ κ ðθ−St Þdt þ σ dW t

market proxies. Overall, the conclusions we draw here are directly comparable to those of Masset and Weisskopf (2010) on a different dataset.

Mean Reverting Square−Root processðMRSRPÞ pffiffiffiffi dSt ¼ κ ðθ−St Þdt þ σ St dW t

ð3Þ

3. Continuous time dynamics of the Liv-ex Indices

Mean Reverting Logarithmic process ðMRLPÞ

ð4Þ

We now focus on capturing the dynamics of the Liv-ex Fine Wine Indices. To this end, we consider four popular models of continuous time dynamics under the actual probability measure: Geometric Brownian motion processðGBMPÞ

ð1Þ

dSt ¼ μSt dt þ σSt dW

Table 5 Parameter estimates of diffusion and jump-diffusion processes for the Liv-ex 50 index. Diffusion

d lnðSt Þ ¼ κ ðθ− lnðSt ÞÞdt þ σ dW t These models have been used in a variety of applications including the modelling of stock and commodity prices (Merton, 1976; Schwartz, 1997) and that of interest rate and volatility (Chan, Karolyi, Longstaff, & Sanders, 1992; Detemple & Osakwe, 2000; Pan, 2002; Windcliff,

Table 7 Parameter estimates of diffusion and jump-diffusion processes for the Liv-ex 500 index. Diffusion

Jump diffusion

Jump diffusion

Parameter

GBMP

MRGP

MRSRP

MRLP

GBMPJ

MRLPJ

Parameter

GBMP

MRGP

MRSRP

MRLP

GBMPJ

MRLPJ

μ

–

–

–

μ

–

–

–

Θ

–

σ

λ

0.0484 (14.6047) –

0.1317 (2.5400) 22.2828 (0.4391) 7.5086 (14.6855) –

0.1672 (3.2708) 47.6694 (1.7261) 0.5854 (14.6822) –

0.0775 (1.5895) 3.5666 (4.1342) 0.0477 (14.5983) –

μj

–

–

–

–

μj

–

–

–

–

σj

–

–

–

–

–

σj

–

–

–

–

η

–

–

–

–

0.0504 (7.8170) 7.0845 (2.0486) 0.0061 (0.9491) 0.0374 (6.9191) –

σ

λ

0.1148 (14.6579) –

0.0878 (2.0737) 3.7473 (5.4078) 0.0450 (9.6396) 6.6534 (1.8747) –

k

Θ

0.1314 (1.4822) 3.9571 (5.2416) 0.1130 (14.6363) –

0.0687 (2.8841) –

–

0.2611 (2.4834) 59.8676 (1.5434) 1.6159 (14.6605) –

0.1043 (6.4622) –

–

0.2379 (2.1417) 50.0736 (0.8061) 24.1333 (14.6593) –

0.0958 (3.0568) –

–

k

0.1426 (3.7265) –

η

–

–

–

–

ℑ BIC

− 330 669

− 364 742

− 342 697

− 324 662

− 310 639

47.0986 (6.4942) − 308 634

ℑ BIC

− 226 461

− 237 489

− 226 467

− 220 454

–

Numbers in brackets denote t-statistics. The table also gives the Log-Likelihood value (ℑ) and the Bayes Information Criterion (BIC). The data are sampled at a monthly frequency between July 2001 and July 2010.

– 0.0311 (5.4255) 8.5377 (1.8675) 0.0043 (1.3989) 0.0127 (4.9650)

− 224 467

0.0892 (1.8679) 3.7514 (5.8575) 0.0405 (6.0846) 7.8987 (1.2587) – – 155.6344 (1.9656) − 224 467

Numbers in brackets denote t-statistics. The table also gives the Log-Likelihood value (ℑ) and the Bayes Information Criterion (BIC). The data are sampled at a monthly frequency between July 2001 and July 2010.

A. Kourtis et al. / International Review of Financial Analysis 22 (2012) 30–37 Table 8 Parameter estimates of diffusion and jump-diffusion processes for the Liv-ex Inv index. Diffusion Parameter

GBMP

μ k

0.0102 (4.1025) –

Θ

–

σ

MRGP

Jump diffusion

MRSRP

MRLP

–

–

–

λ

0.0893 (14.6468) –

0.2051 (2.2570) 50.2634 (0.9309) 17.6605 (14.6786) –

0.2244 (2.5188) 57.6893 (1.5609) 1.2267 (14.6698) –

0.1130 (1.4789) 3.8863 (5.0040) 0.0880 (14.6309) –

μj

–

–

–

–

σj

–

–

–

–

GBMPJ 0.0807 (3.3081) – – 0.0410 (7.1711) 5.9523 (1.0384) 0.0070 (1.3027) 0.0303 (6.8406)

η ℑ BIC

− 300 609

− 330 674

− 310 635

− 294 603

− 283 584

MRLPJ – 0.1285 (2.8489) 4.1312 (3.8345) 0.0411 (9.2313) 5.3321 (0.9279) – – 55.3954 (5.4140) − 278 574

Numbers in brackets denote t-statistics. The table also gives the Log-Likelihood value (ℑ) and the Bayes Information Criterion (BIC). The data are sampled at a monthly frequency between July 2001 and July 2010.

Forsyth, & Vetzal, 2006). Excluding the GBMP model which has a proportional structure (μ is the percentage drift), the remaining correspond to mean-reverting processes with a speed of mean reversion κ and an unconditional long-run mean θ. In all cases, σ stands for the percentage volatility and Wt is a standard Wiener process. The parameters of the four models considered are estimated for each one of the Liv-ex indices under study using a standard Maximum Likelihood (ML) methodology. Tables 5–8 (columns 2–5) summarise the estimates obtained for each one of the four wine indices along with corresponding t-statistics in brackets, log-likelihood values ( I) and the Bayesian Information Criterion (BIC). The results indicate that in terms of both likelihood and parsimony the best model is the MRLP, followed by the GBMP. This finding is in line with the commodity literature where mean reversion is a typical finding (e.g., see, Schwartz, 1997). We now consider the possibility of discontinuities or jumps in the returns. Since the MRLP and GBMP models stand out as the best, we augment these with a jump process in order to investigate if performance can be further enhanced. The resulting models are: GBMP augmented by JumpsðGBMPJÞ

though we do not report these results here for conservation of space (they are available upon request), we find that the jump-diffusion processes perform again better than their continuous counterparts with the MRLPJ being the dominant model in both subsamples. Finally, we also assess the ability of the stochastic models under study to capture the empirical distribution properties of the original wine indices series. Following Pan (2002) and Jones (2003), we compare the skewness and the kurtosis of the actual series of indices returns with those of returns generated by the models under consideration. The model-implied higher moments are estimated via a Monte Carlo simulation procedure using the estimated parameters which are reported in Tables 5–8. We generate 1000 samples of 110 observations from each model in order to replicate the size of the actual price series. In this manner, we obtain the model-implied empirical distribution from which we estimate the third and fourth moments. Table 9 presents the respective quantiles for the higher moments of the simulated data for the four models that we found to best fit the actual data, i.e., the GBMP, MRLP, GBMPJ and MRLPJ processes. Since the conclusions drawn were very similar for all indices, we report here only the results for the Liv-ex INV and Liv-ex 100. Overall, the higher moments of the simulated series from the MRLPJ are the closest to those of the actual series. As expected, the model without jumps, GBMP and MRLP, fail to capture the excess negative skewness and the kurtosis in the returns. Incorporating jumps in the GBMP process does not offer a significant improvement in this regard. In contrast, the MRLPJ model is capable of reproducing the non-normality of the actual index to a large extent by producing substantially more negative skewness and higher levels of kurtosis than the remaining models. For instance, the kurtosis coefficient of the actual Liv-ex INV returns is 12.15 which is much higher than the 99% quantile value for the GBMP, GBMPJ and MRLP. However, it is within the 50% and 90% quantile of the kurtosis coefficient distribution for the MRLPJ. 4. Derivatives on wine indices

ð5Þ

The discussion in Section 3 implies that the MRLPJ process best describes the dynamics of the four Liv-ex indices. On this basis, we present a framework that can be used to price option and futures derivative contracts on fine wine indices. We assume that the underlying asset can be traded and that there is no model risk, i.e., the MRLPJ model is the true data-generating process. We also adopt the standard assumption that “jump risk” is not priced (eg., see, amongst others, Merton, 1976). 1 Then, the price Ft of a futures contract, and the price C(St, T − t ; K) of the call option with strike price K at time t with maturity T, are given by Eqs. (8) and (9), respectively:

ð6Þ

F t ðST Þ ¼ Exp4e

dSt ¼ μSt dt þ σSt dW þ ydqt MRLP augmented by JumpsðMRLPJÞ

35

2 −kðT−t Þ

  !3 −kðT−t Þ   1−e−2kðT−t Þ λ η−e −kðT−t Þ 2 5 ð8Þ þ lnðSt Þ þ θ 1−e σ þ ln η−1 k 4k

d lnðSt Þ ¼ κ ðθ− lnðSt ÞÞdt þ σ dW t þ ydqt where dqt is a compound Poisson process with parameter λdt and y is the jump size. In the GBMPJ process, y is lognormally distributed with mean μj and standard deviation σj. In the case of MRLPJ, the jump size is drawn from an exponential distribution with density: f ðyÞ ¼ ηe

−ηy

1fy≥0g

ð7Þ

where 1/η is the mean of the jump. The estimation results in the last two columns of Tables 5–8 indicate that the addition of jumps improves the performance of both the MRLP and GBMP model. Amongst the two jump-diffusion processes examined, the MRLPJ is marginally superior. In order to investigate the robustness of the estimation results in Tables 5–8, we divide each Liv-ex time series in two subsamples (July 2001 to December 2005 and January 2006 to July 2010) and then reestimate the processes under consideration in each subsample. Even

C ðSt ; T−t; K Þ ¼ e

−r ðT−t Þ

  e−kðT−tÞ St W ðt; T−t ÞΠ 1 ðt; T−t Þ−KΠ 2 ðt; T−t Þ

ð9Þ

where r is the risk-free interest rate, and the probabilities Π1 and Π2 are determined by

Π j ðt; T−t Þ ¼

" −isðlnK Þ # e  ψj ðt; T−t; sÞ 1 1 ∞ þ ∫0 Re ds; j ¼ 1; 2 is 2 π

ð10Þ

1 When jump risk is not priced, any jump in the price of the underlying is not correlated with the returns on the market portfolio. This assumption allows the simplification of our pricing models without constraining the illustration of their implications. For pricing models that account for a systematic component of the jump risk, see Naik and Lee (1990) and Ahn (1992).

36

A. Kourtis et al. / International Review of Financial Analysis 22 (2012) 30–37

Table 9 Unconditional higher moments of actual and simulated distribution logarithmic returns.

Actual

Skewness Kurtosis Skewness

Simulated

Kurtosis

Liv-Ex INV

Liv-Ex 100

− 1.1003 12.1452

− 1.2948 13.5621 GBMP − 0.6794 − 0.4705 − 0.3746 − 0.0754 0.2001 0.2796 0.4031 2.1832 2.3830 2.4558 2.8727 3.5431 3.7731 4.4534

1% 5% 10% 50% 90% 95% 99% 1% 5% 10% 50% 90% 95% 99%

GBMP − 0.5572 − 0.4493 − 0.3559 − 0.0684 0.2105 0.2992 0.4828 2.2409 2.3833 2.4672 2.9006 3.4856 3.7542 4.3337

GBMPJ − 0.5600 − 0.3830 − 0.2956 − 0.0271 0.2580 0.3327 0.5022 2.1823 2.3694 2.4694 2.8796 3.5165 3.7895 4.2823

MRLP − 0.5693 − 0.3662 − 0.2888 0.0117 0.3054 0.3770 0.5625 2.1824 2.3896 2.4627 2.8758 3.5127 3.7934 4.2996

MRLPJ − 3.3452 − 1.9276 − 1.3739 0.1084 1.5832 2.1116 3.3843 3.6199 4.1047 4.6008 7.3560 15.0616 19.3026 35.3399

GBMPJ − 0.5935 − 0.4025 − 0.3149 − 0.0249 0.2491 0.3366 0.4760 2.1735 2.3547 2.4475 2.8668 3.4545 3.7383 4.3784

MRLP − 0.5978 − 0.3688 − 0.2899 − 0.0115 0.2840 0.3747 0.5818 2.1964 2.3784 2.4617 2.8915 3.5754 3.8160 4.4657

MRLPJ − 3.8043 − 2.0843 − 1.5580 0.0689 1.7130 2.3089 3.7567 3.8684 4.5448 4.9439 7.7628 16.1367 19.7808 33.0843

Fig. 4. The value of a call option written on the Liv-ex Fine Wine Investables Index. Value of the call option as a function of time-to-maturity (T-t) estimated for three different moneyness levels: 20% ITM, ATM and 20% OTM. The dotted line corresponds to the case where the underlying follows the MRLP process for k = 0.1130, θ = 3.8863, σ= 0.0880. The solid line corresponds to the case where the underlying follows the MRLPJ process for k = 0.1285, θ = 4.1312, σ = 0.0411, λ = 5.3321, η = 55.3954. We assume that r = 5% and St = 200.

where   0 !1   1−e−2kðT−tÞ λ η−e−kðT−tÞ A −kðT−t Þ 2 þ W ðt; T−t Þ ¼ Exp@θ 1−e ð11Þ  σ þ  ln 4k k η−1

ψ1 ðt; T−t; sÞ ¼

ψðt; T−t; s−iÞ ψðt; T−t; sÞ ; ψ2 ðt; T−t; sÞ ¼ ψðt; T−t; −iÞ ψðt; T−t; 0Þ

ð12Þ

and −r ðT−t Þ

ψðt; T−t; sÞ ¼ e

ϕðlnðSt Þ; T−t; sÞ:

ð13Þ

Figs. 4 and 5 depict the price and the delta, respectively, of a call option written on the Liv-ex Fine Wine INV Index as a function of time-to-maturity (T–t) for three different levels of moneyness. In order to demonstrate the importance of jumps, we report results for

both the MRLPJ model and its continuous time counterpart (MRLP). The figures highlight the importance of using the correct diffusion process in pricing applications: the continuous model consistently underprices both the call option and its delta in comparison to the jump-diffusion model. The underpricing can be attributed to two factors. First, the jump part dramatically increases the total variation of the process. Second, the low speed of mean reversion of the underlying (k = 0.1285) does not allow a rapid flattening out of the effects of jumps.

5. Conclusions The rapid global expansion of the wine industry and investment community has increased the need to understand wine price risk along with ways to mitigate it. This paper evaluates the potential for international wine price diversification and proposes the development

Fig. 5. The delta of a call option written on the Liv-ex Fine Wine Investables Index. The delta of the call option as a function of time-to-maturity (T–t) estimated for three different moneyness levels: 20% ITM, ATM and 20% OTM. The dotted line corresponds to the case where the underlying follows the MRLP process for k = 0.1130, θ = 3.8863, σ = 0.0880. The solid line corresponds to the case where the underlying follows the MRLPJ process for k = 0.1285, θ = 4.1312, σ =0.0411, λ = 5.3321, η = 55.3954. We assume that r = 5% and St = 200.

A. Kourtis et al. / International Review of Financial Analysis 22 (2012) 30–37

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