Wine Futures: Pricing and Allocation as Levers Against Quality Uncertainty

Abstract

This study examines the impact of using wine futures in order to mitigate the winemaker’s risk stemming from quality uncertainty. In each vintage, a winemaker harvests grapes and crushes them in order to make wine. A premium wine sits in barrels for 18–24 months. During the aging process, tasting experts take samples and establish a barrel score; this barrel score often indicates the expert’s perception of whether the wine will be a superior wine. Based on the barrel score, the winemaker can sell some or all of her/his wine in the form of wine futures and in advance of bottling. The winemaker makes three decisions: (1) the price to sell her/his wine futures, (2) the quantity of wine futures to be sold in advance, and (3) the amount of wine to be kept for retail and distribution. The wine continues to age for one more year after barrel samples. The tasting experts then provide a bottle score upon the bottling of the wine. At the time the winemaker determines the price and quantity of wine futures, this unrealized bottle score represents the uncertainty that influences the market price of the wine.

This study makes two contributions to the optimization of pricing and quantity decisions and offers insightful recommendations for practicing managers. First, it develops a stochastic optimization model that integrates uncertain consumer valuations of wine both in the form of futures and in bottle, and the uncertainty associated with bottle scores. Second, it provides an empirical analysis using data collected from Bordeaux wineries engaging in wine futures. The empirical analysis demonstrates that wine futures can be used as price and quantity levers to mitigate the negative consequences of quality uncertainty. The results provide clues as to how other markets (e.g. Italy and the U.S.) can establish similar wine futures markets in order to help their small and artisanal winemakers.

Appendix

Proof of Lemma 1

Taking the derivative of (6.1) with respect to q _f provides the result.

$$ \partial \Pi \left({p}_f,{q}_f\right)/\partial {q}_f=\left\{\begin{array}{l}{p}_f-\phi E\left[{p}_r\left({\tilde{s}}_2\left|{s}_1\right.\right)\right]\ \mathrm{if}\ {q}_f<{d}_f\left({p}_f\right)\\ {}0\kern8em \mathrm{if}\ {q}_f\ge {d}_f\left({p}_f\right)\end{array}\right. $$

Because $E\left[{\tilde{s}}_2|{s}_1\right]={s}_1$, the expected retail price in May of calendar year t + 1 is equal to the barrel score, i.e., $E\left[{p}_r\left({\tilde{s}}_2|{s}_1\right)\right]={s}_1$. When ${p}_f\ge \phi E\left[{p}_r\left({\tilde{s}}_2|{s}_1\right)\right]$, the derivative is positive for q _f  < d _f (p _f ), and is equal to zero for q _f  ≥ d _f (p _f ). Thus, increasing q _f to d _f (p _f ) provides a positive improvement in the expected profit. When ${p}_f\ge \phi E\left[{p}_r\left({\tilde{s}}_2|{s}_1\right)\right]$, the winemaker sells all of the wine in Stage 2 in the retail market. □

Proof of Lemma 2

We have $E\left[{p}_r\left({\tilde{s}}_2|{s}_1\right)\right]={s}_1$, and we take the natural log of q _f  = d _f (p _f ) where d _f (p _f ) is expressed as in (6.5). Thus,

$$ \begin{array}{rcl} {q}_f={d}_f\left({p}_f\right)&&=M\left({s}_1\right)\left[\frac{e^{\left(\theta {s}_1-{p}_f\right)/\beta }}{2+{e}^{\left(\theta {s}_1-{p}_f\right)/\beta }}\right]\Rightarrow \frac{q_f}{M\left({s}_1\right)}\left(2+{e}^{\left(\theta {s}_1-{p}_f\right)/\beta}\right) \\ &&={e}^{\left(\theta {s}_1-{p}_f\right)/\beta}\Rightarrow \frac{2{q}_f}{M\left({s}_1\right)-2{q}_f}={e}^{\left(\theta {s}_1-{p}_f\right)/\beta }. \end{array} $$

Taking the natural logarithm of both sides provides:

$$ \operatorname{ln}\left[\frac{2{q}_f}{M\left({s}_1\right)-2{q}_f}\right]=\beta \left(\theta {s}_1-{p}_f\right) $$

Rearranging the terms, we obtain the futures price expression in (6.6).

$$ {p}_f\left({q}_f\right)=\theta {s}_1-\beta \operatorname{ln}\left[\frac{2{q}_f}{M\left({s}_1\right)-{q}_f}\right]=\theta {s}_1+\beta \operatorname{ln}\left[\frac{M\left({s}_1\right)-{q}_f}{2q}\right]. $$

□

Lemma A1

Maximizing the objective function in (6.3) is equivalent to maximizing the expected profit expression in (6.1).

Proof of Lemma A1

The objective function in (6.3) can be rewritten as follows:

$$ \Delta \Pi \left({p}_f,{q}_f\right)=\left(1/\Pi \left({p}_f^0,{q}_f^0\right)\right)\left(\Pi \left({p}_f,{q}_f\right)\hbox{--} \Pi \left({p}_f^0,{q}_f^0\right)\right)\times 100\% $$

Because the values of ${p}_f^0$ and ${q}_f^0$ are given, the expected profit expression for the winemaker’s current profit level, described with $\Pi \left({p}_f^0,{q}_f^0\right)$, is constant. Thus, maximizing ΔΠ(p _f , q _f ) is equivalent to maximizing the expected profit expression Π(p _f , q _f ) in (6.1). □

Proof of Proposition 1

From Lemma A1, we know that maximizing ΔΠ(p _f , q _f ) in (6.3) is equivalent to maximizing the expected profit Π(p _f , q _f ) in (6.1). Thus, we focus on the properties of (6.1). Moreover, we know that Π(p _f , q _f ) can be expressed as a single decision variable function as in (6.7). Thus, it is sufficient to show that Π(q _f ) is concave in q _f . Following the proof of Theorem 1 in Li and Huh (2011); it can be shown that Π^′′(q _f ) < 0. Using the first-order condition and (6.6), we have the futures price can be expressed as follows:

$$ {p}_f\left({q}_f\right)=\phi {s}_1+\frac{\beta M\left({s}_1\right)}{M\left({s}_1\right)-{q}_f}=\beta +\phi {s}_1+\frac{\beta {q}_f}{M\left({s}_1\right)-{q}_f}. $$

Using the approach described in the derivations of Proposition 1 of Noparumpa et al. (2015a), the optimal unconstrained futures quantity can be obtained as follows:

$$ {q}_f^0=M\left({s}_1\right)\left(\frac{e^{\left(\theta -\phi \right){s}_1/\beta -W\left(\frac{e^{\left(\theta -\phi \right){s}_1/\beta }}{2e}\right)}}{2e+{e}^{\left(\theta -\phi \right){s}_1/\beta -W\left(\frac{e^{\left(\theta -\phi \right){s}_1/\beta }}{2e}\right)}}\right) $$

Iff ${q}_f^0\le Q$, then ${q}_f^{\ast }={q}_f^0$, and the optimal profit is equivalent to the unconstrained optimal profit, and

$$ {p}_f^{\ast }=\phi {s}_1+\beta \left[1+W\left(\frac{e^{\left(\theta -\phi \right){s}_1/\beta }}{2e}\right)\right] $$

If ${q}_f^0\ge Q$, then the supply constraint is binding, i.e., ${q}_f^{\ast }=Q$. In this case, the optimal price is obtained by substituting ${q}_f^{\ast }=Q$ in (6.6), and the optimal profit is obtained by substituting the revised price expression into (6.1). □