Mexico, until the eighties, was one of the most closed and protected economies in the world. Among the most representative characteristics of that time, we can mention the following: there was a deep intervention of the state in the agricultural sector, mainly through support prices and the control of entry and exit of goods, the exchange rate was fixed and with wide levels of overvaluation. ^{Pedroza (2018}) mentions that, between 1980 and 1982, the Mexican Food System (SAM, for its acronym in Spanish) program was developed, whose objectives were to give a boost to the agrifood sector, improve the conditions of peasant families and of the sector itself for greater economic and social stability.

Then the SAM program was abolished and the exchange of imports and commercial exports with the United States of America increased, in addition, credit institutions were created to promote the modernization of the countryside. It was the beginning of the process of economic freedom in Mexico, although state control was still present (^{Uribe, 2014}).

^{Cárdenas (2010}) mentions that, in 1985, Mexico eliminated the protectionist scheme by eliminating most of the requirements of import permits and tariffs were reduced, in just three years the protectionist apparatus was ended and the institutionalization of the structural change towards a more open economy began.

^{Mella and Mercado (2006}) mention that two conditions made possible the change of structure in Mexico: i) the signing of the North American Free Trade Agreement (NAFTA) in 1992; and ii) the deregulation and liberalization of the economy with a strong export orientation. The trade openness, initiated in the 80s and accentuated with the signing of NAFTA, made producers adapt to the prevailing economic, social and technological conditions, this led them to reconvert and modify their production processes and, consequently, the structure of agricultural production was modified by various factors such as the expansion of the agricultural frontier, crop yields and structure (^{Cruz et al., 2012}).

These facts show that the main structural reforms have been determined by the stabilization and liberalization of the agricultural sector (^{Sánchez, 2014}), so it is pertinent to measure the variability of the real gross income and the risk to which agricultural export products have been exposed, in order to have a basis that allows making an analysis of public policy and assessing a possible review of it. In order to assess the evolution of the financial conditions of the agricultural products analyzed, emphasis was placed on the contrast of two periods identified in Mexico: closed economy (1980-1999) and open economy (2000-2019).

The present work considers the economic theory that indicates that, when the economy opens, risk, understood as the probability that things will go wrong and the estimation of how much can be lost, increases, since there is greater volatility in the international market (^{Brambila, 2011}). It is hypothesized that, in an open economy, it is more profitable and riskier to invest in agricultural products, with these characteristics being accentuated in the case of exportable products. The objective was to measure and compare the variability of the real gross income and risk of agricultural products in a closed economy (1980-1999) compared to an open economy environment (2000-2019).

This analysis considered the concept of risk as the probability of occurrence of an event below a defined threshold. Risk was measured from the assumption that the price of a good or service summarizes all the information on the market given factor costs. Therefore, the variable that is frequently used to measure the risk of a good, bond, stock or service is the behavior of the real price, which is the nominal price deflated for inflation.

Since the real income of the agricultural producer depends on the price and quantity produced, and because both variables are volatile, the study of growth rates gives information on the variation of real income and their average will measure its trend; if this is positive, the variable tends to grow depending on the study period, if it is negative, the variable tends to grow less. In addition, its risk, measured by the standard deviation of growth rates, shows which products perform better than others (^{Ross et al., 2005}).

^{Brambila et al. (2014}) conducted a study using continuous growth rates in which they determined that fruits and vegetables are in a preference zone with a positive income trend and low risk and showed that products with low risk have higher growth rates. In addition ^{Domínguez et al. (2010}) used the critical values to evaluate agricultural projects and found, in the same way, that vegetables and fruits have high critical values compared to cereals, so these products present greater investment risk. Also, ^{Martínez et al. (2005}) conducted a study on the comparison of estimated variances of price indices and found that this variance in fruit and vegetables is greater when compared with that of cereals; that is, investment in the production of fruits and vegetables has a higher level of risk compared to that made in cereals.

^{Cruz et al. (2012}) found that fruits and vegetables have gained relevance in the agricultural sector, representing 35% of the value of national production, although they have a higher level of relative risk. This explains why cereal production has not decreased in the country, since the risk aversion of producers keeps them in the productive structure. The methodology of investment portfolios has been applied in multiple areas of knowledge; for example, ^{León et al. (2015}) applied it to select an agricultural portfolio, ^{Trinidad et al. (2005}) to assess an efficient portfolio in organic agriculture, ^{Ramírez and Blanco (2012}) in the optimization of portfolios with capital in limited risk and ^{García and Sáez (2015}) for the selection of an investment portfolio through the Markowitz model.

Risk, measured by price changes (volatility), was analyzed through the methodology of continuous income growth rates, previously used by ^{Brambila (2011}), and based on the following general formula:

.

Where:

the average discrete motion rate; n= number of periods; FV= final value; Iv= initial value.

To measure the risk and calculate the critical values, initially the behavior of the real incomes (Y) of the products of greater export was obtained, the average rural price of each crop was used, and they were deflated with the general index of consumer prices (base June 2020), in addition, the yield obtained of each crop was used and the real income by crop per year-period was calculated. Subsequently, the growth rate of real income was calculated, which is the natural logarithm of the quotient of income year divided by the income of the previous year (t-1), as follows:

Where:

growth rate; Fv= real growth by crop in year (t); Iv= real income by crop in year (t-1). With these growth rates, the mean and variance of the products under study were calculated.

The average of growth rates was interpreted as the growth trend of real income, if this is positive, it is said that the product has a positive growth trend per ton. The standard deviation was used to measure the risk of the product.

Critical values

The objective of the critical value is to find a minimum value that is greater than the investment in the product in scenarios of volatility and risk, such that it indicates how much higher the value of the project must be than the investment so that there are no losses (^{Domínguez et al., 2010}). To calculate the critical value of the project, the equations of Brownian motion, Ito’s lemma and Bellman’s equation are required, the full development of how the final formulas are reached can be found in (^{Dixit and Pindyck, 1994}; ^{Dominguez et al., 2010}; ^{Brambila, 2011}). The critical value is given by

Where: β= beta value;I= investment in the product; v= critical value.

The beta value is calculated as follows:

Where: α= average of the continuous growth rates of real income; σ² variance of the continuous growth rates of real income;1= discount rate; β= beta value. The value of β is related to the continuous growth rate of product prices. The critical value indicates the level of risk in the benefit/cost ratio to decide to invest in a project; that is, how many times higher the value of the project must be than the investment so that there are no losses.

Investment portfolios

The design of investment portfolios was carried out for export crops, forming the following groups of study: P1= all export products; P2= berries (blueberry, raspberry, strawberry and blackberry); P3= green vegetables (broccoli, cabbage, cauliflower and asparagus); P4= fruits (avocado, walnut, lemon and mango); P5= vegetables (tomato, green chili, cucumber and onion).

The growth rate of the portfolio

was obtained with the sum of the averages of the rates of return of the products multiplied by x_i, proportion that is invested in product i.

Where:

The variance of the portfolio (σ_p ²) was calculated with the matrix of variances and covariances of the products that are included in each of the portfolios.

σ_p ²= variance of the portfolio. σ_ij=variance of product i, if i= j. σ_ij= covariance between product i and product j, if i≠ j. x_i and x_j = proportions assigned to each product.

To form a portfolio, all the desired products can be chosen, in the agricultural case, it is enough to have a dispersion of 10 products (^{Brambila, 2011}). The critical value of β of the investment portfolio is solved with the following equation:

.

Where: β= beta value that depends on α, σ², l. α= mean of the portfolio n. σ²= variance of the portfolio n. Once the beta value was calculated, the critical value of the portfolio was obtained with the previously presented formula.