**2. Methodology**

#### **2.1 Theoretical framework**

Smallholder agro-pastoral farmers are struggling to adapt to climate change and variability in order to maximize their utility (welfare) by safeguarding their livelihoods. The classical economic analysis of decision-making in the presence of risky and uncertain outcomes is based on Expected Utility (EU). EU theory underlies choices under risk [11]. EU theory provides a framework for modeling the choices of a rational individual whose goal is to maximize expected utility [12]. The underlying assumption of EU theory is that individuals have stable and coherent preferences; they know what they want and they examine the available alternatives before selecting the one that they judge to be best [13].

**131**

unfulfilled.

equally [19].

average [21].

*Efficacy of Risk Reducing Diversification Portfolio Strategies among Agro-Pastoralists…*

According to [12], rational choice theory is based on a model comprising two components: 1) a group of alternatives that are possible to realize, under different conditions; and 2) an individual's preferences that reflect their goals. However, the EU theory framework is criticized because it assumes that decision-makers are familiar with the probability distributions of each alternative outcome [12]. This is a serious theoretical flaw underlying EU in the face of climate change, which is inherently endowed with uncertainty [14, 15], not risk. Other complex alternative frameworks are suggested in the literature, including Subjective Utility Theory, Maxmin, α-maxmin, Minmax Regret, Maxmin EU, Smooth Ambiguity and Variational Preferences (Heal and Millner 2013). Kahneman and Tversky (1979) present a critique of expected utility theory as a descriptive model of decision making under risk and develop an alternative model, which they call *prospect theory*. Despite its shortcomings, EU is still a useful theoretical framework for understanding the choices of agro-pastoral household livelihood activities. This is because agro-pastoralists in the semi-arid tropical drylands have lived with the vagaries of weather extremes for generations. In this regard, they have learned the patterns of climatic risks that impact their livelihood activities, meaning that risks due to

Extremely risky situations, such as natural disasters, like climate extremes, have a significant effect on the probability distributions, resulting in the tails of the distribution being emphasized. On the other hand, investment alternatives, such as adaptations, are determined by the shape and symmetry of the expected outcome distributions [12]. Markowitz's method of optimization [16] in the context of Modern Portfolio Theory (MPT), can be adapted to include anomalies, heavy-tailed and asymmetric distributions, as well as more sophisticated measures of extreme risks. These technical attributes support its use in risk analysis in riskier undertak-

In this paper, we extend EU theory into the MPT framework in order to analyze alternative portfolios of crop and livestock types by agro-pastoralists in terms of their returns and associated risks. MPT uses information about the joint probability distribution of outcomes of all possible assets in a portfolio (including means, variances, and covariances) in order to select a portfolio that efficiently manages risk [17]. Although MPT has been applied to financial and corporate portfolio management since the 1950s, its potential for analyzing climate change adaptation and resilience by evaluating returns of livelihood activities and associated risk remains

The MPT framework is increasingly adapted for risk management in agriculture, in particular focusing on diversification in agriculture and forestry for reasonably higher and stable output in the face of uncertain climate [1, 3, 18]. There are three assumptions of MPT for diversification: (i) there is more than one possible investment at any given time; (ii) these investments are subject to risk; and (iii) that the same economic and environmental conditions do not affect all investments

The livelihood resilience of agro-pastoralists in the face of climate change and variability would be enhanced if crop-livestock portfolios generate upgraded returns with minimal variances. Optimal diversification by combining activities with low positive covariance and income-skewing is a primary risk reducing strategy. This is achieved by reducing the risk of the overall return by selecting a mixture of activities whose net returns have a low or negative correlation [20]. This means that farmers spread risk by diversifying the allocation of productive assets across various income-generating activities, often preferring farm plans that provide a satisfactory level of security even if this means sacrificing income on

ing such as crop and animal agriculture in the dryland farming systems.

*DOI: http://dx.doi.org/10.5772/intechopen.94133*

climate change will not be a completely new experience.

#### *Efficacy of Risk Reducing Diversification Portfolio Strategies among Agro-Pastoralists… DOI: http://dx.doi.org/10.5772/intechopen.94133*

According to [12], rational choice theory is based on a model comprising two components: 1) a group of alternatives that are possible to realize, under different conditions; and 2) an individual's preferences that reflect their goals. However, the EU theory framework is criticized because it assumes that decision-makers are familiar with the probability distributions of each alternative outcome [12]. This is a serious theoretical flaw underlying EU in the face of climate change, which is inherently endowed with uncertainty [14, 15], not risk. Other complex alternative frameworks are suggested in the literature, including Subjective Utility Theory, Maxmin, α-maxmin, Minmax Regret, Maxmin EU, Smooth Ambiguity and Variational Preferences (Heal and Millner 2013). Kahneman and Tversky (1979) present a critique of expected utility theory as a descriptive model of decision making under risk and develop an alternative model, which they call *prospect theory*.

Despite its shortcomings, EU is still a useful theoretical framework for understanding the choices of agro-pastoral household livelihood activities. This is because agro-pastoralists in the semi-arid tropical drylands have lived with the vagaries of weather extremes for generations. In this regard, they have learned the patterns of climatic risks that impact their livelihood activities, meaning that risks due to climate change will not be a completely new experience.

Extremely risky situations, such as natural disasters, like climate extremes, have a significant effect on the probability distributions, resulting in the tails of the distribution being emphasized. On the other hand, investment alternatives, such as adaptations, are determined by the shape and symmetry of the expected outcome distributions [12]. Markowitz's method of optimization [16] in the context of Modern Portfolio Theory (MPT), can be adapted to include anomalies, heavy-tailed and asymmetric distributions, as well as more sophisticated measures of extreme risks. These technical attributes support its use in risk analysis in riskier undertaking such as crop and animal agriculture in the dryland farming systems.

In this paper, we extend EU theory into the MPT framework in order to analyze alternative portfolios of crop and livestock types by agro-pastoralists in terms of their returns and associated risks. MPT uses information about the joint probability distribution of outcomes of all possible assets in a portfolio (including means, variances, and covariances) in order to select a portfolio that efficiently manages risk [17]. Although MPT has been applied to financial and corporate portfolio management since the 1950s, its potential for analyzing climate change adaptation and resilience by evaluating returns of livelihood activities and associated risk remains unfulfilled.

The MPT framework is increasingly adapted for risk management in agriculture, in particular focusing on diversification in agriculture and forestry for reasonably higher and stable output in the face of uncertain climate [1, 3, 18]. There are three assumptions of MPT for diversification: (i) there is more than one possible investment at any given time; (ii) these investments are subject to risk; and (iii) that the same economic and environmental conditions do not affect all investments equally [19].

The livelihood resilience of agro-pastoralists in the face of climate change and variability would be enhanced if crop-livestock portfolios generate upgraded returns with minimal variances. Optimal diversification by combining activities with low positive covariance and income-skewing is a primary risk reducing strategy. This is achieved by reducing the risk of the overall return by selecting a mixture of activities whose net returns have a low or negative correlation [20]. This means that farmers spread risk by diversifying the allocation of productive assets across various income-generating activities, often preferring farm plans that provide a satisfactory level of security even if this means sacrificing income on average [21].

*Agrometeorology*

coping strategies and adaptations.

farmers in the dryland areas of SSA.

face a changing climate.

**2.1 Theoretical framework**

**2. Methodology**

Effects of climate change on agriculture will be most adverse in regions that already suffer from high temperatures and low precipitation [3]. Such regions include the semi-arid drylands of SSA, where over three-quarters of the cropland is depends on the weather as it is rain-fed, hence further amplifying the sensitivity of agriculture to precipitation [3]. The expected increases in temperature for SSA is estimated to range from 2.0 to 4.5°C by 2100, while the annual rainfall for indi-

vidual countries is expected to change by −39 to +64 mm by 2030 [4].

In order to cope with, and adapt to, climate change and variability, agropastoralists in the tropical areas of SSA are pursuing diversified livelihood strategies in crop and animal agriculture for enhancing food security. Crops are grown and livestock kept in diverse mixtures of varying sensitivity to production risks in order to ensure farm income and reduce the risk of failure [5]. Ref. [6] shows clearly that in semi-arid environments, combining crop production and livestock diversifies livelihoods. With limited public investments in planned adaptations, agro-pastoralists remain vulnerable to climatic risks while relying mostly on their autonomous

The strategic diversification choices not only spreading risk [7], but also provide an important hedge against risk [8]. It is not prudent to invest all resources in highly correlated activities that may all perform poorly at the same time. Therefore, investing in two or more activities, whose returns are not full correlated, reduces the overall volatility below that of each one being taken separately [9]. As managers, agro-pastoralists guarantee food security by reducing the volatility of their farming by seeking a mix of farming activities that have either a small or negative correlation of related returns. This is critical for agro-pastoralists pursuing their livelihoods amid climatic risks are being further aggravated due to climate change.

Moreover, agricultural diversification enhances food security and farm income thus mitigating climate-related production risks [10]. Each crop-livestock combination has specific returns and risks. However, few studies evaluate the returns and risks associated with various crops and livestock portfolios among agro-pastoral

This paper contributes to bridging this research gap by evaluating the levels

pastoralists in the semi-arid areas of Northern and Central Tanzania. The Modern Portfolio Theory (MPT) was used to evaluate risk in corporate and financial portfolio management, to evaluate the returns and risk of different crop-livestock portfolios which enhance food security. The results of this study inform the strategic diversification choices for enhanced resilience of agro-pastoralists in the

Smallholder agro-pastoral farmers are struggling to adapt to climate change and variability in order to maximize their utility (welfare) by safeguarding their livelihoods. The classical economic analysis of decision-making in the presence of risky and uncertain outcomes is based on Expected Utility (EU). EU theory underlies choices under risk [11]. EU theory provides a framework for modeling the choices of a rational individual whose goal is to maximize expected utility [12]. The underlying assumption of EU theory is that individuals have stable and coherent preferences; they know what they want and they examine the available alternatives

before selecting the one that they judge to be best [13].

of returns and risks associated with crop-livestock portfolios among agro-

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#### *Agrometeorology*

Agro-pastoralists might wish to avoid income fluctuation and to maximize income at the same time. Since farms can be thought of as assets within an overall portfolio, agricultural producers might behave in a manner like investors who pay attention to the concept of diversification. However, agro-pastoralists might not have considered diversification in the same way that the typical financial investor might: they often look at diversification as changing their crop mix, rotational system, and livestock breeds, or even as cultivating spatially separated farms [22] and splitting livestock across distant grazing locations [23]. Despite the relevance of considering these forms of diversification, our analytical scope is limited to diversification of alternative combinations of crop and livestock enterprises. However, it highlights possible future research for increasing the scope of portfolio diversification in SSA.
