Intertemporal Risk Management Decisions of Farmers under Preference, Market, and Policy Dynamics

We solve the GEU optimization problem by dynamic programming using GAUSS for
risk aversion parameter ranging from -5 to 1 (Arrow-Pratt CRRA coefficient from 0 to 6), time
discount factor from 0.1 to 0.9, and substitution preference from -5 to 1. The examinations are
conducted separately for each of the preferences. We change only one preference parameter at a
time, while holding the other two preferences at the same level as in the base scenario.
Theoretical restrictions on the parameters have been considered so that only feasible values were
assigned within each range.

At this time, the farmer can choose from hedging in the commodity futures market and a
no-load MPCI yield insurance. He or she is also able to receive government payments through
DP, LDP, and CCP. The parameterization for these risk management instruments is at the base
level. Results show that differences in the optimal portfolio are only in hedge ratios, the crop
insurance purchase ratios are always at 85% level. Therefore, we focus on the variation in hedge
ratios in the following discussion.

Risk Aversion

Figure 3.1 displays how hedge ratios in the next five years respond to risk aversion (α)
changes⁸. In general, the farmer’s optimal hedge ratios⁹ are sensitive to variations inα . In the
first year, which is the most responsive, a 1% increase in α (from around -3 to close to 1) results
in a 0.74% decrease in the hedge ratio (from 35% to close to 0). Regarding the evolution of
hedge ratios for each year, it shows a similar pattern throughout the five years. All ratios first
increase very slowly when the farmer’s risk aversion varies at higher levels (αfrom -3 to -1 or
CRRA from 4 to 2). Then the ratios switch one by one to decrease as risk aversion gets smaller.

⁸ We only select some “typical” values of risk aversion to display in the graph for space consideration. We
did the same in the graphs of time preference and intertemporal substitutability. Complete results are
available upon request.

⁹ Here all hedge ratios are in short positions. When referring to hedge ratios, we usually mean the
magnitude rather than the sign unless specifically stated.

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