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Risk management in agribusiness Essay Example
 Category:Macro & Microeconomics
 Document type:Math Problem
 Level:Masters
 Page:3
 Words:1607
Table of Content
Expected utility model and possible investment advice
Lecturer
TABLE OF CONTENTS
1.0 Introduction 3
2.0 Expected utility computation 3
3.0 Expected money value 5
4.0 Crop with greatest utility 6
5.0 Certainty equivalence 7
6.0 Risk premium for the crops 8
7.0 Choice of insurance with government subsidy 8
8.0 Disease insurance 9
9.0 Hedging table 10
REFERENCES 11
1.0 Introduction
Making the right choices during investments is very key. This is because risk is real and could quickly reduce a person’s investments without warning (Bolton, Chen, and Wang, 2013). However, Pattillo (2016) affirms thattaking risks is also part of investment since fear of risk is also fear of prosperity. Careful investors according to the advice of Rubaltelli, et al. (2015) can therefore only minimize risk levels or avoid obvious risks when they plan through an assessment of all possible alternatives and their scales of risk. This paper provides an expert advice on risk management and decisions for investment in an Agricultural setup.
2.0 Expected utility computation
In economics, expected utility is a term that summarizes the expected utility that an entity should probably reach under certain circumstances and is calculated by computing weighted averages of all probable outcomes under specific circumstances (Fishburn, 2013). The weights, Cerreia‐Vioglio, Dillenberger, and Ortoleva (2015) intimates, are assigned as likelihood to occur or the value of probability of a certain event occurring. Fishburn (2013) argues that the expected utility model teaches that the all possible utility levels’ weighted average, under a level of uncertainty, will be equal to utility at a given time.The utility of the farmer at different income levels is as follows:
Utility of farmer Sally Whitwell at different income levels 

Expected income (AUD’ 000) 
Sally Whitwell’s utility 
0 

From the table, the expected utility is computed with regression analysis as follows:
Regression Statistics 

Multiple R 
0.978778329 
0.958007018 

Adjusted R Square 
0.952757895 
Standard Error 
65.80673409 
The rsquare value is 0.958 implying about 95.8% perfection in the model used. The standard error is quite high at 65.80 implying that the risk value for the expected utility is also high. However, the significance of this is estimated using ANOVA shown below.
Significance F 

Regression 
790355.79 
790355.79 
182.5080242 
8.64955E07 

Residual 
34644.21001 
4330.526251 

The ANOVA data shows a very significant relationship for the standard error with a high Fvalue of 182 significant at 99% confidence interval. Regression coefficients are shown below:
Coefficients 
Standard Error 
Lower 95% 
Upper 95% 

Intercept 
82.884607 
44.597783 
1.85849 
0.1001623 
185.7272 
19.958066 
Sally Whitwell’s utility 
8.97112133 
0.6640575 
13.50955 
8.6495E7 
7.439801 
10.502440 
The regression data shown above leads to a computation of the utility line plot shown below.
The y intercept is presented by 82.885 i.e. expected income against the expected utility of 8.9711. this means that at estimated utility of 8.9711, Sally would get a loss of $82.885 implying a high risk. Sally therefore needs a utility value of at least 10.50 to earn an estimated $19.95. The advice is that Sally should consider heavy investment, more than $100 to have substantial utility.
At expected income of $600, risk aversion, absolute and relative is given as follows;
Absolute risk aversion (600) = 8.9711x — 82.885
682.885=8.9711(x)
x=76.1205426
Relative risk aversion = absolute risk±standard error
= $76.1205426±44.597783
=315223 or 120.7182
3.0 Expected money value
Expected money value is computed for each of the following crops
Investment options 


Carrot=20(200)+25(500)+30(700)+25(200)
=4000+12500+210005000

Corn =2000+7500+120007500

Kale = 6000+10000+150002500

Lettuce=6000 – 2500+12000+12500

Tomato=2000+7500+180002500
4.0 Crop with greatest utility
Expected utility is given by the function _{}
Expected utility (x) is given by:
EU(x)=_{}.
The carrot produceshighest money hence, since it is a directly proportional function, the highest utility is from the carrot crop: substituting EU(x)= _{} with the carrot expected income is given as= _{}
=32582.885/8.9711
= 3631.98.
5.0 Certainty equivalence
The certainty equivalence was ascertained from the 95% confidence interval of each of the crops as shown with the descriptive statistics below.
Carrot 

Standard Error 
195.789002 
154.784796 
131.497782 
193.1105038 
149.303940 
Standard Deviation 
391.578004 
309.569593 
262.995564 
386.2210075 
298.607881 
Sample Variance 
153333.333 
95833.3333 
69166.6666 
149166.6667 
89166.6666 
Kurtosis 
0.7684310 
0.757655955 
2.23486718 
4.40922568 
0.4161062 
Skewness 
0.5995806 
1.13762436 
1.4430588 
0.1692376 
0.42252141 
Confidence Level(95.0%) 
623.087986 
492.594304 
418.484630 
614.563809 
475.15177 
The certainty for each crop i.e. what ought to be invested to yield income at 95% confidence interval is as follows:

Carrot = 623.0879863

Corn = 492.5943048

Kale = 418.4846304

Lettuce = 614.5638092

Tomato = 475.151774
Certainty level for carrot is best of all the crops while kale crop remains the most uncertain based on the computations shown above. Insurance is therefore recommended for the high risk crops i.e. kale, corn and tomato.
6.0 Risk premium for the crops
According to Damodaran (2016), risk premium is defined as the risk free rate less the return on an investment that is expected to be yielded. The form of compensation that investors can tolerate in case of extra risk, argues Peng and Wang(2016), is called an asset risk premium while a risk free asset is one that demonstrates no risk in case of an investment. The risk premium for each crop is given by the function Y= 8.9711x — 82.885 from the regression analysis where y is the sum of expected crop investment. Thus _{}. The risk premium for the crops is therefore as follows:
Carrot _{}= 143.002
Corn x = _{} = 64.97
Kale x = _{} = 131.86
Lettuce x = _{} = 64.97
Tomato x = _{} = 109.56
7.0 Choice of insurance with government subsidy
The risk premium less the $30 government subsidy for weather is given as follows:
Carrot = 113.002
Corn = 34.97
Kale = 101.86
Lettuce = 34.97
Tomato = 79.56
The data indicates that without the whether risk using government subsidy, the risk is still significant for kales, carrots and tomato. Insurance is therefore still advised for these three crops but can be foregone for corn and lettuce crops.
8.0 Disease insurance
Expected profit per crop is 70% while the probability of the disease risk is 30%. This has the implication that the expected profits for each crop is as follows (refer back to expected money value.
Carrot = 70% of $32500 = $22750
Corn = 70% x $14000 = $9800
Kale = 70% of $28500 = $19950
Lettuce = 70% of $16000 = $11200
Tomato = 70% of $25000 = $17500
Insurance value is therefore given by Disease risk of 30% of money value for crop multiplied by the cost per dollar. The computations per crop is as follows:

Carrot = 30% of 22750*35 cents
=$2388.75

Corn = 30% x $9800 x 35 cents

Kale = 30% x $19950 x 35 cents
=$2094.75

Lettuce = 30% x $11200 x 35 cents

Tomato = 30% x $17500 x 35 cents
=$1837.5
9.0 Hedging table
In finance and insurance, hedging is a strategy that investors use to reduce the risk of a peril hence the price of asset movements risk (Moschini, and Hennessy, 2001). As Conlon, Cotter and Gençay (2016) posit, hedging could involve taking things such as security for example a futures contract. Other scholars refer to hedging as the same thing as an insurance policy hence hedging is confined to taking an insurance policy for the specific risks that are prone in a particular area of investment (Turcic, Kouvelis, and Bolandifar, 2014). In this case probable insurance policies would be crop disease policy and weather insurance policy. Hedging also is considerate of riskreward tradeoffwhich is meant to reduce the risk potentially though it may also chip away probable gains. Hedging’s shouldn’t be though as free in the end because some gains are lost in an equal manner as potential risks. For example, when an insurance policy is meant to cover weather conditions such as floods, whereas the monthly bills goes up,in case there is no flood, the holder of the policy gets no payout. However, a perfect hedge helps an investor to eliminate a portfolio of risks in a position hence referred to as 100% inverse correlation in relation to the investment thought to be vulnerable (Conlon, Cotter and Gençay, 2016). The table below refers to the hedging for the case study preparing hedge with options (constant cash and future prices) where the basis is held constant.
Cash and futures 
Options price 
Today 1^{st} Futures 1 
(pay $1,000 plus commission) 
Later 1^{st} Futures 1 
Option expires worthless 
Less option premium loss $0.20/bushel 
List of References
Bolton, P., Chen, H. and Wang, N., 2013. Market timing, investment, and risk management. Journal of Financial Economics, 109(1), pp.4062.
Cerreia‐Vioglio, S., Dillenberger, D. and Ortoleva, P., 2015. Cautious expected utility and the certainty effect. Econometrica, 83(2), pp.693728.
Conlon, T., Cotter, J. and Gençay, R., 2016. Commodity futures hedging, risk aversion and the hedging horizon. The European Journal of Finance, 22(15), pp.15341560.
Damodaran, A., 2016. Equity risk premiums (ERP): Determinants, estimation and implications–The 2016 Edition.
Fishburn, P.C., 2013. The foundations of expected utility (Vol. 31). Springer Science & Business Media.
Moschini, G. and Hennessy, D.A., 2001. Uncertainty, risk aversion, and risk management for agricultural producers. Handbook of agricultural economics, 1, pp.87153.
Pattillo, C., 2016. 4 Risk, Financial Constraints and Equipment Investment. Investment and Risk in Africa, p.96.
Peng, X. and Wang, W., 2016. Optimal investment and risk control for an insurer under inside information. Insurance: Mathematics and Economics, 69, pp.104116.
Rubaltelli, E., Agnoli, S., Rancan, M. and Pozzoli, T., 2015. Emotional Intelligence and risk taking in investment decisionmaking (No. 15107). Universita di Modena e Reggio Emilia, Dipartimento di Economia» Marco Biagi».
Turcic, D., Kouvelis, P. and Bolandifar, E., 2014. RiskAversion Happens: Hedging Commodity Material Purchases in a Bilateral Supply Chain.