Risk management in agribusiness Essay Example

Expected utility model and possible investment advice

Lecturer

TABLE OF CONTENTS

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 r-square 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	8.64955E-07
Residual		34644.21001	4330.526251

The ANOVA data shows a very significant relationship for the standard error with a high F-value 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	8.6495E-7	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

=31-5223 or 120.7182

3.0 Expected money value

Expected money value is computed for each of the following crops

Investment options

1. Carrot=20(200)+25(500)+30(700)+25(-200)

=4000+12500+21000-5000

1. Corn =2000+7500+12000-7500

1. Kale = 6000+10000+15000-2500

1. Lettuce=-6000 – 2500+12000+12500

1. Tomato=2000+7500+18000-2500

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:

1. Carrot = 623.0879863

2. Corn = 492.5943048

3. Kale = 418.4846304

4. Lettuce = 614.5638092

5. 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: