Chapter 22 - Risk Management
This chapter explains the basic techniques for reducing a farm’s exposure to risk: making risky decisions, payoff and regret matrices, decision trees, probability of success; and scenarios for risk management planning. The chapter starts by identifying and classifying the different sources of risk, showing how to prioritize risks on the basis of potential impact and probability of happening, and describes the main methods for reducing risk. The chapter includes appendices on crop and livestock insurance in the U.S. and on estimating probabilities.
After completing this chapter, you will be able to:
- Identify and classify sources of risk as production, marketing, financial, legal, human resource, moral, and political
- Prioritize risks on the basis of potential impact and probability of happening
- Describe the 5 main methods for managing risk
- List several specific ways to manage or control risk
- Develop payoff and regret matrices
- Describe and use decision criteria for making risky decisions
- Estimate the probability of success
- Develop and use scenarios
- Estimate subjective probabilities
- Every decision involves some risk, so risk needs to be incorporated into the decision process.
- The goal of risk management is to balance a farm’s risk exposure and tolerance with the farm’s strategic and financial objectives.
- Risk can be described as coming from five main sources: production, marketing, financial, legal, and human resources.
- In order to decide which risks need attention first, sources of risk can be prioritized by considering their probability of happening along with the potential impact. Those risks which have a large potential impact and a high probability of happening need immediate attention.
- Risk can be managed or handled in one of five ways: retain risk, shift risk, reduce risk, self-insure, or avoid risk.
- A manager has many specific options for managing risks, including insurance, hedging, contracting, diversification, and financial reserves.
- Crop insurance has become an important risk management tool, especially in combination with the futures market so both yield and price are protected—Crop Revenue Coverage (CRC), for example.
- Payoff matrices, regret matrices, and decision trees can be used to organize information and, thus, help a manager make a risky decision.
- Decision criteria for risky decisions include maximin, minimax, maximum simple average, maximum expected returns, minimum expected regrets, safety-first rule, and probability of success.
- Managers can develop scenarios to better understand the impact of alternative views of the future and so make more informed decisions.
- Key points from Appendix 22.1: Crop and Livestock Insurance in the United States
- USDA’s Risk management Agency (RMA) provides several crop and livestock insurance programs.
- Crop insurance options include catastrophic coverage; yield only coverage; and several revenue coverage plans.
- Livestock insurance options include gross margin and price coverage.
- USDA’s Farm Service Agency (FSA) provides crop and livestock disaster programs.
- Key points from Appendix 22.2: Estimating Subjective Probabilities
- Subjective probabilities can be estimated in five ways: direct estimation, cumulative probabilities, conviction weights, sparse data method, and triangular distribution.
- The choice of method depends upon how much information is available and upon personal preference.
- Conviction weights can be used when we have some knowledge and understanding of the events but have very little data.
- The sparse data method is used when we have some empirical data but not enough to perform statistical analysis.
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- Conviction weights: Weights or scores based on our personal, subjective opinion as to whether a certain event will occur.
- Cumulative probability: The increasing probability that a certain event (price, yield, weight, and so on) will occur as the range of possible occurrences increase. The cumulative probability ranges from 0 to 1.
- Decision criteria: a set of rules that can be used to evaluate the information available and make a decision even though the end results are no known with certainty.
- Expected regrets: For each alternative action, the sum of the estimated regrets under each event multiplied by each event’s probability of occurring.
- Expected returns: For each alternative action, the sum of the estimated returns under each event multiplied by each event’s probability of occurring.
- Financial risk: Financial risk has four components: (1) the cost and availability of debt capital, (2) the ability to meet cash flow needs in a timely manner, (3) the ability to maintain and grow equity, and (4) the increasing chance of losing equity by larger levels of borrowing against the same net worth.
- Human resource risk: Disruption in the business due to death, divorce, injury, illness, poor management, improper operation and application of production and marketing procedures, poor hiring decisions, improper training, and so on.
- Interval probability: The probability or chance that a certain event (such as the actual price or yield being within a certain interval) will occur. An interval probability will range from 0 to 1. The sum of all the interval probabilities for a certain event will equal 0.
- Legal risk: Unknown and unanticipated events due to business structure and tax and estate planning, contractual arrangements, tort liability, and statutory compliance, including environmental issues.
- Marketing risk: not knowing what prices will be. Unanticipated forces, such as weather or government action, can lead to dramatic changes in crop and livestock prices.
- Maximin: This decision criteria chooses the action that, after identifying the minimum return of each possible action, has the largest minimum return. In other words, this decision criteria chooses the maximum of the minimums.
- Minimax: This decision criteria chooses the action that, after identifying the maximum regret of each possible action, has the smallest maximum regret. In other words, this decision criteria chooses the minimum of the maximums.
- Moral risk: devious and less-than-truthful behavior by individuals and other companies as well as corrupt and criminal behavior.
- Payoff matrix: a table of potential returns or payoffs that could be obtained if certain actions are taken and certain events occur
- Political risk: disruption in plans due to changing policies — both governmental and institutional policies (such as lending policies at a bank).
- Probability of success: The estimated probability of exceeding income goals or covering costs of production.
- Production risk: Not knowing what actual production levels will be. The major sources of production risk are weather, pests, diseases, technology, genetics, machinery efficiency and reliability, and the quality of inputs.
- Regret matrix: A table of potential regrets that, if a certain event happens having chosen a certain action instead of having chosen any other alternative action. A regret matrix is calculated from a payoff matrix.
- Risk: We know all the possible outcomes and the objective probability of each outcome occurring.
- Safety-first rule: A decision rule with two objectives: first, to eliminate options that do not obtain a minimum return with a certain probability, and second, to choose the best option from those remaining.
- Scenarios: Descriptions of different views or possibilities of what the future may be like.
- Sparse data method: Estimating probabilities using only a few observations.
- Subjective probabilities: Probabilities based on subjective views and not objective data.
- Triangular distribution: estimating probabilities using only three values: most likely, lowest, and highest.
- Uncertainty: We know some (or maybe all) of the possible outcomes, but we cannot quantify the probabilities.
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Every decision involves some degree of risk. We can’t avoid it. But if we don’t take risks, we may not accomplish our financial and strategic goals. Managing risk is the process of balancing the potential pitfalls and potential benefits of taking risks.
A farmer once described risk management to me as “protecting income, protecting resources.” It is this broad view of risk and risk management that we use in this chapter, not just price and weather risk.
Both risk and uncertainty refer to variation and change which cannot be completely controlled. Sometimes distinctions are made between risk and uncertainty in statistical terms and in terms whether everything is known or not known. But in this class, we won’t worry about those distinctions, risk and uncertainty will be used interchangeably.
In a general sense, we can say that the ultimate goal of risk management is to increase the chances of positive outcomes and to decrease the chances of negative outcomes. The goal is not to make the right decision because risk doesn’t allow us to see and know all. In another sense, we can describe the goal of risk management as striving to optimize and balance the expected progress on all of our goals and objectives after considering the sources of risk, the methods of reducing risk, the ability and the willingness to take risks, and the potential results of following alternative strategies.
The goal of risk management is NOT to minimize risk only. We may think we can do that by not producing anything and putting all the money in a savings account but even that may increase some risks -- such as the risk of insufficient income. Risk management involves choosing how we use our resources (time, abilities, land, money, for example) to best achieve our personal and business goals.
SOURCES OF RISK
Let’s start by considering the main sources of risk. By understanding these main sources, we can begin to narrow the choice of methods to reduce our exposure to that risk. In this class, we talk about seven sources of risk.
Production risk: not knowing for certain what the yield or productivity will be. This source of risk is mainly biological due to differences in how our plants and animals react to differences in weather, pests, diseases, genetics, input quality, and so on.
Marketing risk: not knowing for sure what prices will do or, in some instances, whether the market will be open to buy and sell — although this could be seen as extremely low prices such as the highly publicized price of $8 per cwt. for hogs in December, 1998.
Financial risk: not knowing for certain (1) whether we can obtain a loan and at what interest rate, (2) whether we will be able to pay all our bills on time, (3) whether we can increase our net worth, and (4) to what degree borrowing more money will increase the chance of losing net worth. That last definition of financial risk is, perhaps, the most important source of financial risk and the one we have the most control over.
Legal risk: not knowing for certain the impact of contracts and laws on our ability to operate and additional, new sources of risk exposure. For instance, signing a contract may reduce our exposure to one source of risk by, say, setting a price for our product but the same contract may expose our farm to new risks such as liability accounts, guaranteed quantity and quality of products, specified timing of deliveries, and so on. Also, new laws and regulations may take away the possibility to use certain inputs or production methods. Legal risk includes political risk which is the risk of changing policies, both governmental and institutional policies. Political risk is not knowing for certain what the governments’ and institutions’ policies will be and how they will affect a farm.
Human resource risk: not knowing for certain whether the right persons or firms are hired or how people will respond to management and to situations that arise. Moral risk is not knowing for sure whether a person is behaving in a morally responsible way or in devious and even corrupt or criminal ways.
Try this: List some of the risks that a farmer faces. Work through part 1 of Worksheet 22.1.
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With all these possible sources of risk, a farmer can decide which sources need attention first by considering two criteria: (1) the potential impact on the business and (2) the probability of the risk happening. With these criteria, a farmer can decide which sources of risk should have the highest priority and thus immediate attention compared to those sources on which action can wait or not even be needed. A graph (such as Figure 22.1 in the text) can help a farmer visualize the needed priorities without having to give a specific, numeric ranking.
A farmer can use the ideas embodied in this simple graph to decide whether, for example, current market and weather conditions indicate a high probability of low prices and low yields happening (which would be catastrophic) and thus a higher need for action compared to another year when market and weather conditions may not create such a heightened need for protection. Another example would be fluctuating weather conditions causing concern about the quality of stored grain compared to the need to start spring tillage this morning. A lower level of trust in a business relationship may increase the perceived probability of deception happening so a farmer may monitor differently or insert different clauses in a contract than in a relationship with higher levels of trust. Knowledge of the biology and movement patterns of insects, such as aphids, may help a farmer develop more accurate estimates of potential impacts and the probability of them happening. Farmers in different areas may have different estimates for the same insect.
Try this: Look over the list of risks you developed in part 1 of Worksheet 22.1 and now prioritize them by placing them in the graph in part 2 of Worksheet 22.1.
Methods for Dealing with Risk and Uncertainty
There are five main methods to deal with and manage risk and uncertainty in decision making:
- retain - doing nothing to protect from downside risk
- shift - use a contractual obligation (insurance, for example) to pay someone else to take the chance of downside risk
- reduce - using institutional and management options to decrease exposure to risk
- self-insure - maintain emergency financial reserves or pay for duplicity and backup to avoid risk due to failure of power sources or illness and death of business principals
- avoid risk - choosing not to do some activities and thus not take on the risk inherent in that activity
To consider these main methods in more detail, let’s look at the different options by classifying them into three groups based on how they are available to farmers and how they are used by farmers. The three classifications are:
- institutional instruments,
- management alternatives, and
- strategy development.
Institutional instruments are risk management tools developed and/or made available by institutions such as the government, futures markets, insurance companies, and so on. These include:
- Marketing methods: hedging, forward contracts, options, and so on
- Insurance: crop, health, fire, life, liability
- Government programs: AMTA, CRP, conservation subsidies, and so on
- Contracts: sales, production, or resource providing contracts
Management alternatives are risk management tools that a farmer can choose and implement on his or her own farm without needing a third party’s policy or program. These include (and are described in the text):
- Choice of activities and enterprises
- Crop and variety selection
- Renting versus owning
- Share-crop vs. cash rent
- Sharing machinery
- Retain experts to monitor business
- Obtain more and better information
- Shorten lead times in production
- Vertical integration
- Learn new skills and knowledge
- Environmental control
- Financial reserves
- Financial control
- Flexibility in plans
Strategy development is a management tool that seeks to position the farm in its economic environment to increase the chances accomplishing the goals and objectives of the farm as well as to avoid or minimize the risk of not accomplishing those goals and objectives. The aspects of strategy development that are important to risk management include:
- Industry or external analysis
- Developing scenarios
- Crafting strategy
- Combinations of these
Try this: For the sources of risk you identified as high priority in part 2 of Worksheet 22.1, complete part 3 in Worksheet 22.1 by choosing 1 or 2 methods that could be used to reduce the farm’s exposure to risk due to each source.
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MAKING RISKY DECISIONS
There are five parts to a risky decision problem.
- Actions - the options and alternatives that are available to choose
- Events (states, conditions) - those items which can’t be controlled (weather, competitors, and so on)
- Payoffs - the estimated returns of each action under each event
- Probabilities - the chances that each event may occur
- Decision criteria - a set of rules to help make risky decisions
Let’s look at two ways to organize the first four pieces of data:
- payoff matrices, and
- regret matrices.
The name, “payoff,” comes from gambling but its an appropriate name for showing the different net returns or payoffs that could be made by taking certain bets (that is, making certain decisions). It is called a matrix because the information is organized in a table or matrix form. Organizing the information in this way can take what may look like messy information and put in a structure that allows a manager to get a better grasp of the decision environment and increase the chances for making a better decision.
As an example, consider the payoff matrix in Table 22.1 in the text. In this simple example, a farmer is trying to decide whether to sell his feeder cattle now or wait for a week to sell. Across the top of the matrix, the columns are labeled with the farmer's two choices: sell now or sell next week. On the left side of the matrix, the rows are labeled with three possible events: price down, steady, and up compared with the price now. Within the table (or matrix) are the expected returns (or payoffs) for each choice under each event (i.e., price level).
In the example, if the manager decides to sell now, he will receive a net return of $31 per head regardless of what the price does during the next week. If he decides to wait and sell next week and the price is steady, he will receive a net return of $30 after paying for the extra feed and other costs and benefitting from a slightly heavier animal. If price would go down 5 cents, he would lose $20 per head. If the price goes up, he would receive $80.
From the text: Table 22.1. Example Payoff Matrix and Regret Matrix
A regret matrix uses the same information as a payoff matrix but looks at the decision in a different way. A payoff matrix shows the potential returns (or payoffs) for having chosen a particular action for each of the events. A regret matrix shows the potential regret a manager might have after having chosen a specific alternative. That is, a regret matrix shows the potential lost return (or lost payoff) of not having chosen the best action for the event that actually occurs.
The easiest way to understand how to construct or develop a regret matrix is to consider the potential payoffs if each event were to happen. That is, develop the regret matrix by considering one row of the payoff matrix at a time. The size of the regret for a particular decision is the difference between the payoff for that particular decision and the highest payoff in that row. As an example, consider again the decision to sell now or sell next week in Table 22.1.
To start let’s look only at the row showing the potential payoffs or returns if the price were to go down. In that event (i.e., row), the highest return is estimated to be obtained by selling now: $31. So, we can say that if the farmer sold now and the price went down, the farmer would have no regret at having sold now because that is the choice having the highest return when the price drops. So we place $0 in the regret matrix at the intersection of the column for selling now and the row for the price going down.
In that same row (for the price going down), the payoff for selling next week is estimated to be -$20. If the farmer were to decide to sell next week and the price goes down, the manager would regret the decision because the return is lower than if he had sold now and not waited. The size of the regret is $51 which is calculated by subtracting the estimated payoff for this action (-$20) from the highest return in that row ($31). So we place $51 in the regret matrix at the intersection of the column for selling next week and the row for the price going down.
In the next row for the event of the price remaining steady, the best choice is also to sell now (and not wait). So we place $0 in the regret matrix at the intersection of the column for selling now and the row for the price remaining steady. In this row the payoff for selling next week, the payoff is $30 which is only $1 less than selling now when the price remains steady. Using the strict definition of regret, the farmer would regret the decision to sell next week because even though the difference is small the return is for selling next week is still less than the return for selling now when the price remains steady. So we place $1 in the regret matrix at the intersection of the column for selling next week and the row for the price remaining steady.
But if the price were to go up, the returns are higher when the cattle are sold next week. So the farmer would have no regrets due to waiting. So we place $0 in the regret matrix at the intersection of the column for selling next week and the row for the price going up. If the price were to go up, the farmer would regret having sold now and receiving less money than waiting and selling next week. The size of the regret is the difference in potential returns: $80 minus $31 (or $49). So we place $49 in the regret matrix at the intersection of the column for selling now and the row for the price going up.
For some decisions, the information is easier to understand if it is organized as a decision tree. This is especially true if there is more than one decision made and events happen sequentially.
A simple decision tree is shown in Figure 22.2 in the text. The decision to either sell now or sell next week is drawn on the left, the price events are in the middle, and the estimated returns are shown on the right. The decision tree shows very clearly that price changes next week do not affect the return from selling this week.
There are three types of probabilities:
- Empirical probabilities developed from historical and experimental data. For example, empirical probabilities include the historical chance of frost by a certain date and the range of milk production estimated from feeding experiments.
- Deductive probabilities based on knowledge of the potential events, such as assuming the potential for male and female offspring is 50% each.
- Subjective probabilities cam be developed even when we don’t have enough information to calculate empirical probabilities. There are several ways to estimate subjective probabilities. These are described in Chapter 22 and Appendix 22.2 in the text and later in these notes.
Even after we have our information organized into payoff and regret matrices, we need some system or criteria to make a choice between alternatives. In the cattle selling example (Table 22.1), the farmer had the option of selling now or selling next week. However, the price might change between now and next week. After estimating the potential returns or payoffs and the regrets for each option and price event, the farmer needs to make a decision.
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Let’s look at seven decision rules or criteria that can be used to make risky decisions.
The maximin rule is used for returns or payoffs (not regrets). Its name comes from the rule itself; that is, with this rule we choose the option that has the maximum of the minimum returns.
The first step for maximin rule is to find the minimum return or payoff for each option. In the example (Table 22.1), the minimum return from selling now is $31 per head; the minimum return from selling next week is -$20.
The second step with the maximin rule is to choose the action which has the largest of the minimum returns. When using the maximin rule and the data in the example payoff matrix, the farmer would choose to sell now because selling now has the largest minimum return, $31, compared to a minimum return of -$20 for selling next week.
The advantage of the maximin rule is that it protects the lower end of the income. The disadvantage is that it ignores the potential for high returns that may occur as well as the average returns that may occur. The maximin also ignores the probabilities or chances that the returns may occur.
The minimax rule is used for regrets (not returns or payoffs). It’s name also comes from the rule itself; that is, with this rule we choose the option that has the minimum of the maximum regrets.
The first step for minimax rule is to find the maximum regret for each option. In the example (Table 22.1), the maximum regret from selling now is $49 per head; the maximum regret from selling next week is $51.
The second step with the minimax rule is to choose the action which has the smallest of the maximum regrets. When using the minimax rule and the data in the example payoff matrix, the manager would choose to sell now because selling now has the smallest maximum regret, $49, compared to a maximum regret of $51 for selling next week.
The advantage of this rule is that it avoids those actions which would cause large regrets. The disadvantage of this decision rule is that it ignores high return potential. The minimax also ignores the probability that the returns may happen.
- Maximum Average Returns (or Minimum Average Regrets)
Sometimes we can’t decide how likely each event will happen. In these cases, we could choose the option which has the largest simple average of all possible returns. Or we could choose the option that has the minimum average regret.
Using the maximum simple average rule, the farmer in the example (Table 22.1) would choose to sell now because it has a simple average return of $31 compared to the simple average of $30 for selling next week. In this example, selling now also has the minimum average regret.
- Maximum Expected Returns (or Minimum Expected Regrets)
If we estimate the probability of each event occurring, we can calculate the expected returns and regrets. Each potential return is multiplied (or weighted) by the probability or chance of the event occurring and the products are summed for each option or choice. The best option is chosen on the basis of the largest expected return which is the total of the sum of the weighted potential returns. (Alternatively, the best option is chosen on the lowest expected regret.)
In the cattle selling example (Table 22.1), the farmer decided that given market information there was a 50% chance (or probability of 0.5) that the price will remain steady between now and next week. He also decided that there was a 20% chance (or probability of 0.2) that the price could go down and a 50% chance (or probability of 0.3) that the price could increase. With these probabilities, the expected net return from selling next week is $35 (.2*-20 + .5*30 + .3*80). The expected return from selling now is $31 (.2*31 + .5*31 + .3*31). Using the maximum expected return rule, the feedlot manager would choose to sell next week.
The same estimated probabilities can also be used with the regret matrix (Figure 22.1). With these probabilities, the expected regret from selling now is $14.7 (.2*0 + .5*0 + .3*49). The expected regret from selling next week is $9.7 (.2*51 + .5*1 + .3*0). Using the minimum expected regret rule, the feedlot manager would choose to sell next week.
In this example, the maximum expected return and minimum expected regret rules indicate a different answer than the first three rules. This discrepancy is due to incorporating more information into the decision criteria. This rule includes both the highs and lows as well as the information on how likely each event is. If the farmer is not worried about the impact of losing money if the price goes down, he should wait and sell next week. However, if he is worried about the impact of a negative return, he can use the safety-first rule which is discussed next.
The advantage of the expected returns and regrets decision rule is that it accounts for the variability in returns (and regrets) and the potential that some events will be more likely to occur than other events. It incorporates both the highs and lows. The disadvantage of this rule is the additional work and time needed to estimate the probabilities of the events occurring.
- Safety-First Rule
The safety-first rule is more complicated but is often used to minimize the chances of adverse results. A farmer may use safety-first rule to ensure that minimum levels of cash flow and financial security are achieved before marketing and production risks can be taken.
The safety-first rule consists of two steps. The first step is to eliminate any option or alternative that does not meet a minimum return with a certain probability. An example of this is rejecting the option of storing all our grain unpriced because the price could drop too low and we wouldn’t have enough to pay production costs.
The second step of the safety-first rule is to choose the best option from those remaining. Usually the maximum expected returns rule is used to choose from the remaining options.
If the farmer in the cattle feeding example (Table 22.1) decides that he cannot take the chance of a negative return, the safety-first rule says he should eliminate selling next week since it includes a negative return if the price declines. Then the farmer would sell now since that is the only option left in this simple example.
The safety-first rule incorporates two good points. And many people follow this rule without formally saying they are. Safety-first allows us to eliminate options and alternatives that, for our situation, are too likely to produce disasters. Then we can use the maximum expected returns (and minimum expected regrets) to choose from the remaining potential options.
Try this: The selling cattle example has only two options: sell all the cattle now or sell all the cattle next week. Complete Worksheet 22.2, by estimating the potential returns and regrets for a third option of selling half of the cattle now and half next week. Would adding this option change the farmer’s final choice?
For another example of using payoff and regret matrices, consider the choice of tillage system that the Glenda and Paul Christianson were facing in Example 22.1.
Probability of Success
Another way to improve decision making in the face of risk is to estimate not only the average return but to also estimate the probability or chance of success. For example, a farmer may estimate an enterprise budget that shows a positive net return for a new crop if average yields, average prices, and average costs were to happen. However, he may also have discovered while gathering information on this new crop that its price and yield varies considerably. So even though the average return is positive, he may hesitate to decide to grow the new crop because he doesn’t know the chances of having a negative net return, that is, gross returns below his costs. By doing a few more calculations, this farmer could estimate the probabilities of the crop’s prices and yields and, by putting these together, estimate the probability of gross return being less than his costs. Or stated in other words, he can use the price and yield probabilities to estimate his probability of success, that is, a positive net return.
Suppose a farmer is considering whether to buy a group of feeder calves to feed out to market weight. He has the feedlot capacity and normally does buy feeder calves to feed, but he also normally checks the future market conditions and evaluates whether he has a good enough chance to make a profit. The group of calves he is considering weigh 550 pounds (each), and he expects that it would take him just over 8 months to feed them to 1250 pounds. The feeder price is $565 per head. He has estimated his feed costs to be $183 per head, other operating costs (veterinary, interest, labor, death loss, transportation, and so on) to be $102 per head, and his fixed costs for his facilities to be $40 per head. The total cost of the feeder calf, feed and other costs is $890 per finished animal which gives him a breakeven price of $71.20 per cwt.
Using the futures prices at the Chicago Mercantile Exchange and the historical basis for his area, this farmer estimates that his expected local price will be about $75 per cwt. in 8 months. Based on this estimated price, his profit will be $3.80 per cwt or $47.50 per head.
But this farmer also knows that this profit is not guaranteed. As part of his decision process, he wants to know how often will the market price in 8 months be above the breakeven price of $71.20; that is he wants to know his probability of success. Using the price probabilities estimated in the next section, this farmers notes that his breakeven price of $71.20 is in the interval from $67.51 to $72.50, and is about 3/4ths of the way from the lower boundary of $67.51 to $72.50. With this information he estimates the probability of having a price lower than $71.20 is 0.42 by adding the probabilities of the lower intervals (i.e., .03, .08, and .14 in the example) and 3/4ths of the probability of the interval around $70 (i.e., 3/4*0.23=0.17). So, the probability of having a price higher than his breakeven price, that is his probability of success, is estimated to be 0.58 (or 1-0.42).
This farmer can now use both the estimated profit of $47.50 per head (if the price occurred as predicted) and his probability of success of 58% to help him decide whether to buy the feeder calves and feed then for just over 8 months. By taking the time to estimate the probability of success, this farmer has increased his information and his ability to make a better decision. At this point (we won’t in this lesson), this farmer could consider the opportunity to hedge or buy an option to protect his price and profit. Doing so would probably increase his probability of success even though the cost of the hedge or option would decrease his estimated profit slightly.
For another example of estimating and using the probability of success, consider how a farmer decided to sign a sweet corn contract on not in Example 22.2
- Mean and Variance
For some decisions, the first six decision criteria do not allow a manger to develop a sufficient understanding of the risk involved in alternative choices. This is especially apparent in strategic planning. In these decisions, the mean-variance criteria can be a useful tool.
In mean-variance analysis, as its name implies, the mean and variance of the returns are calculated and compared. The coefficient of variation and a graphical portrayal of each alternative’s mean return and its variance can quickly show how a higher average return may also have a higher variance. This allows a manager to see the tradeoff between higher returns and stability of returns. A rational decision may be to accept a lower average return because a higher return has a higher variability.
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SCENARIOS FOR MANAGEMENT PLANNING
For many decisions, we don’t know what the future may hold because so many factors affect what may happen. This is especially true for long run plans such as making major expansions or choosing a new strategy for the farm. This results in a rather cloudy picture of the future at the precise time of making major expenditures and investments when we would rather have a clear picture of the future.
For occasions such as this we can develop and use scenarios of what paths we think current conditions will take into the future. Scenarios are not clear pictures of the future. Rather, a good set of scenarios will enable us to analyze how different strategies and decisions will perform in the different view of the future. If we develop a set of scenarios that encompass the range of what may happen in the future, we can craft a robust strategy that will perform well in each of several views or scenarios of the future.
Developing a set of good scenarios can be done in a fairly simple set of steps. These are summarized here and explained more fully in the text.
- Identify the uncertainties by considering each element (such as price, productivity, policy, competitors’ actions, and so on) that will affect the farm and classifying them as having a constant, predetermined or uncertain value in the future.
- Classify the uncertainties as either independent or dependent. Independent uncertainties are not affected (or essentially unaffected) by other elements affecting the situation. The U.S. Federal Reserve’s setting of their prime rate is an example of an independent uncertainties; weather is another example. Dependent uncertainties are determined by independent uncertainties. Local crop yields are affected in part by weather. Crop prices in minor production areas are affected by production levels in major production areas. Farmland prices are affected not only by potential income from farming (which is an dependent uncertainty) but also by what is happening to the growth rate in housing and manufacturing in neighboring areas (independent uncertainties). Only independent uncertainties are used to develop scenarios.
- Identify causal factors for independent uncertainties. For example, learn what affects the U.S. Federal Reserve in their interest rate decisions, what determines the growth rates in housing, what affects long-run weather conditions, what affects other farmers’ cropping and livestock decisions, and so on. These causal factors become the “scenario variables” from which we define the potential scenarios of future events.
- Develop internally logical and consistent scenarios. The scenario variables may be related. For example, if we assume bad weather in the U.S. Corn Belt that results in poor corn yields in a major production area, we should not say that corn prices will be low because poor corn production in the Corn Belt will cause prices to increase or to say soybean yields would be high in the Corn Belt because if bad weather decreases corn yields it will most likely decrease soybean yields.
These scenarios can now be analyzed for the potential income for each alternative strategy or other plan, for implications for industry profitability, for competitive advantages for the firm, and so on.
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ESTIMATING SUBJECTIVE PROBABILITIES
While we may not have enjoyed statistics when we took that class, probabilities can be very useful to making better decisions. As mentioned early in this class, the goal of making decisions should be to improve the chances of good results and decrease the chances of bad results. Blindly accepting one view of potential events or results is essentially saying that one view will occur with 100% reliability. Understanding how to estimate and use probabilities, even in a simplistic way, can greatly improve the quality of decision making.
As described in Appendix 22.2 in the text, there are three types of probabilities: empirical, deductive, and subjective. Empirical probabilities are based on historical or experimental data. Deductive probabilities are deduced by the information available or the circumstances present and our understanding of the system. Subjective probabilities are estimated using our personal, subjective views of what may happen; they are used when we have no or insufficient information to estimate empirical probabilities or deduce what the probabilities may be.
Since almost all decisions deal with deciding what to do now with the results not known until a future time or we need to make a decision at a time when we have insufficient information about the situation, we have to rely on subjective probabilities. Even taking historical probabilities and using them to decide what to do for the future is using a subjective opinion that the historical probabilities still hold truth about what may happen in the future. Because of their importance for making decisions for the future, we will concentrate on how to estimate subjective probabilities.
For this class, we will concentrate on three methods to estimate subjective probabilities:
- Conviction weights
- Sparse data
- Triangular distribution
This method of estimating subjective probabilities depends on (and is named for) the strength of our conviction about how likely each interval or category of the specific event will occur. The most common way to use the conviction weight method is to estimate price probabilities by analyzing market information and weighting or scoring each price interval based our conviction that the price of a product (or input) will fall within that interval. These weights are then added up and each interval’s probability is estimated as that interval’s conviction weight divided by the total of all conviction weights.
For example, suppose a farmer is considering whether to buy a load of feeder cattle and wants to know what the potential market price will be when the cattle reach market weight. First, he evaluates current market information and compares it to his past information of how the market behaves. Then he chooses an appropriate price range for the current market conditions. Suppose the market information indicates that the most likely market price when these cattle are ready for market is about $75 per hundred pounds with a probable range from $52.5 to $87.5. As shown in Table 22.2, this price range is divided into seven (7) price intervals of $5 each. The uneven interval boundaries (52.5, for example) allow the midpoints to be round numbers which are easier to understand, remember, and use in subsequent calculations. (This process of setting intervals and boundaries is also described in the text.)
Since this farmer decided that $75 was the most likely price, the first step is to give that price interval a score or weight of 100. Remembering that this is a subjective estimation process, this score of 100 is used as a starting point to score or weight our conviction that the future market price may indeed occur in another price interval. For instance, suppose the market information supports the possibility that the future price is more likely to move down than up and that with of these moves is quite possible. This farmer may decide to give a weight of 85 to the interval with a midpoint of $70 and a weight of 70 to the interval with a midpoint of $80. Again, based on his interpretation of the market information and advice of market experts, this farmer gives weights of 10, 30 and 50 to the three lower price intervals and 20 to the highest interval. Since he has decided to not put prices below $52.5 and above $87.5 in the table, the farmer is implicitly giving these prices a conviction weight of 0.
The next step is calculate the total of all the conviction weights (365 in this example). Then the interval probabilities are estimated by dividing each conviction weight by the total of all weights. For example, the interval probability for the $55 price interval is 10/365 or .03. These are rounded to hundredths for simplicity.
As a check, the interval probabilities are totaled to be sure they sum to exactly 1.0 as statistics tells us they should. In this example, the interval probabilities (rounded to hundredths) sum to 0.99. In cases such as this, the conviction weight method allows individual probabilities to be adjusted up or down to make the sum equal to one. After reconsidering the estimates without rounding, this farmer decides that the highest interval is the closest to being rounded up and so sets it equal to 0.06. This is done just to satisfy the requirement that the probabilities have to sum to 1.0.
In another instance, perhaps the estimated probability was just over half way to the next hundredth (.1952, for example ) and, thus, rounded up (to .20 for example). If the total ended up to be just over 1.00, the “rounded up” probability (e.g., 0.19 to 0.20) could be adjusted back to .19. (Remember these are subjective estimates, not hard science.)
If the check of rounding does not result in obvious adjustments, one could either adjust the largest probability (thinking that this is the smallest relative impact) or adjust on of the smallest probabilities (thinking that these are indeed least likely to happen). The interval probabilities could also be graphed to see what shape they form compared to our subjective expectation of what the graph should look like.
Remember: setting these weights is highly subjective and your ability will improve with experience. And because they are subjective, they need to be used with that in mind and any results based on them have to be interpreted with that in mind. Obviously, the validity and thus usefulness of the resulting interval probabilities will depend on the market knowledge and wisdom of the estimator. But don’t let that keep you from trying a first time, experience and improvement are gained only by starting and trying many times.
As an example of using conviction weights to estimate price probabilities, read how one farmer evaluated the market information and developed her estimates of what corn prices might do in Example 22.3.
Try this: Using current market information develop your own conviction weights and then your probabilities of what future prices might be for either hogs or soybeans in Worksheet 22.4.
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Many times we have some good data, but not enough to estimate empirical probabilities for the entire range of possibilities. For these occasions, we can use the sparse date method because it uses often sparse data to help start the estimation of interval probabilities. This method is most often used to estimate the probabilities for crop yield or animal productivity. This method is not appropriate for prices.
As with other probability estimations, we start with gathering information on the range of possibilities for the crop yield or animal productivity (e.g., daily milk production) and divide this range into intervals. We then note which intervals the known observations (that is, the sparse data) belong to.
In the sparse data method, the next step is to estimate a preliminary cumulative probability. That is, at what is thought to be the lowest possible corn yield, for example, we think there is a 0 probability of the yield being below that lowest yield. At what is thought to be the highest possible corn yield, we think there is a 1.0 probability (or 100%) chance that the yield will be at or below that highest yield. The sparse data are used to help us estimate how the cumulative probability “grows” from 0 through the range of possible yields to 1.0. After they are placed in their appropriate intervals, the observed sparse data are ranked from the lowest to the highest. We then use the following equation to estimate the preliminary cumulative probability for those intervals with any observed data.
preliminary cumulative probability = k / (n+1)
where k= the rank of the highest observation in a certain interval and n is the total number of observations. Once we have the preliminary cumulative probabilities, we use our knowledge that the complete cumulative probability will smoothly change from 0 to 1 to estimate a refined cumulative probability for each interval. When we are satisfied with the refined cumulative probability, the interval probabilities are estimated by subtracting the refined cumulative probability for that interval’s lower limit from the refined cumulative probability for that interval’s upper limit.
For an example of using sparse data to estimate probabilities, read about how a farmer estimated the probabilities of what his sweet corn might be in Example 22.4.
Try this: using the sparse data method, estimate the probabilities of wheat yield or another crop of your choosing in Worksheet 22.5.
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Triangular Distribution Method
The triangular distribution method can be used when we don’t have enough observations to use the sparse data method but we do know enough information about the situation or similar situations to identify three events: the lowest possible, most likely, and highest possible yield or animal productivity. The lowest and highest values form the lower and upper boundaries for the range of possible yields, for example. The most likely value is used as a boundary near the middle of the range. By assuming that the underlying yield or productivity have a normal distribution, we can estimate interval probabilities in 3 steps.
- The interval boundaries are given values between 0 and 1. The lowest boundary is given a value of 0. The boundary which is the most likely value is given a value of 0.5. the highest boundary is given a value of 1.0.
The boundaries between the lowest and the most likely event are given values between 0 and 0.5; the boundaries between the most likely event and the highest boundary are given values between 0.5 and 1.0. The boundaries on each side of the most likely value are given values calculating by first dividing 0.5 by the number of intervals and adding the result incrementally to 0 for the boundaries below the most likely event and to 0.5 for the boundaries above the most likely event. For example, if there are four intervals on the lower side, the increment is 0.125 (which is 0.5/4) and the values of the interval boundaries are 0, 0.125, 0.250, 0.375, and 0.5.
- These boundary values are transformed into subjective probabilities that the event will be greater than that boundary. (This is the opposite idea of the cumulative probability that shows the probability of being less than a certain value.) This transformation is done in different ways.
- For the lowest boundary, the probability that the event (say, the yield or price) is greater than or equal to the lowest possibility is 1.0.
- For interval boundaries between the lowest and the most likely value, the transformation is done by the following equation where x is the boundary value:
Probability = 1- (x2/0.5)
- For the interval boundary at the most likely value, the probability is 0.5 that the yield or price will be greater than the most likely value.
- For interval boundaries between the most likely value and the highest, the transformation is done by the following equation where x is the boundary value:
Probability = (1- x2)/0.5)
- For the highest boundary, the probability that the event (say, the yield or price) is greater than or equal to the highest possibility is 0.
- The probability that the actual price or yield will be in a specific interval is the difference between the probability that the value will be greater than the lower boundary and the probability that it will be greater than the upper boundary.
As an example of using the triangular distribution method, read how one farmer estimated the yield distribution for corn on a farm he was considering to buy in Example 22.5.
Try this: using the triangular distribution method, estimate the yield probabilities of wheat for a farm in Worksheet 22.6.
In this lesson, we studied the basic techniques for reducing a farm’s exposure to risk. We looked at the different sources of risk (production, marketing, financial, legal, human resource, moral, and political). We learned how to prioritize risks on the basis of each risk’s potential impact and its probability of happening. We considered the many options that a farmer has available to manage and control his or her exposure to risk. We learned how to develop payoff and regret matrices and then how to use decision criteria to make risky decisions. We also learned how to estimate the probability of success and how that idea can be used to help make risky decisions. and uncertainty so that we can increase the probability of success and decrease the probability of failure. At the end we learned how to develop and use scenarios for management planning and how to estimate subjective probabilities.
Worksheet 22.1 Sources of Risk & Management Options.pdf
Worksheet 22.2 Expanded Cattle Marketing Payoff & Regret Matrices.pdf
Worksheet 22.3 Estimating probability of success.pdf
Worksheet 22.4 Estimating probabilities using conviction weights.pdf
Worksheet 22.5 Estimating yield probabilities using sparse data.pdf
Worksheet 22.6 Estimating Yield Probabilities Using the Triangular Distribution Method.pdf
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