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Calculate supplied risk scenarios and distinguish diversification from guaranteed protection
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Calculate supplied risk scenarios and distinguish diversification from guaranteed protection
A budget is a conditional account, not a guarantee that every receipt will occur. Percent changes apply to a stated starting amount. Different future scenarios can be compared without predicting which one will happen.
| Term | What it means |
|---|---|
| Risk | Exposure to uncertain outcomes that matter for the stated objective. |
| Return | A gain or loss over a period, measured as an amount or a percentage of a stated starting value. |
| Expected value | A probability-weighted average under a supplied probability model. |
| Concentration | Placing a large share of exposure in one source or closely related sources. |
| Diversification | Combining different exposures so that some source-specific changes may offset or matter less. |
| Common shock | An event affecting several exposures together. |
| Insurance | An arrangement that exchanges a specified payment for defined protection against stated losses, subject to its terms. |
| Uncertainty | Lack of knowledge about which outcome or model will apply. |
A future outcome can differ from a planned amount. A fictional event may attract fewer visitors, equipment may fail or the price of a needed input may change. Risk concerns how those possibilities affect the objective being considered. A calculation that assumes every receipt occurs as planned is one scenario. It should not be presented as proof that other outcomes are impossible.
Different people or organizations can care about different features of the same uncertain arrangement. One may focus on average resources, another on avoiding a balance below a required payment. A choice with a higher average can also have a worse low outcome. Ranking the choices requires a stated objective and relevant constraints, not just a list of possibilities. The lesson grades comparisons under supplied rules rather than a learner's willingness to take risk.
Return can be measured in dollars or as a percentage of the starting value. A twenty-dollar gain on one hundred dollars is twenty percent; the same twenty-dollar gain on two hundred is ten percent. The period also matters. A ten-percent change over one month is not automatically comparable with ten percent over several years. Use compatible starting values and periods before comparing percentages.
The examples use fictional holdings and known classroom scenarios. They are not suggestions for actual investments or forecasts of returns. Real probabilities and future values are often uncertain, and a historical pattern does not guarantee repetition. Our purpose is to learn what a stated scenario table establishes and what remains outside it.
Another way: Expected value is an average of a model
If a case supplies probabilities, expected value multiplies each outcome by its probability and adds the products. Suppose a fictional activity has a one-half chance of receiving forty dollars and a one-half chance of receiving twenty. Expected receipts are thirty dollars. The activity does not actually receive thirty in either listed outcome. The average summarizes the model rather than naming a guaranteed result for one attempt.
Probabilities must cover the relevant mutually exclusive outcomes and sum to one. If the table omits an outcome or assigns overlapping events without adjustment, adding the weighted amounts can give a misleading total. A probability of one quarter means 0.25, not twenty-five. Converting the fraction or percentage correctly is part of the calculation.
Expected loss is calculated in the same way. A one-quarter chance of a forty-dollar loss and a three-quarter chance of no loss gives an expected loss of ten dollars. This does not mean the loss will be limited to ten. In the bad outcome, the full forty is lost. A budget that cannot absorb forty has a relevant concern that the average alone does not resolve.
A supplied probability is a premise of the exercise. In a real investigation it would need evidence and might be uncertain or change over time. If the probability rises from one quarter to one half with the same forty-dollar loss, expected loss rises from ten to twenty. That sensitivity calculation shows how the conclusion depends on the assumption; it does not predict that the probability will actually rise.
Another way: Diversification depends on how outcomes move together
Concentration means that a large part of the outcome depends on one source. If all two hundred dollars of a fictional holding is exposed to source A and A can rise or fall twenty percent, the final values are two hundred forty or one hundred sixty. The range between those supplied outcomes is eighty dollars. This describes the two-state model, not every possible future loss.
Now split the same two hundred into one hundred in A and one hundred in B. In scenario one, A rises twenty percent while B falls ten percent. The changes are plus twenty and minus ten, so the total rises to two hundred ten. In scenario two, A falls twenty percent while B rises ten percent, giving minus twenty plus ten and a final total of one hundred ninety. The range is twenty dollars, smaller than the concentrated range under these particular opposite-moving outcomes.
The reduction comes from the relationship between the sources, not merely from having two labels. If A and B both fall twenty percent in a common-shock scenario, each one-hundred-dollar holding loses twenty and the combined total falls to one hundred sixty. Splitting the original amount does not eliminate that shared loss. Two sources exposed to the same underlying event may provide much less diversification than their names suggest.
The example therefore supports a conditional conclusion: combining the supplied partly offsetting exposures reduces the spread in the two specified scenarios, but a common shock can still affect both. It does not establish that every split has the same benefit or that diversified holdings cannot lose value. A real comparison needs information about the exposures and how they may move together.
Another way: A higher possible return is not a guaranteed reward
A risky arrangement may offer the possibility of a larger gain to attract participants, but taking more risk does not guarantee a higher realized return. An unfavorable outcome can produce a loss. Even a model with a higher expected return can include a lower worst outcome. The words expected and possible should remain visible rather than being replaced with a promise.
Consider two fictional options costing the same amount. One returns one hundred five dollars for certain within the model. Another returns one hundred twenty or eighty with equal probabilities, giving an expected value of one hundred. The second is more variable but has a lower expected value in this supplied table. Risk alone does not force the average to be higher. A general economic discussion of compensation for risk is not permission to rewrite any table so that the riskier option automatically wins.
If a decision rule is supplied, apply it precisely. A rule requiring at least ninety dollars in every listed scenario excludes the eighty-dollar outcome option. A rule choosing the highest supplied expected value compares the weighted averages instead. These can produce different choices because they optimize different criteria. Neither arithmetic result should be presented as the only reasonable personal preference.
Past outcomes provide evidence about what occurred, not certainty about future outcomes. A sequence of gains does not logically rule out a later loss, particularly if the conditions change. A claim that an uncertain arrangement guarantees both a high return and no loss needs a clearly specified and credible mechanism, not just an attractive number. The classroom response is to identify what the supplied contract or model actually guarantees and what it merely projects.
Another way: Pooling and protection change the distribution of losses
Insurance is one way to change who bears specified losses. Participants pay a premium and receive protection defined by a contract. The arrangement can pool risks across many participants, but its effectiveness depends on the losses, how they are related, costs and the promised coverage. If every participant suffers the same loss at once, pooling does not make that total loss disappear.
A deductible is a stated portion of a covered loss that the participant bears before or alongside the insurer's payment under the supplied rule. If a classroom contract covers a forty-dollar loss after a ten-dollar deductible, the insurer pays thirty and the participant bears ten of the loss, plus any premium paid. The premium and deductible are different entries. Subtracting the premium from the loss before applying the deductible would use a different rule unless the contract said so.
Risk reduction, risk sharing and risk avoidance are also different. A precaution might reduce the probability or size of a loss. Insurance can shift part of the financial consequence without necessarily preventing the event. Avoiding an activity may remove one risk while forgoing its benefits. A complete comparison accounts for the cost of the precaution, premium or forgone alternative as well as the changed outcomes.
This lesson does not select actual protection or investment products. Their exclusions, fees, access rules and legal protections require current specific information. It provides a method: state the scenarios, calculate changes on the correct bases, check common exposures, separate averages from individual outcomes and identify the decision rule. That method makes uncertainty visible rather than hiding it behind a single confident-looking total.
A fictional club studies two hypothetical exposures, A and B, rather than purchasing any real asset. It assigns one hundred dollars to each for a total starting value of two hundred. In scenario one, A gains twenty percent and B loses ten percent. Their values become one hundred twenty and ninety, totaling two hundred ten. In scenario two, A loses twenty percent and B gains ten percent, producing eighty plus one hundred ten, or one hundred ninety.
If the club had assigned all two hundred to A, the same A scenarios would produce two hundred forty or one hundred sixty. The split arrangement has a smaller range in these two supplied scenarios. That is a valid diversification comparison because the starting total and the scenario definitions are held constant. It is not enough merely to count the number of names in the table.
A third scenario introduces a common shock: both exposures lose twenty percent. The split arrangement now totals one hundred sixty, the same result as a twenty-percent loss on the original total. The earlier reduction in variation did not guarantee protection from every shared event. If no probability for that third scenario is supplied, the class should not invent one to calculate an overall expected value.
The club also has a rule requiring at least one hundred eighty dollars in every considered scenario. The common-shock result fails that rule. Another objective based on a supplied probability-weighted average would ask a different question. The exercise therefore ends by recording the scenario results and the rule's consequence, without recommending a real allocation or pretending that an uncertain future has been predicted.
Expected value need not be an outcome that ever occurs. Diversification depends on how exposures move together and cannot eliminate every common shock. A higher possible return is not a guaranteed gain, and a more variable table need not have a higher average.
Identify the two starting holdings.
A=100; B=100 dollars
The starting total is twice the per-source amount.
Calculate A in scenario1.
100 times1.2=120
A gains twenty percent of its own base.
Calculate B in scenario1.
100 times0.9=90
B loses ten percent of its own base.
Combine scenario1 and calculate scenario2.
Totals=210 and 190
Scenario2 uses factors0.8 for A and1.1 for B.
Calculate the common-shock total.
2 times100 times0.8=160
A shared twenty-percent decline affects the whole starting amount.
Identify the two starting holdings.
A=200; B=200 dollars
The starting total is twice the per-source amount.
Calculate A in scenario1.
200 times1.2=240
A gains twenty percent of its own base.
Calculate B in scenario1.
200 times0.9=180
B loses ten percent of its own base.
Combine scenario1 and calculate scenario2.
Totals=420 and 380
Scenario2 uses factors0.8 for A and1.1 for B.
Calculate the common-shock total.
2 times200 times0.8=320
A shared twenty-percent decline affects the whole starting amount.
Identify the two starting holdings.
A=300; B=300 dollars
The starting total is twice the per-source amount.
Calculate A in scenario1.
300 times1.2=360
A gains twenty percent of its own base.
Calculate B in scenario1.
300 times0.9=270
B loses ten percent of its own base.
Combine scenario1 and calculate scenario2.
Totals=630 and 570
Scenario2 uses factors0.8 for A and1.1 for B.
Calculate the common-shock total.
2 times300 times0.8=480
A shared twenty-percent decline affects the whole starting amount.
Compare with concentration in A.
All in A: 720 or 480
The split narrows the first two scenarios but does not prevent the supplied common shock.
Identify the two starting holdings.
A=400; B=400 dollars
The starting total is twice the per-source amount.
Calculate A in scenario1.
400 times1.2=480
A gains twenty percent of its own base.
Calculate B in scenario1.
400 times0.9=360
B loses ten percent of its own base.
Combine scenario1 and calculate scenario2.
Totals=840 and 760
Scenario2 uses factors0.8 for A and1.1 for B.
Calculate the common-shock total.
A fictional reserve holds 500 dollars in A and 500 dollars in B. Scenario1 changes A by +20 percent and B by -10 percent; scenario2 changes A by -20 percent and B by +10 percent; a separate common-shock scenario changes both by -20 percent. No fees or other entries occur. Calculate the combined final value in each scenario. No probabilities or forecasts are implied.
| Your result | |
|---|---|
| Scenario1 dollars | |
| Scenario2 dollars | |
| Common shock dollars |
Two fictional holdings each start at 700 dollars. In one scenario A gains20 percent and B loses10 percent. A separate common shock reduces both by20 percent. No other entries occur.
Update A in the first scenario.
700 times1.2=a
The gain uses A's own base.
Update B in that scenario.
700 times0.9=b
The loss uses B's own base.
Calculate the separate common-shock total.
1400 times0.8=c
Both holdings share this decline.
Match each supplied statement to the feature it describes.
| Potential diversification across those scenarios | Common shock | Expected-value calculation | |
|---|---|---|---|
| Different sources move in opposite directions in the listed scenarios. | |||
| All sources lose value in the same event. | |||
| Outcomes are weighted by supplied probabilities and added. |
A fictional reserve holds 600 dollars in A and 600 dollars in B. Scenario1 changes A by +20 percent and B by -10 percent; scenario2 changes A by -20 percent and B by +10 percent; a separate common-shock scenario changes both by -20 percent. No fees or other entries occur. Calculate the combined final value in each scenario. No probabilities or forecasts are implied.
Scenario1 dollars: b0
Scenario2 dollars: b1
Common shock dollars: b2
A fictional event has a 25 percent probability of a 40-dollar loss and a 75 percent probability of no loss. A separate stated protection contract would pay 30 dollars if the loss occurs. Calculate expected loss without protection, the participant's loss remaining in the bad event with protection before any premium, and expected remaining loss before any premium. These probabilities are supplied assumptions.
| Your result | |
|---|---|
| Expected unprotected loss | |
| Bad-event remaining loss | |
| Expected remaining loss |
A fictional reserve holds 800 dollars in A and 800 dollars in B. Scenario1 changes A by +20 percent and B by -10 percent; scenario2 changes A by -20 percent and B by +10 percent; a separate common-shock scenario changes both by -20 percent. No fees or other entries occur. Calculate the combined final value in each scenario. No probabilities or forecasts are implied.
| Your result | |
|---|---|
| Scenario1 dollars | |
| Scenario2 dollars | |
| Common shock dollars |
Lesson test: one question per skill, one attempt each, no hints. Your answers are checked when you submit.
A fictional reserve holds 900 dollars in A and 900 dollars in B. Scenario1 changes A by +20 percent and B by -10 percent; scenario2 changes A by -20 percent and B by +10 percent; a separate common-shock scenario changes both by -20 percent. No fees or other entries occur. Calculate the combined final value in each scenario. No probabilities or forecasts are implied.
| Your result | |
|---|---|
| Scenario1 dollars | |
| Scenario2 dollars | |
| Common shock dollars |
Explain how to calculate supplied risk scenarios and distinguish diversification from guaranteed protection. Show a fresh example and check its result.
10. Each fictional holding begins at 400 dollars. Scenario1 is A+20 percent/B-10 percent; scenario2 is A-20 percent/B+10 percent; a common shock is -20 percent for both. No other entries occur., step 5
2 times400 times0.8=640
A shared twenty-percent decline affects the whole starting amount.