Questions & explanations
1. Compare controllable and uncontrollable risks: which type is easier to manage?
Controllable risks are generally easier to manage because the company can take direct actions to reduce them. For example, a company can improve employee training to lower accident rates. Uncontrollable risks are harder to manage because the company has little or no influence over them. For instance, a company cannot stop a hurricane from happening. However, companies can still prepare for uncontrollable risks by building resilience, such as having backup suppliers or insurance. The key difference is that controllable risks require proactive measures inside the company, while uncontrollable risks require adaptation and contingency planning. Both types need attention, but controllable risks offer more opportunities for direct improvement.
2. Compare the management approach for high-frequency/low-severity risks vs low-frequency/high-severity risks.
For high-frequency/low-severity risks, companies typically use prevention and control measures to reduce how often the risk happens. They may also accept the small losses as a normal expense. For low-frequency/high-severity risks, companies often transfer the risk through insurance because a single event could bankrupt them. They also prepare emergency response plans. The first type needs constant monitoring and process improvements, while the second type needs financial protection and crisis readiness. Both are important, but the strategies are very different. High-frequency risks are managed by the operations team, while high-severity risks involve top management and insurance decisions.
3. A factory has a risk of fire and a risk of a new competitor entering the market. Which is controllable and which is uncontrollable? Explain.
The risk of fire is partially controllable because the factory can install fire alarms, sprinklers, and train workers on safety procedures. The risk of a new competitor entering the market is mostly uncontrollable because the company cannot stop other firms from starting business. However, the factory can still manage the competitive risk by improving its own products and customer service. So fire is more controllable, while new competition is more uncontrollable. This example shows that some risks have both controllable and uncontrollable elements, but one side is stronger. Understanding this helps the factory decide where to invest in prevention versus where to focus on adaptation.
4. How does the time horizon affect how a company plans for a risk?
For short-term risks, companies plan with immediate actions like having backup inventory or emergency drills. These plans are updated frequently and focus on quick recovery. For long-term risks, companies set strategic goals, invest in research, and build flexibility into their operations. Short-term plans are detailed and specific, while long-term plans are more general and involve scenario thinking. The time horizon also determines how much money to set aside: short-term risks need cash reserves, long-term risks need capital investment. Both types should be part of a comprehensive risk management framework. Ignoring long-term risks can be as dangerous as ignoring short-term ones.
5. Compare the risk-neutral valuation approach used in both Black-Scholes and binomial models.
Both models use risk-neutral valuation, which means that under the pricing formulas, investors do not require extra return for risk. Instead, the expected return on the stock is assumed to be the risk-free rate. This allows pricing by discounting expected payoffs at the risk-free rate. In Black-Scholes, this leads to the partial differential equation. In binomial, we use risk-neutral probabilities for up and down moves. The advantage is that we do not need to know the stock's real expected return, which is hard to estimate. Both models give the same answer for European options if the binomial step size is small enough. The risk-neutral approach is a key idea in derivatives pricing.
6. An investor owns shares in 50 different companies. A new government regulation affects all companies in the same industry. Is that risk diversifiable? Explain.
This risk is not fully diversifiable because the regulation affects an entire industry, and the investor's 50 companies might all be in that same industry. If they are, then the loss is concentrated. True diversification requires owning companies across different industries. If the investor's 50 companies cover many industries, then the impact of a regulation on one industry is reduced because other industries are not affected. So the risk is diversifiable only if the portfolio is spread across unrelated industries. In this case, the risk is partially diversifiable depending on the portfolio's composition. The investor should ensure they are not overexposed to any single industry.
7. Why is it important to use a coherent risk measure when aggregating risks across an enterprise?
Coherent risk measures ensure that aggregation does not produce illogical results. For example, subadditivity guarantees that diversification reduces risk. If a risk measure is not subadditive, the aggregate capital requirement could be higher than the sum of standalone capitals, which discourages diversification. Coherent measures also allow consistent capital allocation across business units. They align with risk management intuition: more risk requires more capital, and diversification is beneficial. Using non-coherent measures like VaR can lead to misleading conclusions and poor capital decisions. Therefore, regulators and firms increasingly adopt coherent measures like TVaR.
8. Why can't an investor remove systematic risk by diversifying?
Systematic risk affects all investments in the market, so no matter how many different stocks an investor owns, they still feel the effect of a market crash. Diversification only reduces the specific risks of individual companies (idiosyncratic risk). For example, if the entire economy slows down, all companies see lower earnings. Even bonds and real estate can be affected. Therefore, systematic risk is unavoidable and must be managed through asset allocation, hedging, or accepting lower returns. It is a core principle of finance that only risk that cannot be diversified earns a risk premium. So investors cannot eliminate it, but they can choose how much market risk to take.
9. Give an example of a risk that a business can control.
A business can control the risk of workplace accidents by training employees and installing safety equipment. Another example is the risk of poor product quality, which can be managed through better production processes. Controllable risks are those a company can reduce or prevent by its own actions. These are also called internal risks because they come from within the organization. For instance, a restaurant can control food hygiene by following strict cleaning routines. Managing controllable risks often requires operational decisions and investment in safety measures. By focusing on controllable risks, a company can directly improve its performance and reduce losses.
10. Compare diversifiable and non-diversifiable risks: which type is more worrying for an investor?
Non-diversifiable risks are more worrying for an investor because they cannot be eliminated, and they affect the entire portfolio. During a market crash, all investments suffer. Diversifiable risks can be almost removed by owning many different assets, so they are less concerning if the investor diversifies properly. However, if an investor does not diversify, diversifiable risks become very dangerous. In theory, investors are only compensated for taking non-diversifiable risks, because they cannot avoid them. Therefore, a well-diversified investor worries mainly about non-diversifiable risks like economic downturns, while poor diversification makes all risks worrying.
11. Compare short-term and long-term risks: which type is harder to predict?
Long-term risks are generally harder to predict because they involve many uncertain factors over a long period. For example, predicting technological disruption in ten years is very difficult. Short-term risks, like a machine breakdown, are easier to foresee based on past data and maintenance schedules. However, long-term risks can have bigger consequences if ignored. Companies use trends and expert opinions to estimate long-term risks, but there is always high uncertainty. Short-term risks allow for more precise forecasting and quick adjustments. Therefore, companies often focus more on short-term risks, but must also develop resilience for long-term changes.
12. Describe one method for aggregating operational risk with market risk in a risk capital model.
One method is to use a correlation matrix that assumes a constant correlation between operational and market risk, say 0.25. Then the total capital is the square root of (market capital² + operational capital² + 2*correlation*market*operational). This assumes both risks are normally distributed and linearly dependent. Another method uses copulas to combine distributions directly, allowing for tail dependence. More advanced models simulate scenarios that affect both risks simultaneously, such as a financial scandal causing market losses. The chosen method should reflect the actual relationship, but often data is limited, so simple correlation is used initially.