Questions

Question 1

TIPS FOR EXAM TO REMEMBER

Answer 1

1. Mitigating one risk increases another
2. Comprehensive and holistic. Only want to transfer residual, undesirable risks. Don’t hedge away all risk because you’d lose all returns.
3. When critiquing, start with where the comment is correct. Then critique EACH item that is incorrect.
4. People tend to underestimate the impact of low probability, high severity events.
5. Even if risks aren’t material now, remember to assess their potential to become material in the future.

Question 2

The Board is asked to consider the following questions. Identify how these questions relate to the Board’s risk appetite statement.
1. How much risk is the firm currently taking?
2. How much risk should the firm be taking?
3. What is the maximum amount of risk the Board wants to take?
4. What is the maximum amount of risk the firm can take without jeopardizing operations?

Answer 2

Risk profile
Risk target
Risk tolerance
Risk capacity

Question 3

ExAir is a company offering low-cost holiday travel between Country A and Country B. Give examples of risks they might pursue.

Answer 3

1. Pricing Risk: Offering a low-cost travel options means ExAir may get increased market share, but risk of reduced profit margins.
2. Strategic and Business Risk: The strategy of being a price leader means ExAir may invest in more aircraft to increase capacity. If/when competitors reduce prices, market share may reduce again. ExAir would be taking a risk that they don’t recoup their investment in a large number of aircrafts.

Question 4

ExAir is a company offering low-cost holiday travel between Country A and Country B. Give examples of risks they might avoid.

Answer 4

1. Technology Risk: They may choose to only use certain aircrafts to avoid certain maintenance and safety risks.
2. Legal Risk and Reputational Risk: They may choose to only operate in airports of a certain quality to avoid safety risks.

Question 5

ExAir is a company offering low-cost holiday travel between Country A and Country B. Give examples of risks they might transfer.

Answer 5

1. They may insure their aricrafts to transfer the risk of high costs to repair damaged aircrafts.
2. They may purchase liability insurance to transfer risk of passenger and employee injuries and accidents.

Question 6

ExAir is a company offering low-cost holiday travel between Country A and Country B. Give examples of risks that can be frequency-mitigated.

Answer 6

1. Operational Risk: They may use clear and strict safety procedures to reduce the frequency of passenger and employee injuries and accidents.
2. Project Risk: They may implement time buffers into scheduling (like after passengers deplane and before new passengers board) to reduce the frequency of delays for passengers.

Question 7

ExAir is a company offering low-cost holiday travel between Country A and Country B. Give examples of risks that might be retained by informed decision.

Answer 7

1. Reputation Risk: Because ExAir focuses on offering low cost travel rather than a luxury experience, they may retain some reputation risk by informed decision. For example, they may expect and retain occasional complaints from passengers about the comfort of the experience.
2. Some Physical Climate Risk would have to be retained because planes cannot travel in poor weather conditions.

Question 8

A car manufacturer uses the following strategies relating to risk. Identify with risk treatment method is used in each case.
1. Multiple suppliers from multiple countries for key raw materials
2. Enters into an exchange rate swap with a bank
3. Improves workplace safety training
4. Invests in research and development of a self-driving car
5. Buys product liability insurance which will partially reimburse the manufacturer in the event of legal liability from a defective product
6. Closes its factory in a country which is experiencing civil unrest

Answer 8

1. Mitigate the severity of late supply deliveries or failure of a supplier. (If one has an issue, there are others available so production can continue)
2. Transferring risk from exchange rate movements
3. Mitigate the frequency (and maybe severity) of workplace accidents
4. Pursue the risk of not being able to recoup the investment, hoping for a profit
5. Transferring legal risk
6. Avoiding political risk

Question 9

An insurer is considering offering a supplemental product that covers health expenses that exceed the policyholders’ primary plan (through their employment). Identify at least one factor from each of the PESTLE categories that would be significant for the risk management of this product.

Answer 9

Political: If the government offers a new or increased public health coverage, this health insurance plan may not be profitable anymore.
Economic: The insurer must analyze the claims frequency and severity that could arise if inflation and unemployment rise. Morbidity claims frequency and severity often increase in recessionary environments.
Social: Analyze demographics. What are the careers that the target clients have? What is their likelihood to be hospitalized? Important for pricing.
Technical: Keep data secure and mitigate risk of cyber threats.
Legal: Prepare for claim litigation.
Environmental: A pandemic could dramatically increase claims frequency and severity.

Question 10

A car manufacturer decides to revise its risk appetite to be more conservative with respect to variability in annual earnings. Explain how this might impact the following stakeholders:
1. The marketing department
2. Shareholders
3. Credit rating agencies
4. Customers

Answer 10

1. The firm will likely reduce spending on aggressive marketing that would create large sales spikes. Emphasis will shift to more steady marketing for more predictable income streams.
2. Less variable earnings means a lower risk, but also a lower potential profit. This will attract some and deter other shareholders, depending on their risk appetite.
3. The agency would likely assess the firm at a higher credit rating because less volatile earnings means more predictable ability to meet obligations (less liquidity and credit risk).
4. A firm that is targeting earnings stability may offer more consistent, predictable products. There would be fewer experimental product launches and less trend following.

Question 11

Company X currently uses the following practices to identify top risks: survey managers, expert and industry surveys, and internal data. Identify the potential shortcomings of each of these practices.

Answer 11

1. Surveying managers works well for operational risks since the managers should know the risks they handle daily. But some risks are better identified from the top of the firm like cyber risk. Senior management should participate in the risk identification process as well.
2. Expert and industry surveys reveal more about the risks that competitors are facing. There may be similar risk in Company X, but every company has a unique risk profile and needs to analyze its own risks.
3. Internal data is not forward looking. A high quality ERM system is holistic and forward looking.

Question 12

P Inc’s business is removing impurities in silver. The refining process is very energy-intensive, so energy costs are a large proportion of its total costs. Customers provide raw silver to P which it then refines for a fixed fee. P uses coal as its only source of energy. Its fixed costs are extremely stable. The cost of coal is the only variable cost P incurs. The coal costs currently exceed the refining fee charged. This situation has occurred several times in recent history. The CEO asks you to apply the PESTLE framework to identify the general environment risks P faces.

Answer 12

Political: Political instability in coal producing countries may cause the price of coal to increase dramatically and/or for a sustained period, causing losses for P.
Economic: Inflation reduces the purchasing power of money. If inflation rises unexpectedly, P would suffer losses since they charge a fixed refining fee and the price of coal would increase due to purchasing power decrease.
Social: There may be reputation risks related to climate change if P continues using coal.
Technical: Innovation, research, and development. P should improve as technology advances so that they are not left behind.
Legal: Governments may increase restrictions and costs on using coal, gas, and oil for energy.
Environmental: If floods, droughts, hurricanes, etc. impact coal producing countries, the price of coal will increase.

Question 13

Describe 5 major risks that are suitable for quantitative analysis, then 4 major risks that are not.

Answer 13

Risks that are suitable for quantitative analysis are ones that are well-defined, quantifiable, material, and are supported by sufficient and relevant historical data.
Quant Ex: mortality risk, lapse risk, interest rate risk, credit risk, and equity risk
Qual Ex: reputation risk, political risk, strategic risk, culture risk, and people risk

Question 14

Explain why long-term bonds government bonds are less liquid than short-term government bonds.

Answer 14

Long term bonds are more sensitive to changes in interest rates, so small changes in interest rates can cause larger price fluctuations. This makes them more risky than short-term government bonds, so they are traded less frequently, so they are less liquid.

Question 15

Explain why a corporate bond is generally less liquid than a government bond with the same term to maturity.

Answer 15

The credit risk of corporate bonds is higher because the company is more likely to fail than the government is, so investors trade these higher risk bonds less frequently, meaning lower liquidity. Also, government bonds are more standardized, so they are more easily traded by a wider audience.

Question 16

Explain why a work of art is an illiquid asset. Why would an individual invest in a work of art, given its lack of liquidity?

Answer 16

A work of art is an illiquid asset because it cannot be quickly converted to cash in a cost effective way. Selling it quickly would likely require selling it at a discount. An individual may invest in a work of art because they already have sufficient liquidity from other sources and they hope the market value of the art to increase. In general, very liquid assets do not offer as high of a return on investment because they are less risky.

Question 17

Exercise 2.7 in written examples

Question 18

A firm is modelling operational losses using Monte Carlo simulation. You calculate the 99% VaR and a confidence interval for it using the normal approximation. Then you calculate the VaR using the empirical method and it’s much higher. Suggest, with reasons, a better method to find a confidence interval for the 99% VaR.

Answer 18

The normal approximation is not adequate on this data to estimate the 99% VaR or a confidence interval for it because the normal approximation assumes the distribution is approximately normal. The empirical estimate of the VaR shows that the data has a much longer tail than the normal distribution. Instead, we can use order statistics to make a non-parametric confidence interval. If more accuracy is required and resources allow, stochastic simulation could be done. Run 100 sets of 1000 simulations, calculate the VaR on each set (to get 100 VaR estimates), then use the distribution of the simulated VaR values to calculate the confidence interval. (Non-parametric method tends to give a wider confidence interval.)

Question 19

Explain why subadditivity is a desirable characteristic for a risk measure used for setting economic capital.

Answer 19

Risk measures can be calculated for each business unit, and if the risk measure has the subadditivity characteristic, then the total risk measure of the company will never be greater than the sum of the individual risk measures. This means that business units won’t be able to understate their risk by breaking it up into smaller components. The subadditivity characteristic also means that the total could be lower than the sum of the individual parts. This means diversification benefits are reflected which is beneficial for allocating capital because if 2 business units have offsetting risks, less total capital is required.

Question 20

Consider the positive homogeneity assumption of coherent risk measures. Your colleague asserts that this assumption is unrealistic, and that doubling the size of a portfolio may more than double the risk. Critique your colleague’s opinion.

Answer 20

They’re correct that the risk may not double because very large portfolios are difficult to liquidate quickly. Also, a large liquidation of an asset from a single large firm could noticeably lower the market value of that asset, reducing gains.
However, these situations are not common, they are tail events (very large portfolios, very large liquidations). So the doubling assumption should be close to true in reality under normal market conditions.
It’s a simplifying assumption, but every model is a simplification of reality, and models still produce valuable insights. In this case, the positive homogeneity assumption allows us to easily convert risk measures into other currencies using the exchange rates. This is very useful for firms allocating capital to business units in multiple currencies.

Question 21

Your colleague states: “Expected shortfall is sensitive to the assessment of potential losses far in the tail, so is subjective and has severe model risk. Value at risk (at least for short time horizons) can be estimated and validated based on available data, and is therefore more objective. So in spite of its theoretical shortcomings, value at risk is a better practical measure of risk.” Critique your colleague’s opinion and suggest how the tail value at risk calculation could be adapted to reduce the impact of losses far in the tail.

Answer 21

They’re right that TVaR is subject to potentially extreme model risk. However, this doesn’t indicate that VaR is a better risk measure for all purposes. Ex: Shareholders only care about losses up to bankruptcy, but regulators care about losses beyond. Ex: 2 portfolios may have the same VaR, but very different tail behaviour, so if a firm is considering investing in 2 such portfolios, it’s important for the firm to analyze the tail beyond the VaR to ensure risk appetite isn’t breached. Some suggestions:
1. Instead of measuring the average above VaR, measure the average between 2 quantiles, reducing the impact of very rare data.
2. Declining weights could be applied to the data points to reduce the instability.
3. EVT like POT can be used to model the tail beyond the threshold. A distribution can be fitted to the tail so that it is supported by observed data (more objective) and isn’t biased by fitting to the center of the distribution.

Question 22

You are given a frequency distribution that follows the Poisson distribution and a severity distribution. You can approximate the value at risk for the aggregate loss in two different ways: the normal approximation or the translated gamma approximation. How do you decide which estimate to use? Which one is more accurate?

Answer 22

The normal approximation works well when the frequency is large and the skew of the severity distribution is small. This is because the normal approximation is supported by the Central Limit Theorem that states that with sufficient observations, the distribution approaches a normal distribution which has 0 skewness. Significant skew would produce inaccurate VaR estimates, especially for very high percentiles.
The translated gamma approximation works better when the frequency is small (E(N)<30) and there is material skew in the severity distribution (because the Gamma distribution has skew).
Translated gamma matches the first 3 moments of the aggregate loss instead of just the first 2, so it’s generally more accurate.

Question 23

Describe the advantages of using EVT to calculate tail risk measures of a distribution, compared with a parametric model of the full loss distribution.

Answer 23

A parametric model of the full loss distribution attempts to fit the entire distribution, usually focusing on fitting the center. EVT has the following benefits:
1. It focuses on fitting just the tail of the distribution, so it is an ideal method for purposes that do not require fitting the center of the data. Lower model risk.
2. The POT method is particularly useful in risk management because it focuses on exactly the statistic that is measured with TVaR, a common risk measure. Easy to calculate VaR and TVaR when POT is used.
3. It’s more reliable for extrapolating beyond available data because it focuses on the low frequency, high severity data points.
4. EVT allows you to fit the distribution to the data using parameters to capture the shape of the tail, so it’s flexible.

Question 24

Describe the trade-off involved in selecting block sizes for the block maxima approach to estimating the shape parameter. Explain how the selection influences the bias and the variance of the estimate.

Answer 24

Low block sizes means you have more data points of block maxima to tune the shape parameter. More observations means less variance of the estimate, but the trade off is higher bias. Imagine every data point in the sample is one block. So every data point is a block maxima. The shape parameter would be biased toward lower block maximas.

Question 25

The normal distribution is in the MDA of the Gumbel extreme value distribution. Explain in words what this means. The normal distribution is symmetric while the Gumbel distribution is positively skewed. Explain why this is not inconsistent.

Answer 25

Saying that the normal distribution is in the MDA of the Gumbel distribution means that the distribution of the normalized maxima of independent normally distributed observations converges to the Gumbel distribution as the sample size becomes large. The maximum of a distribution will not necessarily have the same characteristics as the underlying distribution (like symmetry). By focusing on the maximum of a normal random sample, the distribution of the maximum naturally becomes right skewed because the maximum is not likely to fall below the mean of the underlying normal distribution.

Question 26

Describe the trade-off involved in selecting a threshold for the POT approach to estimating the shape parameter. Explain how the selection influences the bias and the variance of the estimate.

Answer 26

Selecting a relatively low threshold means there will be more data above the threshold that will be used to tune the shape parameter. This reduces the variance of the estimate because it will not be as sensitive to one data point, but it increases the bias since lower values are considered to be in the tail. Selecting a high threshold means there will be less data above that threshold, so variance increases (more sensitive to adding one more data point) and less biased.

Question 27

You are given the following information about 3 random variables that are in the MDA of the GEV distribution. State with reasons whether the shape parameter ξ is <0, 0, or >0. 1. X is greater than 0, unbounded on the right side, and has finite kth moment for all k = 1, 2, 3, .... 2. Y = -X 3. Z has a finite number of moments

Answer 27

1. X is unbounded on the right side, so not Weibull. X has infinite moments which means a thin tail, so not Frechet. Therefore, Gumbel with ξ=0 2. Y has an upper bound and no lower bound, so Weibull with ξ<0 3. A finite number of moments indicates a thicker tail, so Frechet with ξ>0

Question 28

Your colleague is comparing 2 TVaR estimates: an empirical estimate and an estimate from the GPD method. What should your colleague consider?

Answer 28

Empirical estimates are limited to the observed data points which could underestimate the true TVaR because future losses could extend the tail. Also, empirical TVaR can be unstable for very high percentiles because there are so few observations. Fitting a GPD to the tail data allows for extrapolation beyond the observed data, so it has potential to be more accurate if an appropriate threshold is chosen. The GPD method introduces model risk.

Question 29

There is an 80% chance of no loss. There is a 19% chance of a minor loss which follows a lognormal distribution. There is a 1% chance of a major loss which follows a pareto distribution. Your colleague claims that the loss random variable will be in the Gumbel MDA because there is a higher probability that the loss will have a lognormal distribution than a pareto distribution. Critique this claim.

Answer 29

The loss random variable is more likely to be in the Frechet distribution because the MDA depends on the shape of the tail of the distribution. Even though the loss is more likely to be a minor lognormal loss than a major pareto loss, the block maximum will more often come from the pareto part of the distribution.

Question 30

If we want to know the probability that X is greater than a certain quantile given Y is greater than its quantile, how can we use the relationships to determine the probability?

Answer 30

1. If X and Y are independent, then knowing Y > q tells us nothing, so the probability is P(X>q). 2. If X and Y are comonotonic, then they are always large (or small) together, so the probability is 1. 3. If X and Y are countermonotonic, then they are never large or small together, so the probability is 0.

Question 31

A commonly held fallacy is that the joint distribution of 2 random variables is fully determined by___

Answer 31

their marginal distributions and correlation. This is false!

Question 32

A common behavioural bias involves underestimating the chance that a low-probability event will occur. Explain the implications for the process of developing adverse scenarios for stress testing.

Answer 32

Bottom-up approach: People have to think about what scenarios would change the model inputs that would produce a given loss. This involves human judgment. Since people tend to underestimate the chance of low-probability events, senior management may see the shocks and the resulting losses and underestimate the probability of such losses occurring. This is what top-down scenario analysis tries to prevent. But people also tend to underestimate the impact of low frequency, high severity events. So given a scenario, they may not shock the model inputs enough. Historical data can be used to reasonability check the shocks, but historical data isn't always comparable.

Question 33

A risk manager presents the stress scenarios to the senior management before inputting them into the firm's capital adequacy models. Explain why getting agreement before the results of the scenario testing are known could be valuable.

Answer 33

To reduce human bias. If the results are presented first, management may dismiss the results because they believe the scenarios leading to those losses have trivial probabilities. Getting their approval of the scenarios as extreme but plausible first will reduce the chance that they will dismiss the results.

Question 34

A risk manager presents the results of 20 stress scenarios to the CEO. In 19 of the scenarios, the firm is projected to be adequately capitalized. In one scenario, the firm is projected to be insolvent. The CEO states that this represents a 95% probability that the firm will be solvent, which is within risk tolerance. Critique this interpretation.

Answer 34

1. The CEO misunderstands what the stress scenarios represent. They are implicitly assuming that each of the scenarios are equally likely and that together, they make the probability space of all future events. This is not true. The scenarios may have different probabilities of occurring, and none of them may occur, but the probabilities of the scenarios occurring is not the focus of scenario analysis anyway. 2. Scenario analysis tests the impact of extreme, but plausible events on the firm. Since one of the scenarios tested reveals the the firm would become insolvent, this indicates a serious risk that the firm should address. 3. Additionally, the firm should have risk tolerances for each risk that it faces. The stress scenario that projects insolvency indicates that the firm could potentially have breached one or multiple risk tolerances. Or perhaps if the risk tolerances were not breached, they should be adjusted to prevent the risk profile from entering a state in which that stress scenario would cause insolvency.

Question 35

An insurer issues term and whole life insurance policies. Premiums are invested in a mix of equities and long duration government and corporate bonds. The insurer decided to stress test the portfolio over a one year horizon with the following stress scenario: equities fall by 10%, interest rates for all bonds shift down by 50 bps at all maturities, policy surrenders increase by 10% at all durations. Critique this scenario.

Answer 35

1. Assuming policy surrenders increase by 10% at all durations for all policies is not an effective stress test because higher surrenders give gains for term policies but losses for whole life (because of cash values). These will offset. The stress test should increase lapses for whole life and decrease them for term. 2. A 1 year stress test is useful for testing the relatively immediate impacts of the stresses, but it's also important to test the firm's ability to continue business in a sustained stressed environment 3. A 50 bps shift down in interest rates at all maturities can be a useful simplification, but not a very realistic stress test because interest rate curves don't have parallel shifts in reality. A more robust stress testing framework would test the impact on the firm of curve steepening and flattening. 4. The stress test does not include credit spreads. In a more realistic scenario, when equities fall, credit spreads widen. It's important that the firm tests the combined impact of falling equities, widening credit spreads, and changes in interest rate curves all at once. This is critical because low equities and wide credit spreads means reduced asset value, and reduced long term rates means increased liability value.

Question 36

What impacts should a life insurer expect to see when interest rates steepen? Flatten?

Answer 36

1. Steepening usually means the long term rates increase more than short term rates (but it can mean only short term rates decrease or decrease by more than the long term rates). When long term interest rates increase, the MV of current long duration bond prices decrease (because new bonds at higher rate are more attractive) and liability values decrease (because larger DR reduces the PV). If liabilities are longer than assets, this is a gain. If assets are longer, this is a loss. 2. Flattening can mean short term rates increase more than long term rates. When short term rates rise while long term rates stay flat or fall, the MV of current long-duration bond prices increases and liability values increase (because smaller DR increases PV). Can hurt solvency if liabilities are more sensitive than assets.

Question 37

What's the relationship between equities and credit spreads?

Answer 37

Equities and credit spreads have a strong negative relationship. When equities fall, credit spreads widen because investors expect firms will get lower earnings from equities which means increased stress and greater default probability. So they want more compensation for the increased risk through the credit spread. Also, in stressed markets, investors move from risky assets (equities) to safer assets (government bonds). The selling pressure pushes equity and corporate bond prices down (so spread widens).

Question 38

What's the relationship between interest rates and credit spreads?

Answer 38

It can be a complicated relationship, but in general, when interest rates fall due to economic weakness, credit spreads widen. When interest rates rise due to economic strength, credit spreads tighten.

Question 39

What impacts should a life insurer expect to see when credit spreads widen? Tighten?

Answer 39

When credit spreads widen, this means investors are demanding more compensation for the increased credit risk. Therefore, the corporate bonds the firm already has lose value. If the firm wants to sell the corporate bonds, they have to lower the price to offer the higher yield at the market rate. When credit spreads tighten, the MV of the firm's current bonds increases.

Question 40

You are interested in the probability that a stock price will drop by more than 10% in the next six months. Would you use the risk-neutral or real-world measure for this calculation? Justify your answer.

Answer 40

Use the real world measure because I'm interested in the chance that the event happens. The risk neutral measure adjusts expected returns to the risk-free rate, not the real expected returns. Risk neutral is used for calculating the market value of cash flows today. The real world measure uses real expected values, so it's most appropriate for forecasting and risk analysis.

Question 41

What is meant by volatility clustering? How does GARCH capture it? How does RSLN capture it?

Answer 41

1. In stock prices, volatility is not constant. There are periods of high volatility and periods of low volatility. Periods of high/low volatility tend to cluster together. 2. GARCH shows that volatility will suddenly increase and slowly trend back to a lower value. 3. RSLN allows sudden jumps up or down in volatility.

Question 42

Describe 3 features of the ILN model that are inconsistent with real world stock price movements.

Answer 42

1. ILN assumes volatility is constant, but this is not true. 2. ILN assumes log-returns are symmetric about the mean, so jumps up are just as likely as jumps down. In reality, stock prices fall fast and recover slowly. 3. Assumes stock prices are independent of previous or subsequent values. This is not true because market participants react to news which can cause sustained, correlated movements

Question 43

Suppose you know the log-return of a stock in the first month. Can you know whether it's more likely that the regime is 1 or 2 if you have no information about the regime at time 0? Does the situation change if you know the regime at time 0?

Answer 43

We can calculate the probability of the regime at time 1 given the log return using Bayes' theorem. If we know the regime at time 0, the probability of the regime at time 1 would change because the probability of staying in a regime is likely not equal to the probability of changing regimes.

Question 44

Explain the difference between funding liquidity risk and market liquidity risk.

Answer 44

Funding liquidity risk is the risk that early liquidation of assets is required to meet payment obligations, resulting in realized losses. Market liquidity risk is the risk that market conditions restrict access to liquidity, so transactions can't be conducted at normal market prices. Ex: the cost of borrowing is high and the market value of assets is low because there are few buyers in the market.

Question 45

Explain the advantages to a firm of issuing debt with a range of maturity dates.

Answer 45

1. Manage liquidity risk: If a firm's assets have very long durations and are not liquid (like real estate), the firm should not issue all of its debt on a short term basis because when the maturity date arrives, it may struggle to pay back the loans because of a lack of liquidity. When assets and liabilities match durations, it reduces this liquidity risk. 2. Manage interest rate risk: If a firm issues all of its debt on one day and the interest rate decreases, this represents a loss for the firm because it locked in at a high cost of borrowing. It's better to issue debt over a range of maturity dates to avoid this concentration of interest rate risk.

Question 46

Deposit insurance refers to programs that offer full or partial protection to bank depositors in the event that the bank can't make the funds available when wanted. Usually, deposit insurance is government run and funded. Explain how deposit insurance impacts liquidity risk, and why governments might choose to protect bank customers in this way, rather than just allow market forces to prevail.

Answer 46

1. Deposit insurance is a method of transferring liquidity risk from banks to the government, and it reduces the likelihood of a tail liquidity risk event. 2. Governments may offer deposit insurance to reduce the likelihood of a run on the bank (because people knowing they have deposit insurance may not panic as much and rush to withdraw their funds). The cost of deposit insurance should be less than the cost of economic collapse. Allowing market forces to prevail means a financial crisis could occur (like in 2008).

Question 47

In some countries, including the US, individuals purchasing long-term life insurance policies have the right to terminate their policies at any time after a specified initial term. The insurer must offer a rebate, based on a schedule that is specified at the inception of the contract. This is called a non-forfeiture clause. Explain the impact of the non-forfeiture clause on the liquidity risk of the insurer.

Answer 47

Non-forfeiture clauses are an important contributor to liquidity risk of an insurer. In ideal circumstances, the insurer expects the policyholder to pay premiums over time and a payout would not occur for decades. But the inclusion of non-forfeiture clauses and cash values at surrender introduce liquidity risk because the policyholder has an option that would require the insurer to have a potentially large cash outflow much earlier than expected. It's important that the firm maintains a sufficient amount of sufficiently liquid assets to pay for lapses.

Question 48

It has been suggested that the worst number of banking counterparties for a firm is around 3. Explain, with reference to both liquidity and credit risk, why 3 might be worse than 1, and why 10 might be better than 3.

Answer 48

1. When using one bank, transactions are centralized, creating great operational efficiency, but significant liquidity and credit risk (if the bank becomes financially distressed). 2. When using 3 banks, operations become more complicated, and barely any diversification benefit is gained because the financial distress of the banks is likely highly correlated. 3. When using 10 banks, diversification benefits are more material.

Question 49

Define model risk, and describe 4 different ways that model risk can lead to loss events.

Answer 49

Model risk is the risk that inappropriate conclusions and decisions are made from model results due to issues in the model itself or the way it was used. 1. Defective model risk: There can be errors in the model methodology, the parameters chosen could be inappropriate, there could be data quality issues with the data used to train the model, and there could be user-generated errors after the model has been installed. 2. Defective model application risk: The model used could be inappropriate for the purpose, there could be poor communication on model results, and there could be over-reliance on the model when results are good and failure to heed the model when results are bad.

Question 50

Explain how Knightian and non-Knightian uncertainty apply to parameter and model uncertainty.

Answer 50

Knightian uncertainty is not measurable or quantifiable (true risk). Non-knightian uncertainty is measurable and quantifiable. 1. Parameter risk can be measured by calculating the standard error of the parameter estimates. If the std errs are small, a valuable confidence interval can be made for the values of the parameters. You could test the impact on the model output of using the parameter bounds of the interval. Or the Bayesian Approach can be used to model parameter risk by treating the parameters as random variables. If instead, the confidence interval for the parameter estimates is very large and/or the variation in the model output is large due to changes in parameters, this indicates a large amount of parameter risk. In this case, parameter risk can be considered a knightian uncertainty because the parameter estimates are very uncertain and not realistically measurable. 2. Model risk can be measured by calculating the differences in model outputs of various candidate models. If all candidate models fit the data well, then the variation in their outputs may be small. This would indicate that the model risk is small non-knightian because it is measurable and quantifiable.

Question 51

You're working in a team responsible for the risk management of options embedded in life insurance policies. The current model used to project cash flows assumes that returns each month are independently and lognormally distributed. You propose exploring other models, but your manager says that "if the model is good enough for Black and Scholes, it's good enough for us." Outline the points you would make in response to your manager. In particular, you should identify features of the model that may not adequately capture the risks being modelled.

Answer 51

The exercise of options embedded in life insurance policies depends on policyholder behaviour which depends on the state of the market. Ex: if our products offer guaranteed rates that are higher than the market rates, we should expect that lapses will be very low. And if the market is in a recessionary state, we may see higher lapses and less contributions as people find they don't have the funds for their policies anymore. This suggests that the cash flows should not be independent and lognormally distributed. If the model has been providing an adequate fit in the recent history, it could be because the market has been in a stable state. If there is a sufficient change tomorrow, we should expect to see some very different policyholder behaviour in the near future. I would suggest a more robust model that can take into account the market interest rates and other factors to predict lapse behaviour, contribution patterns, and other policyholder behaviour.

Question 52

There are 2 candidate models generating very different economic capital values for a section of the business, even when fitted to the same historical data. They both satisfy standard goodness of fit test, although the powers of the tests are low because there are many parameters and not much data. The first model generates a 98% VaR of 100 million, TVaR of 200 million, and the estimated standard error of TVaR is 30 million. The second generates a 98% VaR of 120 million, TVaR of 150 million, and the estimated standard error of TVaR is 20 million. The CEO says "Since both models are shown to fit the data, we can choose either one. The first is conservative in TVaR, the second is conservative in VaR. Moreover, the second is more accurate because the standard error of TVaR is lower. Therefore, I propose we adopt the second model." State with reasons whether you agree with the CEO's comments. Which ESG, if either, would you recommend the bank should adopt?

Answer 52

1. I agree that with this info, neither model is clearly better than the other, so we can use our judgment to select one. But with more info, one may become clearly superior. 2. Many parameters and not much data means the models may have the Curse of Dimensionality. The models may overfit the training data, modelling noise instead of underlying patterns. I'd like to know how the models perform on unseen data. 3. The CEO is misunderstanding what the standard error of the TVaR measure represents. It doesn't mean that parameter or model risk is low. It means that IF the model provides a good fit for the data, then X is the standard error of the TVaR estimate. 4. To choose a model, do they perform equally on unseen data? Are they equal in terms of complexity vs accuracy trade off? Is one better suited for the purpose for any reason (like user friendliness, operational ease, etc)? If they are the same except for the risk measures, I'd recommend the more conservative one for the risk measure the firm normally uses to calculate economic capital values.

Question 53

Critique the following statement. "Out of these 3 models, each with several sets of potential parameters, the second one has parameters that look pretty stable between sets. That must be the most accurate model."

Answer 53

This is not necessarily true. The parameters could be stable and none of those models provide an adequate fit.

Question 54

Critique the following statement. "The Bayesian approach just averages the correct model with some incorrect models. We should identify the true model and discard the others."

Answer 54

This is not an accurate description of how the Bayesian approach works. The Bayesian approach treats the parameters as random variables with their own distributions. It allows us to quantify parameter uncertainty.

Question 55

Critique the following statement. "We should select the most conservative model."

Answer 55

First, we should attempt to produce a model that gives an accurate fit. If we have multiple candidate models that provide equally good fits, we should consider the complexity vs accuracy trade off. If they are equally complex and accurate, then choose the most conservative model.

Question 56

Example 14.8 of written examples

Question 57

Why would a firm purchase a business line with a relatively poor RAROC?

Answer 57

In isolation, the RAROC may be low, but it may hedge the losses of one or more other business lines, thereby increasing the total RAROC of the firm.

Question 58

You are a risk manager in a bank. Your CEO has decided that maintaining any capital in excess of the regulatory minimum is unnecessary. Outline the points that you would make supporting or opposing this view.

Answer 58

1) Capital is held to meet regulatory standards, but also to grow the business, take advantage of opportunities, and cover losses. 2) The minimum regulatory capital should not be the target capital level because even a relatively small adverse event could cause the firm's capital to go below the threshold, triggering the regulator to intervene in the business. 3) Regulatory minimums are for the industry as a whole. They're not specific to the firm's circumstances, so the bank should have its own perspective of its target and minimum capital levels. 4) Holding only the minimum would reduce investor, rating agency, customer, and counterparty confidence in the firm's ability to meet obligations. Cost of borrowing would be higher. 5) The CEO is correct, in a sense, because holding only what regulators require would not trigger intervention and could increase returns (by investing the excess in riskier assets for higher return). But there are additional costs that make holding more capital than the minimum worth it.

Question 59

Describe why a firm with a large number of employees in a regulated industry might want to manage risk.

Answer 59

1) As firm size increases, financial, operational, reputation, and regulatory risks increase as well. Risk management becomes essential for success. 2) It's important to train employees on applicable laws and regulations to reduce the risk that they break the rules, leading to consequences for the firm. 3) It's important to manage risk top-down in a regulated industry to ensure that the aggregate levels of various risks can be monitored, reported, and the appropriate required capital can be calculated.

Question 60

Give reasons for and against separating the roles of chairman and CEO.

Answer 60

1) Why they should be separate: avoid conflict of interest, reduce concentration of power (lowering the risk of poor decision making and abuse of authority). Investors and regulators prefer separation for these reasons. 2) Why they should be the same: If they're the same person, decisions are probably quicker and more consistent. Some responsibilities are the same, so if the roles are separate, need to be clear on responsibilities. For small companies, it can be more practical and cost-effective to have the same person do both.

Question 61

Describe the impact that tax and insolvency have on the choice of capital structure.

Answer 61

Taxes encourage firms to use debt to finance their capital because interest paid on debt is typically tax-deductible while dividends to shareholders are not. But when a firm takes on debt, this increases the risk of insolvency, and when a firm has a lot of debt, the cost of borrowing more increases. So firms try to strike a balance between reducing their taxable income through the use of debt and keeping risk of insolvency low through the use of equity.

Question 62

Describe why agency risk may arise from company directors acting on behalf of company shareholders.

Answer 62

Directors act on behalf of shareholders, and they should and normally do have financial incentives to act on behalf of shareholders. However, the following risks exist. - Directors may prioritize personal benefits like high salaries and bonuses over maximizing shareholder value. - Shareholders may want a higher risk strategy to increase firm value, but directors may avoid risk to protect their positions.

Question 63

State why, despite agency risk, it makes sense for shareholders to appoint directors to run a company.

Answer 63

- Directors bring skill, experience, and industry knowledge to guide firm operations. This allows investors to invest in the firm without having any of these skills or knowledge themselves. - When a firm is very large and has millions of shareholders, management from the shareholders directly is impractical. - Agency risk can be reduced by using performance-based pay, audits, and regulations.

Question 64

List the ways in which a government can protect investors in and customers of financial services firms.

Answer 64

1) Require regulation and licensing. Follow strict rules for conduct, capital requirements, and risk management. Use audits to check compliance. 2) Disclosure requirements for transparency, informed decision making, and reduced fraud risk 3) Government often insure deposits and investments up to a certain limit 4) Consumer protection laws that prevent deceptive and abusive practices (like criminally higher interest rates charged on customers) 5) Governments investigate and prosecute fraud, insider trading, and market manipulation

Question 65

Describe in words the meaning of the phrase "negatively skewed distribution" in the context of investment returns.

Answer 65

- A negatively skewed distribution means the left tail is longer than in a normal distribution. If the distribution of investment returns has a negative skew, this means the left side (which represents investment losses) is longer than would be expected if a normal distribution was assumed. - This has a dangerous implication because if investors assume the distribution is approximately normal, they are underestimating the cost of large losses (Severity) because the true distribution tail extends beyond that of the normal distribution tail.

Question 66

Explain briefly why an assumption that investment returns are normally distributed may be dangerous if they in fact exhibit leptokurtosis.

Answer 66

Leptokurtosis means the distribution has thicker tails than the normal distribution. This is dangerous for an assumption of investment returns because if someone incorrectly assumes the returns are approximately normal, they would be underestimating the probability (Frequency) of tail risk events (both positive and negative).