Past Exam Questions: September 2014 Flashcards
Why might a life insurer charge a different premium from that suggested by its models.
- The premium rates it charges will load margins for expenses and profit on top of the pure risk premium.
- High levels of competition in the market may force an insurer to (temporarily) charge lower premium rates than the risk levels it models are suggesting in order to maintain market share.
- Alternatively, a lack of competition in the market may enable an insurer to charge a much higher premium rate and still retain a healthy market share.
Formula for Pearson’s Rho between two sets, m and n
sₘ = SQRT{ SUM (mₜ - μₘ)² / (T - 1) }
sₙ = SQRT{ SUM (nₜ - μₙ)² / (T - 1) }
sₘ,ₙ = SUM{ (mₜ - μₘ)(nₜ - μₙ) } / (T - 1)
ρ = sₘ,ₙ / (sₙ x sₘ)
Explain what is meant by a risk appetite, including examples of common ways in which it can be expressed.
Risk appetite can be interpreted as reflecting the setting of targets and limits across the organisation as a whole, plus the breakdown of these high level statements into more detailed risk tolerances.
Risk appetite is usually presented as a probabilistic statement.
Examples are:
- The solvency level, X, should stay above the threshold Y with 99.5% probability over the next 3 years.
- The probability that the company’s credit rating is reduced from the current AAA to A, or worse, in the next twelve months should be no more than 1%.
- Earnings volatility over the next year should be no more than Y%.
- The company is prepared to lose $Y with a probability of no more than 0.5% over the next 12 months and $Z with a probability of 0.1% over the next 5 years.
DO QUESTION 6
ALL OF IT
What might be a risk management rational for employing a “loss leader” product strategy?
Diversification between different product lines suggests that the “worst case” scenario for one product is not the same as on another product.
As a result, combining the two products into a single offering may result in a lower combined economic capital requirement.
The benefit of this can be passed on to customers.
Outline the process of GLM modelling as it applies to mortality risk
Generalised linear modelling will be principally used to model the “level” risk.
GLM requires us to first risk rate the data.
This works as follows:
- Divide the data into homogeneous groups
- Derive expressions for the mortality of each group in terms of the risk factors
- Analyse the structure of the group of lives of interest in terms of these risk factors
- Use the risk factor exposures to infer the underlying mortality of the group of interest
GLM usually involves logit or probit regression analysis.
This places the mortality rate as the dependent variable and the risk factors as the independent variables.
Formula for Kendall’s tau
pc = number of concordant pairs:
if both members of one observation are larger than their respective members of the other observations.
pd = number of discordant pairs:
if the two numbers in one observation differ in opposite directions
tau = 2 (pc - pd) / { T (T-1) }
Outline the potential disadvantages of basing a risk appetite statement primarily on profit
- A focus on profit can lead to short-termism amongst the Board and senior management.
- Short termism could also encourage profit reporting manipulation.
- If the remuneration structures are aligned with the profit focus, they could in turn incentivise management and staff to focus on sales rather than longer term value creation.
- There could be a related mis-selling risk.
- High sales volumes could jeopardise the solvency of the company.
- To reduce profit volatility, the company may prefer to offer products that have more stable profit streams: these less risky products may have lower value to customers which could lead to lower sales and lower ultimate added value to the business.
- Basing risk appetite on a balance of different metrics will likely result in relatively less risky (volatile) behaviour for a given targeted return.
Outline the relative merits of Kendall’s tau and Pearson’s rho
Both methods are fairly simple to calculate.
However, Pearson’s ρ depends on the distribution of claims being jointly elliptical.
It the results are not from elliptical underlying distributions, the results may not be valid.
Kendall’s tau depends only on the rank of the data points and so is always valid, irrespective of the underlying distribution of the variables.
Kendall’s tau has a simple relationship with the parameters of a number of copula functions.
Pearson’s ρ can be used directly in some common multivariate distributions.
Define operational risk
Operational risk is the risk of losses resulting from inadequate or failed internal processes, people and systems, or from external events.
Contrast the appropriateness of defining profit as:
- surplus from the regulatory accounts
- profit before tax in financial accounts
- economic profit arising based on economic capital
for use in the risk appetite statement.
- Since regulatory profit is based on prudent assumptions, it will be unrealistic in that the release of margins is materially defined (profits too low early on).
- Accounting profit is likely to be more realistic than regulatory profit.
- However, it won’t fully reflect all the constraints imposed on the company (e.g. the cost of capital as a result of solvency regulations), and it is unlikely to be risk-adjusted.
- Economic profit will allow the most realistic assessment of risk-adjusted profit.
- It can take into account regulation and other business constraints.
- However economic profit is not subject to audit, unlike accounting (and potentially also regulatory) profit.
- It is therefore potentially more readily manipulated.
- As it gives the most realistic assessment, economic profit can be considered to be the most appropriate for the risk appetite statement.
- It may also be easier to assign a probabilistic interpretation to economic profit.
- However, accounting profit will be more widely understood by stakeholders and so could lead to more engagement with staff and better integration of risk into the management of the company.
Comment on the proposal that a small life insurer includes disaster risk in the operational risk component of its economic capital model.
- The company should hold capital against this risk.
- It fits with the definition of operational risk.
- It will help to raise the profile of disaster risk (and the need for a disaster recovery plan) within the company.
- It allows risk diversification, since operational risk is not perfectly correlated with other risks such as market and credit risk.
- It may be difficult, however, to quantify the high severity, low frequency exposures required for economic capital modelling and in particular to obtain sufficient extreme event data with which to calibrate the model.
- It may be necessary to use Extreme Value Theory techniques within the economic capital model, which increases the complexity of the modelling.
- Correlations with other risks will also be difficult to determine. E.g. 1 potential impact on financial markets if the disaster is widespread. E.g. 2 potential positive correlation with insurance risk.
- The mitigating actions that can be taken to minimise the impacts in the event of disaster should be taken into account. This may be difficult to do in an economic capital model as the impact of the actions may not be the same in the high severity, low frequency scenarios as in the lower severity, higher frequency scenarios.
Outline how a small life insurance company could measure its operational risk
The company may want to measure its risk exposure as the impact of operational risk events on one or more of:
- Additional short term costs of staffing, property and systems.
- Fines for failure to comply with regulatory requirements that apply.
- The fall in turnover / reduction in new business sales.
- Reduction in customer satisfaction scores.
- Increase in lapse rates.
- Overall impact on the company’s embedded or economic value.
- Overall impact on surplus capital or VaR / TVaR.
To model this, the company may be able to source data internally or externally through industry databases that may exist.
- By its nature, the risk is bespoke and it may be impossible to get sufficient data to model and measure this risk statistically, particularly for low frequency, high severity events.
- However it may be possible to get input from experts in this field to help guide the assessment of the exposure.
- The experts might be internal / external.
- Both severity and frequency needs to be considered.
- Scenario analysis techniques may be used.
- Correlations between operational risk events need to be considered.
- The exposure measures should reflect the mitigations or controls that are in place.
- It may be necessary to use other losses as a proxy for the exposures to operational risk.
Discuss the relative merits of having a separate / combined Risk and Actuarial functions
SEPARATE:
- one function can provide an independent review of / check on the other
- it facilitates the independence of the risk function
- it allows for clear reporting lines
- it avoids conflicts of interest by separating the risk roles from the front line business operations such as pricing
- it can encourage more communication between teams and parts of the business on risk issues
- it achieves a dedicated central risk function which can cover a wider remit than just “actuarial risk”
TOGETHER:
- it reduces the need for specialised / skilled resource in the firm.
- it may therefore also be cheaper
- arguably it is the more integrated approach, achieving a better relationships between risk specialists and operational staff.
- May be a more collaborative approach: less likely to try to “hide” problems.
- Decisions may be made and implemented more quickly.
- Could reduce the possibility of duplication of effort, if there is a blurred distinction between some responsibilities.
Outline the need for a disaster recovery plan for a small life insurer
- Following a disaster the insurer may not have access to its systems or to its premises.
- Staff may not be able to report for work.
- The disaster may not have affected the insurer directly - the impact might be indirect via its suppliers and customers.
- A disaster recovery plan would help the company focus on critical processes to the business and proactively set out how it will ensure these are able to continue under these circumstances.
