ERM Chapter 30

Question 1

What are the three reasons a business might hold capital?

Answer 1

1. manage its cashflow (working capital)
2. facilitate growth/new ventures (development capital)
3. to cover unexpected losses arising from exposure to risk (risk capital)

Question 2

State the three definitions of capital that result from the three main interpretations of the meaning of ‘adverse outcomes’.

Answer 2

1. the surplus needed to cover all potential outgoings, reductions in assets and/or increases in a company’s liabilities at a given level of risk tolerance over a specified time horizon
2. the surplus needed to maintain a given level of solvency at a given level of risk tolerance over a specified time horizon
3. the excess of the value of the assets over the value of the liabilities at a given level of risk tolerance at a specified time horizon

Question 3

List three metrics that may be used to set an appropriate level of risk tolerance.

Answer 3

1. a certain percentile of the loss distribution
2. extreme loss values
3. the possibility of some key indicator falling outside an acceptable level

Question 4

What can capital models be used for?

Answer 4

• regulatory capital setting
• economic capital requirements
• allocation of capital

Question 5

Outline specific uses of internal models.

Answer 5

• calculate regulatory capital
• determine company or product risk profile
• capital budgeting (allocation)
• working out capital needed in merger and acquisition situations
• insurance product pricing
• risk tolerances/constraints
• setting investment strategy
• calculating risk-adjusted rate of return on capital
• performance measurement
• incentive compensation
• as an alternative to rating agency/regulator requirements
• disaster planning

Question 6

Outline:

• the main outputs of an ICM
• the desirable features of such a model
• the benefits in a model being dynamic in nature

Answer 6

Main outputs:

• future balance sheets
• profit and loss accounts or cashflow statements

Desirable features:

• asset model allows for correlations between different asset classes over time
• liability model considers reinsurance and correlations between classes of risk
• asset and liability model should be integrated, and allow for correlations between assets and liabilities over time
• model is dynamic

Benefits of being dynamic:

• improved understanding of the dynamics of the current strategy
• consideration of the impacts of implementing different strategies
• examination of the impact of using different sources of capital
• useful for due diligence and corporate transactions
• assesses the risk-adjusted performance of different business units
• determines an optimal asset mix
• helps understand the impact of extreme events
• useful in producing FCRs

Question 7

Outline the key differences between internal and generic capital models.

Answer 7

• different views as to volatility of various classes of business
• different allowances for diversification between/within risk types
• different objectives of the model
• inclusion of different risk types, or different treatment of same risks
• different views regarding the availability of certain types of assets as capital

Question 8

What are the six stages required in operating a successful capital model?

Answer 8

1. identify purpose - clearly identifying the purpose will influence matters such as whether the business remains open to new business or runs off, whether contingent management actions will be modelled, and the level of resourcing required and accuracy of the results.
2. identify and rank risks
3. choose the simulation approach for each risk - these may be deterministic or stochastic, depending on the cost/time considerations and benefits gained.
4. define the risk metrics - typically include VaR, tail VaR, time horizon and confidence interval
5. select the modelling criteria - attaining a certain investment rating or some ongoing business criteria as measured by supervisory intervention
6. decide on the method of implementation - type of model should be appropriate to nature, scale and complexity of insurer’s business and could be a set of univariate models together with a method by which to combine them, or a single fully integrated model

Question 9

Capital models are often used as part of an OSRA. What factors should be considered when using a capital model as part of such a continuity analysis?

Answer 9

• what time period should be used?
• should the financial position of the insurer be assessed at a particular point in time, or once specific liabilities have run off?
• what capital reduction/injection policies can be assumed?
• what management actions need to be modelled?
• how reliable are the insurer’s long term forecasts?

Question 10

How can effective capital management help transform risk into increased shareholder value?

Answer 10

• pricing competitively - to ensure adequate return on capital
• reserving - improving estimates of returns needed for outstanding claims
• performance management - enabling business outcomes to be measured and processes to be adopted accordingly
• risk management - establish the overall level of risk tolerance, identifying and assessing risks present and keeping all risks under control

Question 11

Outline a theoretical method of calculating capital requirements.

Answer 11

P(Kt > k x Lt) > 1-a,
where Kt = excess capital at time t (At - Lt),
a = risk tolerance level, k = comfort ratio

• more volatile assets increase the required capital
• higher return on expected assets reduced the required capital
• higher positive correlation between asset and liability portfolios reduces the required capital

D:

• difficulty in obtaining consistent valuations for both assets and liabilities
• the need to select an appropriate risk measure
• difficulty in formulating the necessary assumptions e.g. how assets will be invested
• large number of parameters needed
• difficulty in deriving robust estimates of the various parameters needed
• considerations of Kt only at discrete points in time - ruin could occur between these points

Question 12

What methods are employed by businesses to assess their complex capital requirements?

Answer 12

• Probability of ruin - ruin occurs when a company’s liabilities are larger than their assets. Capital can be assessed as the amount of additional assets required to ensure that the probability of ruin is less than a specified target level
• Economic cost of ruin - looks at the amount key stakeholders can be expected to lose in the event of ruin
• full economic scenarios - a chosen set of economic scenarios is detailed and each BU estimates profitability under each scenario. Results are then aggregated and assessed under a given risk measure
• stress test method - one or more highly adverse economic scenarios are set as the basis for assessing the economic capital
• factor tables - tables of capital requirements per unit risk exposure by risk type are published by supervisors. Capital requirement is then calculated as the number of units of each activity undertaken by the business multiplied by relevant factors from the tables
• stochastic models - can be either univariate or multivarate. Scenarios are generated at random and capital calculated on the basis of the results of these scenarios
• statistical methods - mean, variance, and co-variance of loss distribution are estimated and combined with normal distribution to estimate the capital
• credit risk methods - historical data from rating agencies is used or a Merton model approach is adopted
• operational risk methods - company and industry data is used and combined with expert opinion to enable quantitative results to be obtained
• option pricing theory/Black-Scholes - this approach is effective where the risk event can be assumed to occur only at one certain point in time. Loss situation can be considered to be an option and appropriate models used to calculate its value

Question 13

Basel capital requirements impose a minimum regulatory capital requirement based on market, credit and operational risk to which the bank is exposed.

Describe how the minimum capital required due to credit risk is determined under:

• the standard approach
• Internal Ratings Based approach

Describe how the MCR due to market risk is determined.

Describe how the MCR due to operational risk is determined.

Answer 13

Standard approach:
- every credit rating relates to a risk-weighting category, and therefore a particular risk weighting

IRB approach:

• banks are allowed to categorise and risk-weight their assets based upon credit ratings determined by their own Internal Ratings Based model
• thorough credit assessment is required, and the methodology needs to be approved by the regulator
• after determining these weightings, the bank can calculate the total value of its asset portfolio allowing for these risk weighting

Market risk:

• additional capital required for investing in risky securities
• measured by modelling assets and calculating a 10 day 99% VaR, with a regulatory capital requirement a multiple of this

Operational risk:

• capital set aside for technological failure, mismanagement, fraud, litigation etc.
• regulatory capital requirement is calculated as a function of gross income over the past three years

Question 14

How is minimum capital determined under Basel II?

Answer 14

• bank’s capital is classed in three tiers:
  > Tier 1 = bank’s equity and disclosed reserves
  > Tier 2 = other reserves and various debt instruments
  > Tier 3 = certain types of short-dated capital
• minimum capital is calculated as a percentage of risk-weighted assets in respect of credit risk, plus the capital requirements for market and operational risks multiplied by 12.5
• further constraints were introduced as part of Basel III regarding the amount that must be form each Tier
• Basel III aims at reducing pro-cyclicality, reducing systemic risk, and strengthening short and long-term resilience against liquidity risk

Question 15

How is regulatory capital determined under Solvency II?

Answer 15

Twin peak approach:

• The first peak is a market-consistent valuation, the Solvency Capital Requirement, with failure to maintain capital above this level resulting in action by the regulator
• The second peak is a more basic valuation on the Solvency I Minimum Capital Requirement (MCR), with a firm failing to maintain regulatory capital above this level losing its authorisation

Solvency Capital Requirement:
- must be achievable with 99.5% confidence over a one-year time horizon and may be based on a standard formula or the firm’s approved internal model

Minimum Capital Requirement:

• 3 million euros plus a margin based on premium or reserve amounts
• must be achievable with 80-90% confidence over a one-year time

Question 16

Outline two measures used for risk optimisation.

Answer 16

RAROC:

• can be calculated for the institution as a whole
• can be used to compare different and diverse business activities
• can be based on actual or expected return and actual or expected capital

Economic income created (EIC):

• captures the quantity of return generated by a unit of activity
• EIC = (RAROC - hurdle rate) x Capital
• hurdle rate is the standard against which business activities must be measured

Shareholder value (SHC):
= discounted value of all future cashflows
= Capital x [(RAROC - g) / (hurdle - g)],
where g = prospective growth rate of the business

Shareholder value added (SVA):
= discounted value of economic value added
= Capital x [(RAROC - g) / (hurdle - g) - 1]

Question 17

Outline two key factors when determining an appropriate hurdle rate.

Answer 17

1. Should reflect the cost of capital
2. Should allow for not only risks inherent within the proposal, but also the degree to which those risks diversify existing risks

Question 18

Explain how the allocation of capital affects pricing, risk control limits and performance measurement.

Answer 18

Capital allocation should be set up to link risk to performance measurement e.g. BU’s success should be measured relative to the risk it takes on in its operations, which in turn should reflect the amount of capital the company is willing to allocate to the BU.

Amount of capital that is allocated to each BU:

• determines the BU’s performance (RAROC)
• could affect the remuneration of the unit’s managers and therefore their level of motivation and behaviour
• dictates the amount of business the BU can write
• determines the price at which business can be written

Question 19

How is concentration/diversification allowed for?

Answer 19

Adjustments for correlation and dependency:

• level of dependency between different lines of business and risk categories might be different between time of stress from those experienced under normal conditions
• capital is usually calculated with reference to extreme events, so tail dependency will have to be considered carefully.

Diversification benefit:

• the total capital required will be less than the sum of the capital over all individual risky projects
• some approaches calculate capital required for each BU followed by an adjustment for the benefit of diversification
• an alternative approach is to calculate capital required at the enterprise level and allocate capital in a fair way across units including the diversification benefit
• the appropriate method for allocation will depend on a number of factors, including the purpose of the allocation and the stakeholders to the process

Question 20

Describe general capital allocation principles.

Answer 20

• the method of allocation should have regard to the use of the results and should consider desirable properties such as stability over time
• there is not one method that is best suited to all cases, and typically results from several methods should be compared and judgement used when setting a final allocation
• there can be conflict between the desired properties of capital allocation exercises, so it is important to consider the purpose of allocation and practical impact of methodologies

Question 21

List different capital allocation approaches.

Answer 21

• total capital could be retained centrally
• capital could be allocated using some risk measure e.g. Euler principle
• a marginal approach could be adopted, where each business line receives the change in capital as a result of adding it to the diversified portfolio
• capital could be allocated using some game theory approach
• capital could be allocated on some pro-rata basis
• capital required by each business line could be calculated individually on a stand alone basis and then any remaining capital retained in the main corporate business line

Question 22

Suggest factors that might be used to compare different methods of capital allocation.

Answer 22

• complexity and computational intensity
• ease of communication
• degree to which allocation is affected by the presence of other BU’s
• degree to which allocation is affected by basis
• degree to which method may lead to under-investment in BU’s providing a diversification benefit
• degree to which method may lead to over-investment in risk business units
• correspondence with marginal pricing principle

Question 23

Why may additional capital be held?

Answer 23

• to support its credit rating

- to take advantage of business opportunities in the future