Chapter 29: Risk measurement and reporting

Question 1

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features of a risk that would make it appropriate to model stochastically as opposed to deterministically

Answer 1

• has a high score (high frequence or severity) and there is a high prioristy to assess carefully
• has a high variability of possible outcomes
• has a lot of experience data on which to base probability distributions
• relates to financial guarantees or options
• involves a mismatching of assets and liabilities

Question 2

‘single event’ insurance

Answer 2

one where there can only be a maximum of one claim

Question 3

ways to allow for operational risk within an organisation

Answer 3

• a broad brush approach that does not perform any detailed analysis
• scenario analysis

Question 4

why would we go for scenario analysis instead of stochastic modelling?

Answer 4

• risks might not be suitable for mathematical modelling
• Distribution would need so many subjective parameters so that value of using it would be eroded.

Question 5

Steps in scenario analysis

Answer 5

• Grouping risks into broad categories - all risks involving fraud, all risks involving systsems - input from management may be needed
• development of a plausible adverse scenario - so that it is possible to quatify the impact of the risk, the scenario must be representative of all risks in that group.
• calculations of the consequences of the risk event occuring for each scenario - include redress paid to those affected, fines correcting systems and records and opportunity costs
• total costs calculated are taken as the financial cost of all the risks represented by the chosen scenario

Question 6

What is the limitation to scenario testing ?

Answer 6

it can only quantify the severity of a scenario and not the probability

Question 7

The limitation to scenario testing is that it can only quantify the severity of a scenario and not the probability

What are some of the ways to go around this limitation

Answer 7

• The organistation may use their capital model to determine the probability of an equivalent scenairio occuring
• they may have an idea of the probability of the scenario occuring and use this in conjuction to the severity to help caliberate or validate the capital model

Question 8

stress scenario test

Answer 8

scenario testing + stress testing

Question 9

two types of scenario stress test

Answer 9

• to identify the “weak areas” in the portfolio and investigate the effects of localised stress situations by looking at the effect of different combinations of correlations and volatilities
• to gauge the impact of maor market turmoil affecting all model parameters, while ensuring consistency between correlations while they are “stressed”
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Question 10

reverse stress testing

Answer 10

• construction of a stress scenario that just allows the firm to be able to continue to meet its business plan
• identifying a scenario which would just be enough to stop the company fulfilling its strategic plan

Question 11

Stochastic modelling as an extension of stress testing

Answer 11

• full stochastic model with all the variables that give rise to risk being incorporated as probability distributions
• and a full set of dynamic interactions between the variables specified
• the model can then determine the capital necessary to just avoid ruin at any probability level

Question 12

ways to limit the complexity of a stochatic model

Answer 12

• restrict the duration (or time horizon) of the model
• limit the number of variables modelled stochastically and use a deterministic approach for the other variables - variables that only have an adverse effect when they move in one direction can be modelled stochastically e.g mortality and longevity
• carry out a number of runs with different single stochastic variable and then a single deterministc run using all the worst case scenarios together

Question 13

limitations to stochastic modelling

Answer 13

• difficult to specify and build
• the run times of multiple variables become impractical

Question 14

Explain why the effect of multiple risks may be less than the sum of individual risks

Answer 14

• Impact of diversification or less than perfect (even negative) correlation
• less than perfect correlation means that they are unlikely to occur at the same time

Question 15

Different ways of aggregating risk

Answer 15

• stochastic modelling
• simple formulae if risk events are fully dependent
• correlation matrices
• copulas

Question 16

Propose some likely correlations between risks

Answer 16

• Inflation risk is heavily corealted with expense risk for most long-term financial products
• Traditionaly, equity markets have moved in opposite directions to interest rates but in recent years, the correlation has not been so obvious
• Falling equity markets are likely to be corelated with increasing lapse rates on unit-linked savings products
• operational risk is likely to be weakly correlated with all other risks, because if management are concentrating on some other issue they may not be concentrating on routine operational matters
• In life insurance, the longevity risk on an annuity book is strongly negatively correlated with mortality risk on a term assurance book

Question 17

Limiting property of correlation matrices

Answer 17

They assume that correlations do not vary under different conditions

Question 18

Copula

Answer 18

a function which takes as inputs marginal cumulative distributiion functions and outputs a joint distribution function

Question 19

Why is modelling tail risk particularly important for a financial service provider ?

Answer 19

Capital requirments are typically assessed in relation to events that would fall in the tails of distributiions

Question 20

Deterministic approaches to measuring risk

Answer 20

• notional approach
• the factor sensitivity approach
• scenario sensitivity approach

Question 21

stochastic approaches to measuring risk

s

Answer 21

• deviation - standard deviation and tracking error
• Value at Risk
• probability of ruin
• Tail Value at Risk

Question 22

Different ways to calculate VaR and tVar

Answer 22

• emperical
• parametric
• stochastic approach
• scenario analysis

Question 23

Notional approach to measuring risk

Answer 23

• A notional approach to measuring risk involves a simplified or conceptual method that doesn’t require detailed quantitative data - hence a broad-brush risk measure
• It can be useful when you lack precise data but still want to gain a general understanding of the risk landscape

Notes do not give a precise definition so I used ChatGPT

Question 24

Advantage to the notional approach to measuring risk

Answer 24

• simple to implement and interpret across the diverse range of organisations

Question 25

Disadvantages to the notional approach to measuring risk

Answer 25

* potential undesirable use of a catch all weighting for (possibly heterogeneous) undefined assets classes * possible distortions to the market caused by increased demand for asset classes with high weightings * treating short postions as if they were the exact opposite of the equivalent long postion - they might affect capital requirements differently in practice * no allowance for concentration of risk, as the risk weighting for an asset class is the same irrespective of whether the investment in that asset class consists of a single security or a variety of different securities * the probability of the changes considered is not quantified

Question 26

Factor sensitivity approach

Answer 26

* Determines the degree to which an institution's financial position is affected by the impact that a change in an underlying single factor has on the value of assets and liabilities * the event need not be extreme like in sensitivity testing

Question 27

Advantages of factor senstivity approach

Answer 27

increased understanding of drivers of risk

Question 28

value at risk

Answer 28

the maximum potential loss which is not exceeded with a given probability over a given period of time

Question 29

Disadvantages of factor sensitivity approach

Answer 29

* Not assessing a wider range of risks by focusing on a single factor * being difficult to aggregate over different risk factors * the probability of the changes considered (in the value of assets or liabilities) is not quantified

Question 30

Advantages of using VaR

Answer 30

* simplicity of its expression * the intelligibility of its units - money * its applicable to all types of risk * its applicability over all sources of risk - facillitating easy comparisons between products and across businesses its inherent allowance for the way in which different risks interact to cause losses * the ease of its translation into a risk benchmark

Question 31

disadvantages of VaR

Answer 31

* it gives no indication of the distribution of losses greater than the VaR * it can under-estimate asymmetric and fat-tail risk as it does not quantify the size of the 'tail' * it can be very sensitive to the choice of data, parameters and assumptions * VaR is not always sub-additive * if used in regulation, it may encourage herding, thereby increasing systemic risk

Question 32

risk register/portfolio

Answer 32

* Catergorises the various risks to which a business is exposed * records the impact and probability of each risk

Question 33

Risk response

Answer 33

extending the risk portfoliio to indicate how the risk should be dealt with - avoid, retain, diversify, mitigate

Question 34

for the retained risks, what should the risk register contain details of ?

Answer 34

* control measures * reassessment of the value and impacts after controls * risk owner * board committe/senior manager with oversight over the risk * identification of concentrations of risk and related actions

Question 35

What does the production of a regular risk register allow management to do?

Answer 35

* identify any new risks faced by the business * obtain a better understanding of the risks faced by the business in terms of quantifying the materiality and financial impact of individual risks. * determine appropriate risk and control sytems to manage specific risks * proactively monitor and manage the effectiveness of risk and control systems within its business * assess whether the risks faced by a business change over time * assess the interactions between different individual risks * appropriately price, reserve and determine any capital requirements for its business

Question 36

How is risk reporting likely to be helpful to other stakeholders ?

Answer 36

* Give shareholders or potential shareholders in a business a greater understanding og the attractiveness of that business for investment * help credit rating agencies determine an appropriate rating for the business * give a regulator a greater understanding of the areas within a business that could require more scrutiny

Question 37

issues relating to reporting risks externally

Answer 37

* Whether to use a qualitative or quantitative approach * if quantitative, how to best communicate the level of uncertainty within the figures given and the limitations of the assessment approach used, including simplications * tailoring to the needs of the intended audience