Brehm2

Question 1

Deterministic Project Analysis

Answer 1

ERM uses deterministic inputs to estimate internal rate of return by line; management makes decisions based off on these figures

Question 2

Risk Analysis (DFA)

Answer 2

forecasted distributions of inputs (not single point estimate)

monte carlo simulation then calculates distribution of present value of cashflows and IRR

risk judgement is intuitively applied by decision makers

Question 3

why is Risk Analysis (DFA) better than deterministic project analysis?

Answer 3

directly incorporates uncertainty of critical variables in model

Question 4

Economic value added

Answer 4

EVA=NPV return-cost of capital

if EVA is positive, project adds value to firm and company should move forward

Question 5

cost of capital (RORAC)

Answer 5

RORAC = return on risk adjusted capital

RORAC = risk-adjusted capital*hurdle rate

risk-adjusted return = return measure/risk measure

Question 6

hurdle rate

Answer 6

hurdle rate is similar in concept to required return on capital from Goldfarb

can use CAPM to calc ie k

Question 7

certainty equivalent approach and why it could be beneficial

Answer 7

similar to risk analysis

quantifies risk judgement with corporate risk preference or utility function for consistency

corporate risk policy can help insurer make more consistent and objective management decisions

corporate risk preference isn’t appropriate for diversified investors because investors only care about systematic risk since form specific risk can be diversified portfolio

Question 8

economic capital

Answer 8

economic capital is measured with V@R at remote probability level similar to default probabilities of bonds ie 1-in-3000

VaR is not calculated by summing up contributions of ind business units; instead usually calculated for all risks combined and then allocated down to individual units

• choice of probability level used is fairly artificial
• target level is often selected so economic capital is slightly less than actual capital being held

Question 9

economic capital advantages

Answer 9

provides unifying measure for all risks across an organization

more meaningful for management than risk-based capital or capital adequacy ratios

forces firm to quantify risks it faces and combine them into probability dist

provides framework for setting acceptable risk levels for an organization as whole and for individual business units

Question 10

modeling challenges for economic capital

Answer 10

ERMs aren’t reliable at such remote probabilities because of approximations, assumptions, and lack of data in tail

ie probability level of 1-in-3000 is VWR-99.97 which is impractical to model

Question 11

approach to set capital requirements that overcomes modeling challenges with economic capital

Answer 11

company can use impairment, rather than insolvency as reference point for probability level

ex: if company wants capital level to be adequate so that average 1-in-100 year result destroys no more than 25% of capital, then would set minimum capital requirement at 4x TVaR-99

Question 12

VaR_p%

Answer 12

=percentile of distribution @ probability p%

-it is single point so does not provide much info on distribution

Question 13

TVaR_p%

Answer 13

=E[L|L>VaR_p%] = tail value at risk

-linear in tail so does not reflect that risk that is 2x large is more than 2x as bad

Question 14

XTVaR_p%

Answer 14

=TVaR_p%-mean = excess tail value at risk

Question 15

expected policyholder deficit

Answer 15

EPD=(1-p%)(TVaR-VaR)

-unconditional expected value of defaulted losses if there is a default

Question 16

Tail-Based Risk Measures

Answer 16

• emphasize large losses only
• important to note that losses do not have to be large to cause problems for insurer and this is why measures like exponential moment are advantageous because they reflect all losses but still respond more to large losses

Question 17

Probability Transforms

Answer 17

measure risk my shifting the probability towards unfavorable outcomes and then computing risk measure with transformed probabilities

• primary example=expected loss under transformed probabilities (CAPM and Black-Scholes formula are both transformed means)
• transformed probabilities can be used to overcome some of shortcomings of popular risk measures

Question 18

Generalized moments and blurred VaR

Answer 18

• expectations of RV that are not simply powers of that variable
• can be used to add weight to losses in loss distribution around VaR percentile, using higher weights nearer to percentile

*blurred VaR

Question 19

Moment based measures

Answer 19

• moment of RV like change in capital over an accounting period
• ex: variance and std deviation
• disadvantages: favorable deviations are treated the same as unfavorable ones; may not adequately capture market attitudes to risk (ie understate risk)
• alternatives to variance/std dev that address the issues:

Semistandard deviation – only uses unfavorable

Skewness – higher moment, might better capture market attitudes

Exponential moments – capture effect of large losses on risk exponentially, might better capture market attitudes (allocated more capital to components that lead to larger losses)

Question 20

insurer’s capital level: how different customers respond and insurer’s rating

Answer 20

directly impacts insurer’s rating

some customers shop on price and aren’t focused on insurer capital and rating so they wouldnt’ respond

others are concerned about insurer’s rating

increasing rating level can slowly increase growth but drop in rating can cause rapid decline in business because customers that want higher rating can easily leave

Question 21

consider split between new and renewal busines when setting capital levels

Answer 21

renewal is more profitable

insurer might consider setting capital to have enough to support renewal BOB

insurer would want to have enough capital so that in adverse scenario, only new % of capital would be destroyed

Question 22

proportional allocation

Answer 22

calculate risk measure for insurer and each business unit separately

allocate total risk measure for insurer proportionally using individual risk measure

Question 23

marginal decomposition

Answer 23

calculate overall risk measure for insurer

calculate marginal co-measuers for each business unit

marginal co-measures sum to company’s risk measure

Question 24

why is marginal decomp better?

Answer 24

it reflects how risk from each business unit impacts that total risk profile as opposed to looking at them in isolation

Question 25

how can insurer use capital allocation to help decide which business unit to grow

Answer 25

allocate risk capital to 2 lines of business

calculate risk-adjusted profitability as ratio of profit to allocated capital

if insurer grows business unit with higher ratio, then overall profit-to-risk for insurer will increase when using marginal decomp

Question 26

2 disadvantages of allocating capital

Answer 26

capital allocation is arbitrary - different risk measures give different allocations

it’s artificial - each business unit has access to entire capital of insurer

Question 27

benefit of allocating cost of capital

Answer 27

gives minimum profit target for each business unit

profit that exceeds this is value added to insurer

Question 28

WTVaR

Answer 28

when using probability transform to boost probabilities of unfavorable outcomes, TVaR can be calculated and this is WTVaR

losses will not be treated as linear

Question 29

to calculate each line’c contribution to TVaR for total insurer, must calc

Answer 29

co-TVaR

average loss when insurer’s total loss exceeds VaR threshold

Question 30

risks in risk-based capital model to evaluate capital adequacy of insurance companies

Answer 30

invested asset risk

credit risk

premium risk

reserve risk

accumulation risk

reinsurance dependence

reinsurance diversification

Question 31

accumulation risk AKA event risk

Answer 31

exposure to CATs that impact a large number of insureds

can pose a significant risk to insurer

if not included in model: required capital won’t distinguish between insurers with different CAT risks

Question 32

covariance adjustment

Answer 32

reflects the independence between different risks when risk charges are combined

impact is reduction in required capital

insurer with risk charges that are relatively similar will see greater reduction than insurer with some risk charges that are signifcantly larger than other

Question 33

scenario testing

Answer 33

another approach for evaluating capital adequacy

static or stochastic scenarios can be used to measure capital adequacy