Brehm2 Flashcards
Deterministic Project Analysis
ERM uses deterministic inputs to estimate internal rate of return by line; management makes decisions based off on these figures
Risk Analysis (DFA)
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
why is Risk Analysis (DFA) better than deterministic project analysis?
directly incorporates uncertainty of critical variables in model
Economic value added
EVA=NPV return-cost of capital
if EVA is positive, project adds value to firm and company should move forward
cost of capital (RORAC)
RORAC = return on risk adjusted capital
RORAC = risk-adjusted capital*hurdle rate
risk-adjusted return = return measure/risk measure
hurdle rate
hurdle rate is similar in concept to required return on capital from Goldfarb
can use CAPM to calc ie k
certainty equivalent approach and why it could be beneficial
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
economic capital
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
economic capital advantages
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
modeling challenges for economic capital
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
approach to set capital requirements that overcomes modeling challenges with economic capital
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
VaRp%
=percentile of distribution @ probability p%
-it is single point so does not provide much info on distribution
TVaRp%
=E[L|L>VaRp%] = tail value at risk
-linear in tail so does not reflect that risk that is 2x large is more than 2x as bad
XTVaRp%
=TVaRp%-mean = excess tail value at risk
expected policyholder deficit
EPD=(1-p%)(TVaR-VaR)
-unconditional expected value of defaulted losses if there is a default
Tail-Based Risk Measures
- 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
Probability Transforms
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
Generalized moments and blurred VaR
- 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
Moment based measures
- 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)
insurer’s capital level: how different customers respond and insurer’s rating
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
consider split between new and renewal busines when setting capital levels
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
proportional allocation
calculate risk measure for insurer and each business unit separately
allocate total risk measure for insurer proportionally using individual risk measure
marginal decomposition
calculate overall risk measure for insurer
calculate marginal co-measuers for each business unit
marginal co-measures sum to company’s risk measure
why is marginal decomp better?
it reflects how risk from each business unit impacts that total risk profile as opposed to looking at them in isolation
how can insurer use capital allocation to help decide which business unit to grow
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
2 disadvantages of allocating capital
capital allocation is arbitrary - different risk measures give different allocations
it’s artificial - each business unit has access to entire capital of insurer
benefit of allocating cost of capital
gives minimum profit target for each business unit
profit that exceeds this is value added to insurer
WTVaR
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
to calculate each line’c contribution to TVaR for total insurer, must calc
co-TVaR
average loss when insurer’s total loss exceeds VaR threshold
risks in risk-based capital model to evaluate capital adequacy of insurance companies
invested asset risk
credit risk
premium risk
reserve risk
accumulation risk
reinsurance dependence
reinsurance diversification
accumulation risk AKA event risk
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
covariance adjustment
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
scenario testing
another approach for evaluating capital adequacy
static or stochastic scenarios can be used to measure capital adequacy
