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CAS Exam 9 > Kreps > Flashcards

Kreps Flashcards

1
Q

Total assets and what is supported by each component (2)

Kreps

A

total assets = reserves + surplus

reserves support mean of assets & liabilities

surplus supports variability of assets & liabilities

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2
Q

Total capital (C)

Kreps

A

total capital = mean outcome + risk load

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3
Q

Desirable qualities for an allocatable risk load (3)

Kreps

A
  1. ability to be allocated to any level
  2. allocated risk load for a sum of random variables should = sum of individually allocated risk load amounts
  3. same additive formula is used to calculate risk loads for any sub-group or grouping
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4
Q

General form of riskiness leverage models

Kreps

A

R = integral of f(x) * (x - mu) * L(x) dx
f(x)dx can be called dF-bar for joint probability distributions

where f(x) = joint probability distribution 
and L(x) = riskiness leverage function for total losses
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5
Q

Risk load (R) and capital (C) across multiple LOB

Kreps

A 
R = sum of R(k)'s 
C = sum of C(k)'s

where k = individual LOB

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6
Q

Advantage of co-measures

Kreps

A

they are automatically additive

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7
Q

Disadvantage of co-measures

Kreps

A

can be challenging to find appropriate forms of the riskiness leverage function L(x)

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8
Q

Conditions for negative risk loads (2) and when it is desirable

(Kreps)

A
  1. x(k) < mean
  2. large L(x)

desirable for hedges, occurs when there is a low correlation with total losses

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9
Q

Properties of riskiness leverage models (4)

Kreps

A
  1. desirable qualities for allocatable risk loads are satisfied
  2. no risk load for constant variables - R(c) = 0
  3. risk load will scale with change in currency - R(lambda * x) = lambda * R(x)
  4. may not produce a coherent risk measure
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10
Q

Coherent risk measures

Kreps

A

satisfy sub-additivity requirement

R(x + y) <= R(x) + R(y)

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11
Q

Super-additivity

Kreps

A

R(x + y) > R(x) + R(y)

not coherent

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12
Q

Types of riskiness leverage functions, L(x) (7)

Kreps

A
  1. risk-neutral
  2. variance
  3. VaR
  4. TVaR
  5. semi-variance, SVaR
  6. mean downside deviation
  7. proportional excess
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13
Q

Risk-neutral form of the riskiness leverage function, L(x)

Kreps

A

L(x) = c

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14
Q

Situations when a risk-neutral form of L(x) might be appropriate (2)

(Kreps)

A
  1. risk of ruin if risk of ruin is very small compared to capital OR capital is infinite
  2. risk of not meeting plan if indifferent about making plan
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15
Q

Variance form of the riskiness leverage function, L(x)

Kreps

A

L(x) = (beta / surplus) * (x - mu)

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16
Q

Relevant part of the distribution when using the variance form of L(x)

(Kreps)

A

entire distribution (just as much risk associated with good & bad outcomes)

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17
Q

Surplus (S) when using the variance form of L(x)

Kreps

A

S = sqrt(beta * var(x))

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18
Q

Forms of the riskiness leverage function, L(x) where the risk load increases quadratically (2)

(Kreps)

A
  1. variance

2. semi-variance, SVaR

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19
Q

TVaR form of the riskiness leverage function, L(x)

Kreps

A

L(x) = theta(x - x(q)) / (1 - q)

where theta is a step function with:
theta(x) = 0 for x <= 0 and
theta(x) = 1 for x > 0

x(q) = value of x so F(x(q)) = q

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20
Q

Relevant part of the distribution when using the TVaR form of L(x)

(Kreps)

A

only the high end of the distribution is relevant

21
Q

VaR form of the riskiness leverage function, L(x)

Kreps

A

L(x) = delta(x - x(q)) / f(x(q))

where delta(x) = 0 everywhere except 0 and integrates to 1

22
Q

Coherent riskiness leverage function, L(x)

Kreps

A

TVaR

23
Q

Capital (C) when using the VaR form of L(x)

Kreps

A

C = x(q) = VaR

x(q) = value of x so F(x(q)) = q

24
Q

Relevant part of the distribution when using the VaR form of L(x)

(Kreps)

A

only the single VaR point is relevant

25
Q

Semi-variance, SVaR, form of the riskiness leverage function, L(x)

(Kreps)

A

L(x) = (beta / surplus) * (x - mu) * theta(x - mu)

where theta is a step function with:
theta(x) = 0 for x <= 0 and
theta(x) = 1 for x > 0

26
Q

Risk load when using the risk-neutral form of L(x)

Kreps

A

risk load = 0

27
Q

Risk load when using the semi-variance, SVaR, form of L(x)

Kreps

A

risk-load = semi-variance (only non-zero for results worse than the mean)

28
Q

Relevant part of the distribution when using the semi-variance, SVaR, form of L(x)

(Kreps)

A

only bad results are relevant

29
Q

Mean downside deviation form of the riskiness leverage function, L(x)

(Kreps)

A

L(x) = beta * theta(x - mu) / (1 - F(mu))

where theta is a step function with:
theta(x) = 0 for x <= 0 and
theta(x) = 1 for x > 0

30
Q

Risk load when using the mean downside deviation form of L(x)

(Kreps)

A

risk load = multiple of mean downside deviation

31
Q

Condition when the mean downside deviation = TVaR form of the riskiness leverage function, L(x)

(Kreps)

A

x(q) = mu

32
Q

Riskiness leverage ratio for the mean downside deviation form of L(x)

(Kreps)

A

riskiness leverage ratio = 0 below the mean and constant above the mean

33
Q

Capital allocation using the mean downside deviation form of L(x)

(Kreps)

A

assigns capital for bad outcomes in proportion to how bad they are

34
Q

Proportional excess form of the riskiness leverage function, L(x)

(Kreps)

A

L(x) = h(x) * theta(x - (mu + delta)) / (x - mu)

35
Q

Capital allocation using the proportional excess form of L(x)

(Kreps)

A

individual allocation for any given outcome is pro rata to its contribution to the excess over the mean

36
Q

Sources of risk that could impact riskiness leverage ratio selection (7)

(Kreps)

A
  1. not making plan
  2. serious deviation from plan
  3. not meeting investor expectations
  4. ratings downgrade
  5. triggering regulatory notice
  6. going into receivership
  7. not getting a bonus
37
Q

Management properties of a riskiness leverage ratio (4)

Kreps

A

must:
1. be a downside measure
2. be approximately constant for excess losses that are small compared to capital
3. become much larger for excess losses significantly impacting capital
4. go to 0 for excess losses significantly exceeding capital

38
Q

Regulator properties of a riskiness leverage ratio (2)

Kreps

A

must:
1. be 0 until capital is seriously impacted
2. not decrease (due to risk to state guaranty fund)

39
Q

Reinsurance premium

Kreps

A

reinsurance premium = E[ceded loss] + load % * std. dev(ceded losses)

40
Q

Reinsurance net cost

Kreps

A

reinsurance net cost = reinsurance premium - E[ceded loss]

41
Q

Impact of reinsurance on total return and capital

Kreps

A

positive net cost of reinsurance will reduce total return, but allow firm to release capital

42
Q

Total return

Kreps

A

total return = income / surplus

43
Q

Surplus released from purchasing reinsurance

Kreps

A

surplus release = current surplus - target surplus

44
Q

Reduction in cost of capital from purchasing reinsurance

Kreps

A

reduction in cost of capital = cost of capital * surplus release

45
Q

Determining whether reinsurance treaties are worth pursuing

Kreps

A

if reduction in cost of capital > net avg cost of reinsurance, then reinsurance is worth pursuing

46
Q

Potential actions to take if return on surplus < target return on surplus (3)

(Kreps)

A
  1. write less business (shift volume to more profitable LOB)
  2. purchase reinsurance to reduce required surplus
  3. raise premium by increasing the profit load
47
Q

Potential problems with changing LOB volume when return on surplus < target (3)

(Kreps)

A
  1. LOBs may be two parts of an indivisible policy
  2. regulatory requirements
  3. may not be cost effective to undergo major UW effort
48
Q

Risk load, R(k), for a line of business using riskiness leverage models

(Kreps)

A

R(k) = average of all L(x) * (x(k) - mu(k)) for individual loss amounts

**L(x) is always for total losses, NOT individual LOB

CAS Exam 9 (26 decks)

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