CAS Exam 9 > Kreps > Flashcards

Kreps Flashcards

(48 cards)

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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)

Study These Flashcards
A

only the high end of the distribution is relevant

21
Q

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

Kreps

Study These Flashcards
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

23
Q

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

Kreps

Study These Flashcards
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)

Study These Flashcards
A

only the single VaR point is relevant

25
Semi-variance, SVaR, form of the riskiness leverage function, L(x) (Kreps)
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
Risk load when using the risk-neutral form of L(x) | Kreps
risk load = 0
27
Risk load when using the semi-variance, SVaR, form of L(x) | Kreps
risk-load = semi-variance (only non-zero for results worse than the mean)
28
Relevant part of the distribution when using the semi-variance, SVaR, form of L(x) (Kreps)
only bad results are relevant
29
Mean downside deviation form of the riskiness leverage function, L(x) (Kreps)
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
Risk load when using the mean downside deviation form of L(x) (Kreps)
risk load = multiple of mean downside deviation
31
Condition when the mean downside deviation = TVaR form of the riskiness leverage function, L(x) (Kreps)
x(q) = mu
32
Riskiness leverage ratio for the mean downside deviation form of L(x) (Kreps)
riskiness leverage ratio = 0 below the mean and constant above the mean
33
Capital allocation using the mean downside deviation form of L(x) (Kreps)
assigns capital for bad outcomes in proportion to how bad they are
34
Proportional excess form of the riskiness leverage function, L(x) (Kreps)
L(x) = h(x) * theta(x - (mu + delta)) / (x - mu)
35
Capital allocation using the proportional excess form of L(x) (Kreps)
individual allocation for any given outcome is pro rata to its contribution to the excess over the mean
36
Sources of risk that could impact riskiness leverage ratio selection (7) (Kreps)
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
Management properties of a riskiness leverage ratio (4) | Kreps
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
Regulator properties of a riskiness leverage ratio (2) | Kreps
must: 1. be 0 until capital is seriously impacted 2. not decrease (due to risk to state guaranty fund)
39
Reinsurance premium | Kreps
reinsurance premium = E[ceded loss] + load % * std. dev(ceded losses)
40
Reinsurance net cost | Kreps
reinsurance net cost = reinsurance premium - E[ceded loss]
41
Impact of reinsurance on total return and capital | Kreps
positive net cost of reinsurance will reduce total return, but allow firm to release capital
42
Total return | Kreps
total return = income / surplus
43
Surplus released from purchasing reinsurance | Kreps
surplus release = current surplus - target surplus
44
Reduction in cost of capital from purchasing reinsurance | Kreps
reduction in cost of capital = cost of capital * surplus release
45
Determining whether reinsurance treaties are worth pursuing | Kreps
if reduction in cost of capital > net avg cost of reinsurance, then reinsurance is worth pursuing
46
Potential actions to take if return on surplus < target return on surplus (3) (Kreps)
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
Potential problems with changing LOB volume when return on surplus < target (3) (Kreps)
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
Risk load, R(k), for a line of business using riskiness leverage models (Kreps)
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
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