Flashcards in Kreps Deck (47)

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1

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

(Kreps)

###
total assets = reserves + surplus

reserves support mean of assets & liabilities

surplus supports variability of assets & liabilities

2

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Total capital (C)

(Kreps)

### total capital = mean outcome + risk load

3

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Desirable qualities for an allocatable risk load (3)

(Kreps)

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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

4

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General form of riskiness leverage models

(Kreps)

###
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

5

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

(Kreps)

###
R = sum of R(k)'s

C = sum of C(k)'s

where k = individual LOB

6

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Advantage of co-measures

(Kreps)

### they are automatically additive

7

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Disadvantage of co-measures

(Kreps)

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

8

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Conditions for negative risk loads (2)

(Kreps)

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1. x(k) < mean

2. large L(x)

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

9

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Properties of riskiness leverage models (4)

(Kreps)

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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

10

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Coherent risk measures

(Kreps)

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satisfy sub-additivity requirement

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

11

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Super-additivity

(Kreps)

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

(not coherent)

12

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

(Kreps)

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1. risk-neutral

2. variance

3. VaR

4. TVaR

5. semi-variance, SVaR

6. mean downside deviation

7. proportional excess

13

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

(Kreps)

### L(x) = c

14

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

(Kreps)

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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

15

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

(Kreps)

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

16

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

(Kreps)

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

17

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

(Kreps)

### S = sqrt(beta * var(x))

18

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

(Kreps)

###
1. variance

2. semi-variance, SVaR

19

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

(Kreps)

###
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

20

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

(Kreps)

### only the high end of the distribution is relevant

21

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

(Kreps)

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

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

22

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Coherent riskiness leverage function, L(x)

(Kreps)

### TVaR

23

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

(Kreps)

###
C = x(q) = VaR

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

24

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

(Kreps)

### only the single VaR point is relevant

25

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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

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

(Kreps)

### risk load = 0

27

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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

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

(Kreps)

### only bad results are relevant

29

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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