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Flashcards in Kreps Deck (47)
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1

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

Total capital (C)

(Kreps)

total capital = mean outcome + risk load

3

Desirable qualities for an allocatable risk load (3)

(Kreps)

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

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

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

Advantage of co-measures

(Kreps)

they are automatically additive

7

Disadvantage of co-measures

(Kreps)

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

8

Conditions for negative risk loads (2)

(Kreps)

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

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

9

Properties of riskiness leverage models (4)

(Kreps)

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

Coherent risk measures

(Kreps)

satisfy sub-additivity requirement

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

11

Super-additivity

(Kreps)

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

(not coherent)

12

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

(Kreps)

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

13

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

(Kreps)

L(x) = c

14

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

(Kreps)

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

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

(Kreps)

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

16

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

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

(Kreps)

S = sqrt(beta * var(x))

18

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

(Kreps)

1. variance
2. semi-variance, SVaR

19

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

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

(Kreps)

only the high end of the distribution is relevant

21

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

Coherent riskiness leverage function, L(x)

(Kreps)

TVaR

23

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

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

(Kreps)

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