Flashcards in Butsic Deck (40)

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1

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Relationship between capital, assets, and liabilities

(Butsic)

### capital = assets - liabilities

2

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Criteria for risk-based capital (RBC) methods (3)

(Butsic)

###
1. the solvency standard is the same across all classes

2. RBC is objectively determined

3. ability to differentiate relative riskiness b/w quantifiable measures of risk

3

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Reason that EPD is a better measure of insolvency risk compared to probability of ruin (advantage of EPD method)

(Butsic)

### EPD also contemplates severity of ruin

4

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Expected policyholder deficit (EPD)

(Butsic)

### expected value of the difference b/w insurer's full obligation and actual amount paid

5

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EPD ratio

(Butsic)

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EPD ratio = EPD / expected losses

*always ratio to losses even when assets are risky

6

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EPD when losses are risky (discrete & continuous)

(Butsic)

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discrete: sum where losses > assets of pr(L(i)) * (L(i) - A)

continuous: integral from A to infinity of pr(L) * (L - A) dL

7

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EPD when assets are risky (discrete & continuous)

(Butsic)

###
discrete: sum where losses > assets of pr(A(i)) * (L - A(i))

continuous: integral from 0 to L of pr(A) * (L - A) dA

8

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EPD method for capital allocation

(Butsic)

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if the EPD ratio > the target EPD ratio, then increase capital

cannot solve for capital directly, so need to use an iterative process starting with the largest loss or smallest asset producing a deficit & working backwards to solve for A

9

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Modification to the EPD method for capital allocation when assets are risky

(Butsic)

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use asset relativities since asset values can change throughout the year

relativity = A(i) / E[A]

10

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EPD ratio when losses are risky, d(L), under a normal distribution

(Butsic)

###
EPD ratio = d(L) = k * ϕ( -c / k) - c * Φ( -c / k)

where c = capital / E[L]

k = coefficient of variation (L)

11

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EPD ratio when assets are risky, d(A), under a normal distribution

(Butsic)

###
EPD ratio = d(A) = (1 / (1 - c(A))) * [ k(A) * ϕ( - c(A) / k(A)) - c(A) * Φ( -c(A) / k(A))

where c(A) = capital / E[A]

k(A) = coefficient of variation (A)

12

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Standard normal density function and negative values ϕ(-x)

(Butsic)

### ϕ(-x) = ϕ(x) because it is symmetric around 0

13

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Cumulative standard normal distribution and negative values Φ(-x)

(Butsic)

### Φ(-x) = 1 - Φ(x)

14

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Capital needed for asset risk relative to loss risk with the same beginning balance sheet & EPD ratio under a normal distribution

(Butsic)

###
more capital needed for asset risk compared to loss risk

standard deviation of capital will be larger under the risky asset scenario because assets > losses

15

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Most appropriate time to use the normal distribution for EPD ratios

(Butsic)

### population with known mean where individual losses are independent

16

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EPD ratio when losses are risky, d(L), under a lognormal distribution

(Butsic)

###
EPD ratio = d(L) = Φ(a) - (1 + c) * Φ(a - k)

where a = k / 2 - ln(1 + c) / k

17

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EPD ratio when assets are risky, d(A), under a lognormal distribution

(Butsic)

###
EPD ratio = d(A) = Φ(b) - Φ(b - k(A)) / (1 - c(A))

where b = k(A) / 2 + ln(1 - c(A)) / k(A)

18

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Required capital when assets are risky under the lognormal distribution compared to the normal distribution & rationale

(Butsic)

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lower required capital to achieve the same EPD ratio

b/c the lognormal distribution does not allow negative values

19

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Required capital when losses are risky under the lognormal distribution compared to the normal distribution & rationale

(Butsic)

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higher required capital to achieve the same EPD ratio

b/c the lognormal distribution is skewed and produces a higher probability of large losses

20

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Capital needed for asset risk relative to loss risk under the same beginning balance sheet & EPD ratio under a lognormal distribution

(Butsic)

### more capital needed for loss risk compared to asset risk

21

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Relationship between the difference in required capital under the normal vs. lognormal distribution and coefficient of variation when losses are risky

(Butsic)

### different in required capital increases as CV(L) increases

22

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Factors influencing required capital (2)

(Butsic)

###
1. accounting conventions

2. time horizons

23

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Most appropriate valuation for solvency risk measurement and rationale

(Butsic)

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market value

rationale: firm insolvency would lead to liquidation, which would be evaluated based on realizable market value vs. accounting book value which is subject to accounting bias in recorded values

24

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Accounting practices causing bias for solvency risk measurement (2)

(Butsic)

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1. statutory accounting allows insurers to consistently under- or over-value certain items (ex: undiscounted loss reserves)

2. statutory & GAAP accounting allow inconsistent measurement for identical items across companies (ex: risk margin in loss reserves)

25

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Reason time horizons impact required capital

(Butsic)

### the market value of assets & liabilities change over time which impacts the market value of realizable capital

26

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Determinants of the degree of insolvency risk (2)

(Butsic)

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1. time horizon - longer time intervals lead to more risk

2. volatility of financial statement values - more volatility leads to more risk

27

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Goal of the EPD method considering time horizons

(Butsic)

### meet the target EPD ratio criterion over each time interval by adjusting capital requirements

28

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Factors determining the market value of reserves (2)

(Butsic)

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1. market interest rates

2. risk of adverse development

29

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Difference in evaluating RBC requirements for a going concern business vs. one in run-off

(Butsic)

### need to consider losses & premiums from future business as well as the return on that premium

30