Butsic Flashcards Preview

CAS Exam 9 > Butsic > Flashcards

Flashcards in Butsic Deck (40)
Loading flashcards...
1

Relationship between capital, assets, and liabilities

(Butsic)

capital = assets - liabilities

2

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

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

Expected policyholder deficit (EPD)

(Butsic)

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

5

EPD ratio

(Butsic)

EPD ratio = EPD / expected losses

*always ratio to losses even when assets are risky

6

EPD when losses are risky (discrete & continuous)

(Butsic)

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

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

EPD method for capital allocation

(Butsic)

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

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

(Butsic)

use asset relativities since asset values can change throughout the year

relativity = A(i) / E[A]

10

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

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

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

(Butsic)

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

13

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

(Butsic)

Φ(-x) = 1 - Φ(x)

14

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

Most appropriate time to use the normal distribution for EPD ratios

(Butsic)

population with known mean where individual losses are independent

16

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

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

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

(Butsic)

lower required capital to achieve the same EPD ratio

b/c the lognormal distribution does not allow negative values

19

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

(Butsic)

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

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

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

Factors influencing required capital (2)

(Butsic)

1. accounting conventions
2. time horizons

23

Most appropriate valuation for solvency risk measurement and rationale

(Butsic)

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

Accounting practices causing bias for solvency risk measurement (2)

(Butsic)

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

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

Determinants of the degree of insolvency risk (2)

(Butsic)

1. time horizon - longer time intervals lead to more risk
2. volatility of financial statement values - more volatility leads to more risk

27

Goal of the EPD method considering time horizons

(Butsic)

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

28

Factors determining the market value of reserves (2)

(Butsic)

1. market interest rates
2. risk of adverse development

29

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

EPD as a financial option when losses are risky

(Butsic)

PV(EPD ratio) = call option on ending losses with strike price = ending asset value

insurer has the option to abandon it's promise of full claim payment