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CAS Exam 9 > Butsic > Flashcards

Butsic Flashcards

1
Q

Relationship between capital, assets, and liabilities

Butsic

A

capital = assets - liabilities

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2
Q

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

Butsic

A
  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
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3
Q

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

(Butsic)

A

EPD also contemplates severity of ruin

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4
Q

Expected policyholder deficit (EPD)

Butsic

A

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

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5
Q

EPD ratio

Butsic

A

EPD ratio = EPD / expected losses

*always ratio to losses even when assets are risky

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6
Q

EPD when losses are risky (discrete & continuous)

Butsic

A

discrete: sum where losses > assets of pr(L(i)) * (L(i) - A)
continuous: integral from A to infinity of pr(L) * (L - A) dL

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7
Q

EPD when assets are risky (discrete & continuous)

Butsic

A

discrete: sum where losses > assets of pr(A(i)) * (L - A(i))
continuous: integral from 0 to L of pr(A) * (L - A) dA

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8
Q

EPD method for capital allocation

Butsic

A

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

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9
Q

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

(Butsic)

A

use asset relativities since asset values can change throughout the year

relativity = A(i) / E[A]

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10
Q

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

(Butsic)

A

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

where c = capital / E[L]
k = coefficient of variation (L)

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11
Q

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

(Butsic)

A

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)
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12
Q

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

Butsic

A

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

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13
Q

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

(Butsic)

A

Φ(-x) = 1 - Φ(x)

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14
Q

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

(Butsic)

A

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

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15
Q

Most appropriate time to use the normal distribution for EPD ratios

(Butsic)

A

population with known mean where individual losses are independent

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16
Q

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

(Butsic)

A

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

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

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17
Q

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

(Butsic)

A

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
Q

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

(Butsic)

A

lower required capital to achieve the same EPD ratio

b/c the lognormal distribution does not allow negative values

19
Q

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

(Butsic)

A

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
Q

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

(Butsic)

A

more capital needed for loss risk compared to asset risk

21
Q

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

(Butsic)

A

difference in required capital increases as CV(L) increases

22
Q

Factors influencing required capital (2)

Butsic

A
  1. accounting conventions

2. time horizons

23
Q

Most appropriate valuation for solvency risk measurement and rationale

(Butsic)

A

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
Q

Accounting practices causing bias for solvency risk measurement (2)

(Butsic)

A
  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
Q

Reason time horizons impact required capital

Butsic

A

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

26
Q

Determinants of the degree of insolvency risk (2)

Butsic

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

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

27
Q

Goal of the EPD method considering time horizons

Butsic

A

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

28
Q

Factors determining the market value of reserves (2)

Butsic

A
  1. market interest rates

2. risk of adverse development

29
Q

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

(Butsic)

A

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

30
Q

EPD as a financial option when losses are risky

Butsic

A

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

31
Q

EPD as a financial option when assets are risky

Butsic

A

PV(EPD ratio) = put option on ending assets with strike price = ending liabilities

32
Q

Required capital for multiple LOB vs. required capital for individual LOB

(Butsic)

A

required capital for all LOB < sum of required capital for individual LOB

*unless there is perfect correlation (rho = 1), in which case, the required capital for all LOB = sum of required capital for individual LOB

33
Q

Relationship between the diversification benefit on required capital and correlation

(Butsic)

A

diversification benefit decreases as correlation approaches 1

34
Q

Total risk-based capital (formula)

Butsic

A

total risk-based capital = sqrt( sum of capital(i)^2 across all risks + double sum of correlation(i,j) * capital(i) * capital(j))

35
Q

Modification required when correlated risk elements are on opposite sides of the balance sheet

(Butsic)

A

reverse the sign of the correlation coefficient (ex: bonds & loss reserves)

36
Q

Key results of the Butsic paper (5)

Butsic

A
  1. PV(EPD ratio) = relevant measure of solvency
  2. RBC should use market value of risk elements to remove accounting bias
  3. common time horizons should be used to compare risk b/c insurance risk increases as time elapses
  4. EPD ratio is based on expected market value at the end of each valuation interval
  5. total RBC < sum RBC amounts for each risk element unless the risk elements are fully correlated
37
Q

Risk elements with positive correlation (rho = 1) and which one needs modification (3)

(Butsic)

A
  1. stocks & bonds
  2. loss reserves & LAE reserves
  3. bonds & loss reserves (modification)
38
Q

Risk elements with no correlation (rho = 0) and which one needs modification (3)

(Butsic)

A
  1. cash & real estate
  2. loss reserve & property UPR
  3. stocks & UPR (modification)
39
Q

Risk elements with negative correlation (rho = -1) and which one needs modification (5)

(Butsic)

A
  1. stocks & put options
  2. loss reserves & income tax liabilities
  3. loss reserves & dividend reserves
  4. property/liability stocks & loss reserves (modification)
  5. reinsurance recoveries & loss reserves (modification)
40
Q

Disadvantage of the EPD method for allocating capital

Butsic

A

does not reflect diversification benefits

CAS Exam 9 (26 decks)

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