Butsic Flashcards
(40 cards)
Relationship between capital, assets, and liabilities
Butsic
capital = assets - liabilities
Criteria for risk-based capital (RBC) methods (3)
Butsic
- the solvency standard is the same across all classes
- RBC is objectively determined
- ability to differentiate relative riskiness b/w quantifiable measures of risk
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
Expected policyholder deficit (EPD)
Butsic
expected value of the difference b/w insurer’s full obligation and actual amount paid
EPD ratio
Butsic
EPD ratio = EPD / expected losses
*always ratio to losses even when assets are risky
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
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
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
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]
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)
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)
Standard normal density function and negative values ϕ(-x)
Butsic
ϕ(-x) = ϕ(x) because it is symmetric around 0
Cumulative standard normal distribution and negative values Φ(-x)
(Butsic)
Φ(-x) = 1 - Φ(x)
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
Most appropriate time to use the normal distribution for EPD ratios
(Butsic)
population with known mean where individual losses are independent
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
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)
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
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
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
Relationship between the difference in required capital under the normal vs. lognormal distribution and coefficient of variation when losses are risky
(Butsic)
difference in required capital increases as CV(L) increases
Factors influencing required capital (2)
Butsic
- accounting conventions
2. time horizons
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
Accounting practices causing bias for solvency risk measurement (2)
(Butsic)
- statutory accounting allows insurers to consistently under- or over-value certain items (ex: undiscounted loss reserves)
- statutory & GAAP accounting allow inconsistent measurement for identical items across companies (ex: risk margin in loss reserves)
