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CAS Exam 5 > Last minute Formulas > Flashcards

Last minute Formulas Flashcards

1
Q

LER (Loss elimination Ratio)

A

Total Capped amount / Total expected amount

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2
Q

Calculate the premium for a policy with a $500 deductible.

A
  1. Calculate LER (500)
  2. Deductible Relativity = 1- LER(500)
  3. Calculate the new Loss (LR* deductible relativity)
  4. Usual Premium indicated steps

Indicated rate = (New Loss *(1+ALAE ratio) + Fixed expenses )/ 1- V-Q

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3
Q

Steps
Calculate the total amount of premium discount for a policy with premium of $180,000.

2011 Q16

A
  1. premium in range (Upper - Lower) until max 180 000$ as upper limit
  2. total Expense percentage = (Prod+ General+ Taxes + Profit)
  3. Expense reduction = 1st row of Total expense - your row of total expense
  4. Discount % = Expense reduction / (1- %Tax - % Profit)
  5. $ Discount = Prem in range * %discount
  6. Total $ Discount is your answer !
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4
Q

An insured purchases a $400,000 policy on a property valued at $500,000.

  • The coinsurance requirement for the policy is 90% of property value.
  • No deductible applies.

a.
Calculate the coinsurance penalty for a $300,000 loss and maximum penalty

A
  1. a = min(AOI/(Required coinsurance amount , 1)
    a = min(400/(500*90%);1) = 0.889
  2. Indemnity (I) = min(a * Loss; AOI)
    I = min(0.889 x 300 000 ; 400 000) = 266 667
  3. Penalty (P) = min(L, AOI) - I
    P = min( 300 000, 400 000) - 266 667 = 33 333
  4. Maximum Penalty
    * Maximum Loss is AOI, so the new L = 400 000
    Max indemnity = a* 400000 = 355 556
    P = min( New loss ; AOI) - I
    P = min( 400 000; 400 000) - 355 556 = 44 444
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5
Q

Loss constant Steps

A

For each Range of premiums

  1. Premium Shortfall = (Rept Loss/Target Loss ratio)-Premium
  2. Loss Constant = Premium Shortfall/ # risks
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6
Q

Harwayne Cred as complement of cred for State A class 1
We have State B and C et Class 2

Spring 2017 Q9

A
  1. State A PP
  2. Adjusted PP for B and C with exposures of A
    * (PP B1 x Exposure A1 + PP B2 x Exposure A2 ) / Total Exposures A
  3. Adjustment factor for B and C
    PP A / Adjusted PP B
  4. Adjustment factor x PP B class 1
    Same for C
  5. Complement = (Exposure B1 x Adjusted PP B1 + Exposure C1 x Adjusted PP C1 ) / Sum of Exposures B1 and C1
  6. Cred Wtd PP = Z * A1 x (1-Z) * Complement
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7
Q

Complement of credibility Trended present rates

PP complement

A

PP Complement = Present rate x Loss trend Factor/Premium trend x (Prior indicated Loss Cost / Prior implementated loss cost)

Period for trend : From last indication effective to new indication effective

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8
Q

Complement of credibility Trended present rates

LR complement

Fall 2019 Q3

A

LR Complement = Loss trend Factor/Premium trend factor x (Prior indicated Rate change / Prior implemented indicated Rate change) -1

Period for trend : From last indication effective to new indication effective

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9
Q

Credibility Bulhman

A

Z = N / (N + K)

K = EVPV / VHM
= Expected Process Variance / Variance of Hypothetical Mean

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10
Q

Overall indication section

WC Indication steps

Practice Problem 1 B7 overall indication

A

The main formula is
*(Med LR + Indem LR) x (1+ LAE Ratio)
*

**Step 1 : Projected Loss cost premium **
1a *Trend period *= AAD for latest available year to AAD for effective period)
* *Trend factor *= (1+ Projected annual wage) ^ trend period

1b Projected loss cost for each year and total
Projected loss cost = Industry LC prem x Factor to current (last year is 1.00 and each year accumulates the wage changes) x Trend factor x Experience mod factor
* Experience mod factor = Expected exp mod (EEM) / Hist exp mod (HEM)
**-> Sum of all projected losses :) **

Step 2 Indemnity Loss ratio for each year
2a. Projected Ult Indem losses
= Rept indem losses x Indem CDF x Factor to adjust indem to current x Trend factor
* Trend factor = (1+Future benefit level chg)^Trend period
* factor to adjust = (last year is 1.00 and each year accumulates (1+ benefit level chg) x (1+ inflation chg))
-> Suggestion : Create a column with the combined effect of benefit change and inflation

2b. Indemnity Loss Ratio for each year and total
Proj ult indem losses /Projected Loss Cost (from step1)

Step 3 Medical Loss ratio for each year and total

3a. Projected ultimate medical loss = Rept med loss x CDF x factor to adjust current med level x Trend Factor
* Trend factor = (1+Future combined fees)^Trend period
* Factor to adjust current = (last year is 1.00 and each year accumulates (1+ combined effect from previous year)
-> Suggestion : Create a column with the combined effect because you may have weights for schedule fees and other fees

3b. Medical Loss Ratio for each year and total
Projected ultimate medical loss /Projected Loss Cost (from step1)

**Step 4 Industry and company changes **

  • Indicated rate change = (Med LR + Indem LR) x (1+ LAE Ratio) -1
  • Proposed deviation from industry =( 1/(1-V-Q) ) x (1 + expected loss cost difference)
  • Company indicated rate change = Proposed deviation / Current deviation x (1+ industry chg) - 1

btw 1/(1-v-q) = Expenses and Profit Adj Factor (In case you this instead)

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11
Q

Overall indication

Homewowner indication steps

Battleacts Powerpack p103

A

Projected Ult non cat PP + Projected non-modeled cat PP + Projected modeled cat PP + Projected net reinsurance PP + Projected Fixed Expenses

  1. Projected Ult non cat PP trended
    a. Trend periods
    -> Hist = From CY to last year of experience AAD(07-01 to 07-01)
    -> Future = From last year of experience AAD to Effective AAD
    b. Non Cat ultimate Loss
    = Non Cat rept loss & ALAE x ULAE x Trends
    c. Non Cat ult PP
    =Non Cat ultimate Loss /EE take the avg (in general)
  2. Non-modeled Cat PP trended (Use the most recent year only)
    = CAT-to-AIY-Ratio x AIY-to-EE x ULAE Factor
    a. choose the correct AIY to EE
    If your AAD Effective is 2027-04-01
    You have to put a weight on the 2026 year and 2027 (both have AAD 07-01)
    This must be 0.25 x AIY to EE 2026 + 0,75 x AIY to EE 2027
  • if the trend is not given, you must find it with % of change along the AIY to EE
    3. Net reinsurance cost per exposure = (most recent CY Reinsurance cost (which is ceded premium) - most recent CY reinsurance recoveries) / EE for most recent EE
  1. Trend fixed expenses
    * Trend period : From AWD of most recent year to AWD (eff period) since most expenses are incurred when policy is written
  2. Modeled cat PP is usually given, but if not
    = Projected Avg AIY per exposure x Modeled CAT Loss and ALAE to AIY ratio x ULAE
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12
Q

Large deductible polices premium (100 000$) for example

TIA #4 Q14

A

Premium = (Losses above the Deductible + ALAE + FE + Credit Risk + Risk Margin ) / (1-V-Q)

Notes :
1. Losses above deductible = Ground up losses x Excess Ratio or (1-LER)
2. Do not multiply your losses above deductible by (1+ ALAE %)… deductible does not affect ALAE so you must multiply ALAE by Ground up losses !
3. Credit risk % of expected deductible payments is applied to losses beloew deductible

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13
Q

ISO Experience Modication (Mod)
STEPS

2006 Q49

A

MOD = ((AER - EER) / EER) x Z

Z: Credibility
EER = Expected experience ratio (usually given, put this =1 if MSL is not given)

AER = Basic limit losses + Expected unrept losses / CLSC
CLSC : Company’s subject to basic limit loss…

  1. Basic Limit losses = Follow this order
    a.Limit on Loss
    b. Add ALAE
    c. Limit MSL on Loss + ALAE
  2. Basic limit expected loss and LAE = Prem x LR
  3. CLSC (if not given) = Basic limit expected loss and LAE x detrend factor
  4. Expected unrept losses = CLSC x %unrept x EER
  5. Standard premium = Experience Mod x Manual Premium so If they ask you for Premium write down that you assume that they ask for Manual premium and find the answer
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14
Q

NCCI Experience Plan

Fall 2016 Q15

A

2 formulas

  1. M = (Ap + w* Ae +(1-w) * Ee + B ) / (E + B)
    or
  2. (Zp x Ap + (1-zp) x Ep + Ze x Ae + (1-Ze) x Ee) / E

Ap = Actual Primary (Primary = losses capped)
Ae = Actual excess
Same logic for Expected (Ep and Ee) and Z credibility

E = Ee + Ep
w=Excess loss weighting = Excess cred (Ze) / Primary Cred (Zp)
B = Ballast value = E/ (E+B)

You may have also D-ratio = LER (Loss elim ratio for expected losses) so if you want Ee = (1-D Ratio) * rept losses
NOTE
Standard premium = Experience Mod x Manual Premium so If they ask you for Premium write down that you assume that they ask for Manual premium and find the answer

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15
Q

Retrospective Rating steps

Spring 2018 Q15

A

Retrospective premium = (Basic Premium + Converted Losses )

  • Converted Losses = Rept losses x Loss conversion factor (LCF)
  • Basic Premium = Standard Premium x (Expense Allowance - LCF expenses + Net insurance charge)
    *Standard premium = Manual Premium x M (modification factor)
  • LCF Expense = LR *(LCF-1)
    *Net insurance = (Insurance Charge - Insurance savings) * LR * LCF

You may need to compare you retro premium with min and max retro prem
* min and max retro = Standard prem x min and max factor
You want you retro prem to be between these boundaries !

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16
Q

Reminder Implementation and Univariate
* Credibility
* Indicated territorial relativities vs territorial relativities

A
  1. When you have credibility, you need to normalize your current relativities
    and use them as complement (usually)

Normalized Relativities = Current rel i / Avg current rel

  1. Indicated territorial relativities = Rel change factor x Current relativity
    territorial relativities = Rel change factor

Rel change factor = PP I / Tot PP

17
Q

Shortfall problem with Base Rate
Steps

Essaie le avec Battleacts p.91

A
  1. Total change = (Proposed factor / Current factor) x (1+ Target %) x off-balance
  2. Proposed premium w/o capping = OLEP x (1+Total change i)
  3. Premium above the % cap = OLEP x (Tot change i - % cap)
  4. Base rate adjustment (BR) = (1+%target) /(1+Tot change i)
  5. Prop prem for non-capped levels = Sum of proposed non capped prem
  6. Initial adjustment to non capped rel = Prem above %cap / Total non capped prem
  7. Total Adjustment to non capped rel = BR adjustment / Initial Adjustment
  8. Revised rel of other rel than base = Prop factor / Total Ajust to non capped rel

Revised Base rate = Prop Base rate x BR adjustment

18
Q

Shortfall Problem for non Base Rate

Based on Battleacts Powerpack p.89

A
  1. Total % change and new prop premium for each variable level
    *Total change = (1+ ind rel chg) x off- balance x (1+ target % increase) -1
    * New prem = Premium current * (1+total % change)

2a Cap relativity for non-base level A (exceeding) so the total change doesn’t excees (20% for example) by solving for R

R/Current rel x off-bal x (1+ % target) = (1+ max % cap)

2b. Premium Shortfall created by A

  • Revised premium for A = New prop prem A x R / Indicated rel
  • Shortfall = New prop prem A - Revised Prem A

3a. Redistribute this shortfall across levels B and C by increasing the base rate by a proportionnal amount

  • premium for B and C = Sum of new prop prem
  • Required base rate increase = Shortfall / Premium B and C

3b. We need to back out this increase from level A otherwise the cap will exceed by that same amount
* final indicated rel for A = R / (1 + Base rate increase)

NOTE
Rel B and C are equal to the original ind rel from the beginning

New base rate = Current Base Rate x off-balance x (1+ % target) x (1+ Required Base rate increase)

19
Q

Base Rate required using EoE
Steps

Based on Battle acts powerpack p.83 and Fall 2015 Q11

A
  1. Rebased the relativities if you base is not 1.00
  2. Calculate current avg prem by rerating every combination of Variable 1 x Variable 2
    * Current premium for each combination = In force exposures x (rel 1 xrel2 +fee)
  3. Proposed avg prem = Current avg prem x (1+% target increase)
  4. Choose a Seed (1$ for example) and calculate seed avg prem by rerating every combination of Variable 1 x Variable 2 with proposed rel
  5. Final Proposed Base rate = Base seed (1$) x ( Prop avg prem - indicated fee)/(seed avg prem - indicated fee)
20
Q

Formula Fixed expense per exposure

A

Ap = EF / (1-V-Q)
Fixed exp per exposure / PLR

21
Q

Complement of Credibility

Complement for Increased Limits

Battleacts Powerpack p.73

A

Cap losses at A x [(ILF (A+L) - ILF(A)] / ILF(A)

(A+L) is the higher limit losses
A = Lower limit (not basic limit !)

22
Q

Complement of Credibility

Complement for Lower Limit

Battleacts Powerpack P.75

A

Cap losses at d x [(ILF (A+L) - ILF(A)] / ILF(d)

A = Lower limit (not basic limit !)
d = Basic limit

(A+L) is the higher limit losses

23
Q

Complement of Credibility

Complement for Limit Analysis

Battleacts Powerpack P.77

A

Step 1 Get organised
* d = Basic Limit
* A = Attachement point
* A+L = Higher limit
* ILF(d)
* ILF((A)
* ILF(A+L)

Step 2 Set up the table
(1) d
(2) A+L
(3) Min (d, A+L)
(4) Expected total losses = Premium for each limit d x estimated limits LR
(5) ILF for min(d,A+L)
(6) ILF(A)
(7) ILF(d)
(8) %loss layer = max(0, (ILF for min(d, A+L) / ILF(d))
(9) Expected loss in layer = Expected total losses (4) x % loss in layer (8)
Sum up this column for the final answer!

24
Q

Actual emergence formula

A

Rept losses as of xx - Diagonal last rept

25
Q

Expected Rept claim t, t+ 1

A

(Ult Estimate - Rept claims t) * (% rept t+1 - % Rept t) / (%unrept t)

26
Q

Expected paid claim t, t+1

A

(Ult Estimate - paid claims t) * (% paid t+1 - % paid t) / (%unpaid t)

27
Q

Cape Cod Adjust ECR for prior year (Historical levels from 2012 to 2011 for ex)

A

ECR x (1+ Prem trend) / [(1+Loss trend) * (Tort factor)]

28
Q

Steps Freq X Sev Disposal rates method

Based on 1998 Q44

A

Step 1 Set up
1a. CPC& IPC triangles
1b. IPL triangle
1c. UC values (if not given)

Step 2 Use Disposal Rates (DR) to project incremental counts
2a . CPC triangle (CDR/UC) + Selections for each column
2b. Project IPC for the specific AY
Projection t = (UC- Latest diago cumul count) * (Selected DR t+1 - Selected DR t) / (1- latest Diago selected DR)

Step 3 Project severities
3a. Calculate the trended IPS triangle + Selections for each column
Trended IPS = IPL / IPC x (1+ trend) ^(Trend year - data year)
3b. Calculate the final unpaid amount for each dev period
unpaid = selected incremental sev x selected incremental count

If they ask you for ultimate losses, just add the cumulative paid from latest diago

29
Q

Case Outstanding Development technique (#1) steps

Based on 2001 Q32

A
  1. Remaining on case ratio triangle = Case t / case t-1
    1b. Selections for each period
  2. Project Case O/S = Selected factor step 1 x Previous Case (Projected)
  3. Incremental paid $$
  4. Paid on case Triangle = Paid $ t / Case O/S t-1 (12 to 24 = Paid at 24 / Case O/s 12)
    4b. Selections
  5. Project Incremental Paid = Selection paid on case x Projected Case O/S

Unpaid = Sum of the line under the triangle for a specific AY
*** Please don’t forget that it’s based on incremental paid !!! **

30
Q

Unpaid claims for Case Outstanding method #2 (Industry aka Self insurer)

A

Unpaid claims = Case O/S $$ X Case O/S Factor

Case O/S factor = (1- 1 / Paid CDF ) / (1/Rept CDF - 1/ Paid CDF)

31
Q

Berquist Sherman Paid method linear steps

Based on 1998 Q49

A
  1. CDR (Cumul Disposal rates triangle) and select the last diagonal
  2. Look at the DR which are different from the diagonal (Adjust wisely … if they ask you for unpaid for a specif year, adjust only this specific year, if it’s for Ultimates losses, well you have to adjust more years)
  3. Adjusted paid claims depends if the historical DR is greater or lower than selected DR.
    If it’s greater, you need to reduce your paid claim
    * Paid $$ t-1 + (Paid $ t - Paid t-1) * ( selected DR t - Hist t-1) / (Hist t -Hist t-1)

If it’s less, you need to increase your paid claim
* Paid $$ t + (Paid $ t+1 - Paid t) * ( selected DR t - Hist t) / (Hist t+1 -Hist t)

  1. If they ask for ultimate losses , you calculate the LDF and develop your losses as usual
32
Q

Berquist Sherman Paid method exponential steps

TIA Exam #3 Q21

A

Step 1: CDR triangle (Cumulative Disposal rates triangle)
2. Ajust your claim counts with the DR of the latest diagonal
3. Adjusted Cumulative claims = a x e^b x adjusted claim count

NOTE : The adjusted claim count depends on if your historical DR is greater or lower than selected DR
Greater = ajusted claim count t
Lower = ajusted claim count t + 1

33
Q

Berquist Sherman Both steps

A
  1. Adjust Paid triangle
  2. Adjust Avg Case O/S triangle
  3. Adjust open #
    =cumul rept # - Selected DR * ult claims #
  4. Adjusted reported claim $$ = adj avg case O/S * Adj open # + adj paid claims
34
Q

Recoverable Salvage and Subrogation

A

Ultimate S&S - Received S&S

35
Q

Steps S&S Recoverables

Based on Fall 19 Q22

A
  1. Ratio $$ S&S /Claim$$ triangle

Multiplicative approach
2. LDF and CDF of the triangle step 1
3. Calculate ult ratio = CDF x Latest ratio and do a selection
4. Ult S&S = Ult ratio x latest paid $ claim x cdf (if there some development needed)

Additive approach
LDF and CDF are additive

36
Q

Steps ALAE

Based on Spring 2019 Q24 and 2000 Q39

A
  1. Paid ALAE / Paid claim triangle
  2. LDF and CDF of the ratio you just calculated with multiplicative or additive
  3. Ult paid ALAE = Latest ratio x CDF x Ultimate claims $$
  4. Unpaid ALAE =Ult ALAE - Paid ALAE
    * Paid ALAE = Latest Ratio x Paid claims
37
Q

Unpaid ULAE Classical method

Based on Spring 2018 Q23

A

Main Formula is Unpaid ULAE = % Ratio ULAE x (100% Pure IBNR + 50% (Case O/S + IBNER)
* Pure IBNR = IBYR
* IBNER = known claims but not enough reported

Ratio ULAE = Paid ULAE / Paid Claims

38
Q

Unpaid ULAE Kittel method

Based on Spring 2018 Q23

A

Main Formula is Unpaid ULAE = % Ratio ULAE x (100% Pure IBNR + 50% (Case O/S + IBNER)
* Pure IBNR = IBYR
* IBNER = known claims but not enough reported

Ratio ULAE = Paid ULAE / Average of (Paid Claims and Incurred)

39
Q

ILF (500) avec Basic limit (100) Censored
Ranges (0-100, 100-250, 250-500)

Juste pour que tu te pratiques ! Exemple TIA ou Fall 2013 Q11

A

Voir les exemples
En gros ILF(500)= LAS(500)/ LAS(100 aka basic)
1. LAS (Basic limit)
Le fun commence, car tu dois faire des LAS itératifs

LAS(500) = LAS(250) + Pr(X greater than 250) x LAS(250 xs 250)
LAS (250 xs 250) = Somme Losses dans ce layer là (Ligne) - (Somme des counts # du layer ligne) x lower range amount + Nombre de loss qui seront cappés par l’excess car ils sont dans des layers supérieurs

Lower range amount pour layer 250 xs 250 est dans le layer 250 à 500 donc on prend count du layer et on le multiplie par 250

  • Pr( x greater than 250) = Somme Ligne d’en dessous count vu que c’est > 250 / Somme Colonne a droite, car limite supérieure a 250)

Répéter l’exercice pour LAS(250) car c’est aussi censuré ! donc tu dois recalculer le tout pour ton LAS(500)

CAS Exam 5 (5 decks)

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