Openai/695d4253-5060-8005-95db-586e777927f4

This conversation was exported from ChatGPT

gpt-5-2-thinking

User: You are a chatGPT demonstrating its ability to work as an assistant to actuaries.

You are a chatGPT demonstrating its ability to work as an assistant to actuaries. To do so you need to take and answer like an actuary various FSA exam questions. Any instructions to answer in a Word document or Excel file are to be ignored, just answer in the chat.

Answers are to be clear, complete, but concise enough for a human grader to read them easily.

Here is the first question:

Assistant:

| | | |

| --- | --- | --- | | | | | | | | | | | | | | | | | | | | | | | | |

Plan sponsors (employers/unions):

• Total cost of coverage and cost predictability (rates, renewals, trend drivers)
• Value proposition: network strength, access, disruption analysis, provider discounts
• Administrative ease: eligibility, billing, reporting, implementation timeline
• Employee outcomes and productivity (care management, wellness, Rx management)
• Compliance and governance: plan documents, stop-loss coordination (if self-funded), reporting support

Consumers (members):

• Simplicity and transparency: what’s covered, cost-sharing, common use-cases
• Access: “Are my doctors/meds covered?” network and formulary clarity
• Out-of-pocket affordability: deductible/copays, Rx tiers, HSA compatibility
• Service experience: digital tools, prior auth friction, customer support
• Trust and brand: claims payment reliability, complaint history, quality signals

ACA Individual (commercial individual market):

• Product design is driven by ACA rules and competitive positioning: metal tiers/AV, EHB, cost-sharing structure, network and formulary strategy, exchange requirements and filing timelines.
• Major design objective: attract/retain profitable risk mix under community rating while managing morbidity via plan features (network tiering, cost-sharing, UM) and accounting for risk adjustment, CSR variants, and enrollment seasonality.
• Emphasis on consumer choice/price-point competition, broker/exchange shopping behavior, and rate review/MLR considerations.

Medicaid (managed care):

• Product design is driven by state/CMS contracting and procurement: benefits largely prescribed, eligibility/populations defined, and revenue via capitation under “actuarially sound” rate setting.
• Major design objective: meet contract requirements (network adequacy, access, quality measures, encounter reporting) and manage cost through care management, provider payment models, and compliance operations.
• Emphasis on operational capability, provider/community partnerships, quality/withhold performance, and state-specific program rules rather than consumer-driven plan differentiation.

User: Question 2:

Question 2:

Assistant:

- What to include: acquisition (commissions, underwriting, enrollment), maintenance (billing, customer service, claims ops), overhead/allocated corporate, regulatory/compliance, premium taxes/fees if treated as “expense load.”

• Cost behavior: separate fixed vs variable expenses (per contract, per member, per claim, % premium). Choose an expense basis consistent with how costs emerge.
• Allocation methodology: how overhead/shared services are allocated across products/segments; ensure consistency and avoid cross-subsidies that create anti-selection.
• Trending and efficiency: inflation, wage growth, vendor contracts, planned technology/process changes, scale effects.
• Volume and mix: expected enrollment/contract counts, persistency, group size distribution; impact on unit costs.
• Regulatory/market constraints: filing requirements, reasonableness, MLR impacts (commercial), competitive positioning.

###

• High volatility / low credibility of experience; greater random fluctuation and shock claims.
• Selection and persistency risk: easier to enter/exit; susceptibility to rate shopping and anti-selection.
• Rating constraints (if applicable) limit ability to charge appropriately for risk.

- More credible experience, but still exposed to catastrophic claims, benefit changes, and concentrated industry/geography risks.

• Negotiation/competitive pressure reduces attainable margin; retention risk at renewal.
• Trend leverage: a small pricing miss can create large dollar impacts.

- Concentration risk (a few accounts drive results); large dollar impact from any issue.

• High bargaining power → very thin margins; greater downside if mispriced.
• Catastrophic/complex claim management and network/provider disruption can materially affect outcomes.

Given net premiums:

Contract 1 = 50,000 Contract 2 = 30,000 Contract 3 = 45,000 Contract 4 = 60,000 Contract 5 = 75,000

Compute by contract:

• C1: 0.037×50,000=1,8500.037 \times 50{,}000 = 1{,}8500.037×50,000=1,850
• C2: 0.037×30,000=1,1100.037 \times 30{,}000 = 1{,}1100.037×30,000=1,110
• C3: 0.037×45,000=1,6650.037 \times 45{,}000 = 1{,}6650.037×45,000=1,665
• C4: 0.037×60,000=2,2200.037 \times 60{,}000 = 2{,}2200.037×60,000=2,220
• C5: 0.037×75,000=2,7750.037 \times 75{,}000 = 2{,}7750.037×75,000=2,775

Total proposed expense revenue:

• 1,850+1,110+1,665+2,220+2,775=9,6201{,}850 + 1{,}110 + 1{,}665 + 2{,}220 + 2{,}775 = 9{,}6201,850+1,110+1,665+2,220+2,775=9,620

- 9,620−10,000=−3809{,}620 - 10{,}000 = -3809,620−10,000=−380

Answer: expense revenue decreases by $380 overall.

(Distributional change vs $2,000: C1 −150, C2 −890, C3 −335, C4 +220, C5 +775.)

Goal 1: Encourage larger cases to enroll due to lower gross premiums YoY.

Likely not. A 3.7% load is higher than $2,000 once net premium exceeds 2,000/0.037≈54,0542{,}000 / 0.037 \approx 54{,}0542,000/0.037≈54,054. In the given data, the larger-premium contracts (60k and 75k) have higher expense charges (+$220 and +$775), which would increase gross premium for larger cases relative to the current method (all else equal). That works against attracting large cases.

Goal 2: Use technology to charge a lower overall expense amount for the book. Partially / directionally yes, because total expense revenue decreases from $10,000 to $9,620 (−$380). However:

• The reduction is modest (~3.8% of current expense revenue), and
• If expenses are largely fixed per contract, moving to a % of premium may under-collect on smaller cases and over-collect on larger cases, creating cross-subsidies and potential competitive issues.

Overall assessment: The change reduces total collected expenses slightly, but it shifts more expense burden to larger cases, so it does not align well with the stated objective of making large cases cheaper.

User: Question 3:

Question 3:

Assistant:

Key drivers of employee plan selection include:

• Employee premium contribution (payroll deduction) and perceived affordability.
• Expected out-of-pocket costs (deductible, copays/coinsurance, OOP max), especially given expected utilization.
• Risk preference / financial risk tolerance (preference for predictable copays vs high-deductible exposure).
• Health status and expected care needs (chronic conditions, planned procedures, Rx needs).
• Tax-advantaged features (e.g., HSA eligibility and employer HSA funding for CDHPs).
• Plan understanding / decision support (complexity, transparency tools).
• Family situation (single vs family tier; dependents’ expected use).
• Behavioral factors (status quo bias, inertia, prior-year satisfaction).

Given:

• Plan A premium = 400, expected MLR = 90% ⇒ expected claims at 100% morbidity = 400×0.90=360400 \times 0.90 = 360400×0.90=360
• Plan B premium = 600, expected MLR = 90% ⇒ expected claims at 100% morbidity = 600×0.90=540600 \times 0.90 = 540600×0.90=540
• Morbidity factors by risk group: 0.50, 0.60, 1.10, 1.20, 3.25

Plan A (50 employees):

mˉA=35(0.50)+10(0.60)+5(1.10)50=17.5+6.0+5.550=29.050=0.58\bar{m}_A=\frac{35(0.50)+10(0.60)+5(1.10)}{50} =\frac{17.5+6.0+5.5}{50}=\frac{29.0}{50}=0.58mˉA​=5035(0.50)+10(0.60)+5(1.10)​=5017.5+6.0+5.5​=5029.0​=0.58 Plan B (50 employees):

mˉB=15(0.60)+5(1.10)+20(1.20)+10(3.25)50=9.0+5.5+24.0+32.550=71.050=1.42\bar{m}_B=\frac{15(0.60)+5(1.10)+20(1.20)+10(3.25)}{50} =\frac{9.0+5.5+24.0+32.5}{50}=\frac{71.0}{50}=1.42mˉB​=5015(0.60)+5(1.10)+20(1.20)+10(3.25)​=509.0+5.5+24.0+32.5​=5071.0​=1.42

Plan A actual claims PEPM: 360×0.58=208.8360 \times 0.58 = 208.8360×0.58=208.8

Plan A actual LR: 208.8/400=0.522208.8 / 400 = 0.522208.8/400=0.522

Plan B actual claims PEPM: 540×1.42=766.8540 \times 1.42 = 766.8540×1.42=766.8 Plan B actual LR: 766.8/600=1.278766.8 / 600 = 1.278766.8/600=1.278

Total premium (50 at 400, 50 at 600):

P=50(400)+50(600)=20,000+30,000=50,000P = 50(400)+50(600)=20{,}000+30{,}000=50{,}000P=50(400)+50(600)=20,000+30,000=50,000 Expected claims (90% MLR):

E=0.90×50,000=45,000E = 0.90 \times 50{,}000 = 45{,}000E=0.90×50,000=45,000 Actual claims:

• Plan A: 50×208.8=10,44050 \times 208.8 = 10{,}44050×208.8=10,440
• Plan B: 50×766.8=38,34050 \times 766.8 = 38{,}34050×766.8=38,340

A=10,440+38,340=48,780A = 10{,}440 + 38{,}340 = 48{,}780A=10,440+38,340=48,780 \textbf{A/E} = \frac{48{,}780}{45{,}000} = 1.084 \quad \Rightarrow \quad \textbf{108.4%} (Equivalently, combined actual LR =48,780/50,000=97.56%=48{,}780/50{,}000=97.56\%=48,780/50,000=97.56%; A/E =97.56%/90%=108.4%=97.56\%/90\%=108.4\%=97.56%/90%=108.4%.)

If the universal rate change follows the account A/E, the indicated rate factor is 1.084 (an 8.4% increase).

New rates:

• Plan A: 400×1.084=433.60400 \times 1.084 = 433.60400×1.084=433.60
• Plan B: 600×1.084=650.40600 \times 1.084 = 650.40600×1.084=650.40

Employee contributions (rate − employer $400):

• Plan A: 433.60−400=33.60433.60 - 400 = 33.60433.60−400=33.60 (was 0)
• Plan B: 650.40−400=250.40650.40 - 400 = 250.40650.40−400=250.40 (was 200)

Illustration / implication: The employee price gap between B and A increases from $200 to $216.80, making Plan B relatively less attractive. Given Plan B already has much higher morbidity, this larger employee differential increases the likelihood that healthier employees move to Plan A and higher utilizers remain in Plan B, worsening selection (rate spiral risk).

Practical mitigations (any combination is acceptable):

1. Differentiated rate actions by plan (experience-based pricing) - Increase Plan B more (it is severely underpriced at LR ~128%) and hold flat/decrease Plan A (LR ~52%) rather than a uniform increase. - Justification: reduces cross-subsidy that otherwise encourages healthy migration to A and leaves B underpriced.
2. Change employer contribution strategy to preserve relative affordability - Contribute a percentage of premium (e.g., 80%) or contribute more to Plan B to keep employee differential stable. - Justification: reduces employee-driven anti-selection driven by payroll deduction differences.
3. Implement enrollment/plan-switching controls - Limit mid-year moves; default mapping; active enrollment with decision support; minimum commitment period. - Justification: reduces opportunistic switching based on emerging claims.
4. Adjust plan designs to reduce selection (if permitted) - Narrow the “buy-up” value gap (e.g., align deductibles/OOP features; add HSA seed funding to CDHP; or enhance value-based benefits in A). - Justification: lowers incentive for healthy/low utilizers to disproportionately choose one plan.

Any of the above directly targets the root issue: material morbidity sorting (A ~58% vs B ~142%) that a uniform rate change is likely to exacerbate.

User: Question 4:

Question 4:

Assistant:

- Legislative/regulatory changes: ACA/ERISA, HIPAA, MHPAEA, COBRA, transparency rules, surprise billing, state mandates, Medicare/Medicaid policy shifts that affect providers/prices, tax rules affecting HSAs/FSAs and employer contributions.

• Healthcare cost and market trends: local unit cost inflation, provider consolidation and contracting dynamics, price transparency effects, site-of-care shifts, new high-cost therapies (gene/cell), specialty Rx pipeline and rebates/PBM changes.
• Labor market / competitive benefits environment: what peer employers offer, recruiting/retention pressures, union negotiations, wage inflation (tradeoff between pay and benefits).
• Vendor landscape and performance: carrier/TPA capabilities, PBM and network changes, telehealth vendors, care management outcomes, service levels, and fee trends.
• Provider network/access environment: network adequacy, provider shortages, facility closures, referral patterns, quality/outcomes and patient experience.
• Population health and public health: epidemics/pandemics, behavioral health trends, substance use patterns, local health shocks affecting utilization.
• Litigation/enforcement climate: MHPAEA audits, fiduciary scrutiny (especially around PBM compensation), privacy/security enforcement and breach risk.
• Technology and cybersecurity: interoperability requirements, claims/eligibility transaction standards, cyber threats affecting vendors and employee data.

- Plan designs differ materially (deductibles, copays, coinsurance, OOP max, tiering), and even “similar” plans can produce different member costs depending on utilization.

• Different populations and geographies: demographics, morbidity, income, family mix, provider pricing levels, and market competitiveness vary.
• Funding and accounting differ: fully insured vs self-insured, stop-loss structure, reserves, and treatment of admin fees/rebates can vary.
• Network/PBM differences: contracted rates, formularies, utilization management, and care management programs affect value beyond benefit text.
• Employer contribution strategies differ: percent-of-premium vs flat-dollar, tiers, and wellness incentives change employee affordability and selection.
• Data limitations: incomplete disclosures on rebates/fees, differing measurement periods, and inconsistent metrics.

- Standardized actuarial value / richness metrics: estimate AV or expected paid-to-allowed using a common claim model.

• Benchmarking to a reference plan: normalize to a common plan design and price using the same allowed-cost basis.
• Scenario-based employee cost modeling: compare total cost (premium contribution + expected OOP) for standardized utilization profiles (low/medium/high, chronic condition scenarios) and by coverage tier (single/family).
• Total cost of coverage metrics: employer + employee spend, PEPM allowed and paid, admin load, and trend—adjusted for geography and demographics.
• Benefit scorecards: incorporate non-benefit features (network disruption, Rx coverage, UM rigor, care management, quality/service metrics) with weighted scoring.
• Peer surveys and broker benchmarks: use credible market surveys for prevalence of plan types and contribution strategies, adjusted for industry/region.

User: Question 5:

Question 5:

User: One more piece of 5:

One more piece of 5:

Assistant:

- Utilization: scripts/1,000, days supply mix (30/90), retail vs mail, specialty utilization, adherence impacts, induced utilization from benefit changes.

• Unit cost: ingredient cost basis (AWP/WAC/MAC), negotiated discounts, dispensing/admin fees, network differentials, specialty channel management.
• Mix: generic/brand/specialty mix, formulary tier migration, biosimilar uptake, pipeline/new-to-market drugs.
• Rebates & other recoveries: manufacturer rebates (guaranteed vs performance), DIR/price concessions, spread vs pass-through, timing/settlement risk.
• Trend and seasonality: price inflation, utilization trend, patent cliffs, one-time shocks.
• Member cost share: copays/coinsurance, deductibles, maxs, accumulator policies; elasticity/selection effects.
• Credibility & risk: experience credibility, pooling/high-cost claim volatility, margin/risk load, competitive constraints and MLR impacts (if applicable).

Assumption: ingredient reimbursement = AWP × (1 − discount); then add dispensing fee, vaccine fee, sales tax.

Given AWP (ingredient basis) = $80, sales tax = 0%, vaccine fee = $1.

• New ingredient reimbursement: 80×(1−0.72)=80×0.28=22.4080 \times (1 - 0.72) = 80 \times 0.28 = 22.4080×(1−0.72)=80×0.28=22.40
• Add fees: 22.40+1.50+1.00=24.9022.40 + 1.50 + 1.00 = 24.9022.40+1.50+1.00=24.90

New allowed amount = $24.90

Given: nominal copay = $15, dispensing fee = $1.50, discount = 80%.

Assumptions:

1. Allowed per Rx = AWP×(1−0.80)+1.50=0.20×AWP+1.50 \text{AWP} \times (1-0.80) + 1.50 = 0.20\times \text{AWP} + 1.50AWP×(1−0.80)+1.50=0.20×AWP+1.50.
2. Member pays the lesser of nominal copay and allowed (copay cannot exceed allowed).
3. Ignore taxes/vaccine fee for this part (not provided).

Compute allowed and member pay by AWP band (use given average AWP per script):

| | | | | | | --- | --- | --- | --- | --- | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |

Effective copay:

0.20(3.10)+0.20(7.50)+0.25(15)+0.15(15)+0.20(15)=0.62+1.50+3.75+2.25+3.00=11.120.20(3.10) + 0.20(7.50) + 0.25(15) + 0.15(15) + 0.20(15) = 0.62 + 1.50 + 3.75 + 2.25 + 3.00 = 11.120.20(3.10)+0.20(7.50)+0.25(15)+0.15(15)+0.20(15)=0.62+1.50+3.75+2.25+3.00=11.12 Effective copay = $11.12

Given: sales tax 0%, vaccine fee $1.00, dispensing fee $1.50, ingredient cost $77.00, discount 72.0%, pharmacy rebates 5.0%.

Step 1 — Allowed amount

• Ingredient reimbursement: 77.00×(1−0.72)=77.00×0.28=21.5677.00 \times (1 - 0.72) = 77.00 \times 0.28 = 21.5677.00×(1−0.72)=77.00×0.28=21.56
• Allowed total: 21.56+1.50+1.00=24.0621.56 + 1.50 + 1.00 = 24.0621.56+1.50+1.00=24.06

Assumption for rebates: rebate is 5% of ingredient cost ($77) and accrues to the plan (member cost share unaffected). Rebate = 0.05×77.00=3.850.05 \times 77.00 = 3.850.05×77.00=3.85.

- Member (gross): 0.20×24.06=4.812≈4.810.20 \times 24.06 = 4.812 \approx 4.810.20×24.06=4.812≈4.81

• Plan (gross): 24.06−4.81=19.2524.06 - 4.81 = 19.2524.06−4.81=19.25 (rounding to cents)
• Plan (net of rebate): 19.25−3.85=15.4019.25 - 3.85 = 15.4019.25−3.85=15.40

Result (20% coinsurance):

• Member = $4.81
• Plan = $15.40 net (gross $19.25 less $3.85 rebate)

- Member (gross): min⁡(16.00,24.06)=16.00\min(16.00, 24.06)=16.00min(16.00,24.06)=16.00

• Plan (gross): 24.06−16.00=8.0624.06 - 16.00 = 8.0624.06−16.00=8.06
• Plan (net of rebate): 8.06−3.85=4.218.06 - 3.85 = 4.218.06−3.85=4.21

Result ($16 copay):

• Member = $16.00
• Plan = $4.21 net (gross $8.06 less $3.85 rebate)

User: Question 6:

Question 6:

Assistant:

Prospective experience rating

• Premium is set in advance for the rating period using expected claims (often credibility-weighted experience, trend, benefit changes, etc.).
• Carrier retains favorable results (profit) and bears unfavorable results (loss) during the period.
• Simpler to administer; aligns premium with expected cost, but the customer may feel they “overpaid” if experience is good.

Retrospective experience rating

• Premium is adjusted after the fact (or a refund/dividend is paid) based on actual experience (often with corridors, minimum/maximum, and pooling).
• Shares results between carrier and customer; reduces customer’s cost when experience is favorable but also can introduce settlement timing/complexity.
• If not symmetric (e.g., refunds on gains but no surcharge on losses), it is effectively a one-sided option granted to the customer.

Note: The screenshots do not include the actual net premium and developed claims by year, so I can’t produce numeric totals. Below is the exact calculation method (what a grader expects), which you can apply once the 20X1–20X3 PyP_yPy​ and CyC_yCy​ are provided.

Let PyP_yPy​ = net premium in year yyy, CyC_yCy​ = fully developed claims in year yyy. Target net loss ratio = 96% ⇒ target profit margin = 4%.

Profit in year yyy:

Πycurrent=Py−Cy\Pi^{\text{current}}_y = P_y - C_yΠycurrent​=Py​−Cy​ Total 20X1–20X3:

Πcurrent=∑y=20X120X3(Py−Cy)\Pi^{\text{current}} = \sum_{y=20X1}^{20X3} (P_y - C_y)Πcurrent=y=20X1∑20X3​(Py​−Cy​)

- “Excess profit” = profit above 4% of premium.

• Refund in year yyy:

Ry=max⁡(0, (Py−Cy)−0.04Py)=max⁡(0, 0.96Py−Cy)R_y=\max\big(0,\ (P_y-C_y)-0.04P_y\big)=\max\big(0,\ 0.96P_y-C_y\big)Ry​=max(0, (Py​−Cy​)−0.04Py​)=max(0, 0.96Py​−Cy​)

• Green’s profit after refund:

Πyproposal=(Py−Cy)−Ry=min⁡(Py−Cy, 0.04Py)\Pi^{\text{proposal}}_y = (P_y-C_y)-R_y = \min\big(P_y-C_y,\ 0.04P_y\big)Πyproposal​=(Py​−Cy​)−Ry​=min(Py​−Cy​, 0.04Py​) Total 20X1–20X3:

Πproposal=∑ymin⁡(Py−Cy, 0.04Py)\Pi^{\text{proposal}}=\sum_{y}\min\big(P_y-C_y,\ 0.04P_y\big)Πproposal=y∑​min(Py​−Cy​, 0.04Py​) (Operationally: compute LR each year =Cy/Py=C_y/P_y=Cy​/Py​. If LR < 96%, cap profit at 4% of premium; if LR ≥ 96%, no refund.)

Key concerns:

• Asymmetric risk sharing: Green gives away upside when experience is good, but still absorbs full downside when experience is bad. That is equivalent to giving the customer a free call option on results, which reduces expected profit and increases required capital.
• Volatility / capital strain: With large groups, random fluctuation is smaller than small groups, but severity risk (shock claim years) remains material; removing upside reduces Green’s ability to offset bad years.
• Lapse/anti-selection risk: Groups may stay after good years (collect refunds) and shop/terminate after bad years, worsening Green’s long-run results.
• Settlement lag & disputes: Requires fully developed claims and clear definitions (runout, pooling, eligibility changes), increasing administrative burden and the risk of disagreement.
• Pricing implication: If offered, the expected cost of the refund feature should be explicitly priced (either via higher premium or explicit risk charge), otherwise target LR will not be achieved.

Again, the numeric inputs (annual Py,CyP_y, C_yPy​,Cy​ and the list of claimants ≥$1M by year) are not shown, so below is the required calculation structure.

For each year yyy:

• Target claims threshold: Ty=0.96PyT_y = 0.96P_yTy​=0.96Py​
• Refund: Ry=max⁡(0, Ty−Cy)R_y=\max(0,\ T_y-C_y)Ry​=max(0, Ty​−Cy​)
• Green profit: Πy=min⁡(Py−Cy, 0.04Py)\Pi_y=\min(P_y-C_y,\ 0.04P_y)Πy​=min(Py​−Cy​, 0.04Py​)

Let high-claimant annual costs be Hy,iH_{y,i}Hy,i​ for claimants with ≥$1M in claims.

• Stop-loss recoveries:

Recovy=∑imax⁡(0, Hy,i−1,000,000)\text{Recov}_y=\sum_i \max(0,\ H_{y,i}-1{,}000{,}000)Recovy​=i∑​max(0, Hy,i​−1,000,000)

• Net claims after stop loss:

CySL=Cy−RecovyC^{\text{SL}}_y = C_y - \text{Recov}_yCySL​=Cy​−Recovy​

• Add pool charge cost:

Pooly=0.01Py\text{Pool}_y = 0.01P_yPooly​=0.01Py​

• “All-in” cost used for profit sharing:

C~y=CySL+Pooly\tilde{C}_y = C^{\text{SL}}_y + \text{Pool}_yC~y​=CySL​+Pooly​ Then apply the same profit-sharing rule (96% target unless changed):

ΠySL=min⁡(Py−C~y, 0.04Py)\Pi^{\text{SL}}_y = \min\big(P_y-\tilde{C}_y,\ 0.04P_y\big)ΠySL​=min(Py​−C~y​, 0.04Py​) Interpretation: lowers volatility by capping severity, but reduces expected profit by the pool charge; net benefit depends on how large Recovy\text{Recov}_yRecovy​ is relative to 0.01Py0.01P_y0.01Py​.

This changes the target net LR from 96% to 95%.

• Target claims threshold: Ty=0.95PyT_y = 0.95P_yTy​=0.95Py​
• Green profit under proposal becomes:

Πy5%=min⁡(Py−Cy, 0.05Py)\Pi^{5\%}_y = \min\big(P_y-C_y,\ 0.05P_y\big)Πy5%​=min(Py​−Cy​, 0.05Py​) (If combined with stop loss, replace CyC_yCy​ with C~y\tilde{C}_yC~y​ above.)

Interpretation: improves Green’s retained upside (higher cap), reduces refund frequency/amount, better compensates for volatility and the “optionality” granted to the group.

Define (using target LR 96% unless changed):

• Excess profit available for sharing in year yyy:

EPy=max⁡(0, 0.96Py−C~y)EP_y=\max(0,\ 0.96P_y-\tilde{C}_y)EPy​=max(0, 0.96Py​−C~y​)

• Excess loss above target in year yyy:

ELy=max⁡(0, C~y−0.96Py)EL_y=\max(0,\ \tilde{C}_y-0.96P_y)ELy​=max(0, C~y​−0.96Py​) Let fund balance at start of year yyy be Fy−1F_{y-1}Fy−1​, with F0=0F_0=0F0​=0, cap Fmax⁡=500,000F_{\max}=500{,}000Fmax​=500,000.

Use fund to offset bad years first:

Uy=min⁡(Fy−1, ELy)U_y=\min(F_{y-1},\ EL_y)Uy​=min(Fy−1​, ELy​) Remaining excess loss borne by Green:

ELynet=ELy−UyEL^{\text{net}}_y = EL_y - U_yELynet​=ELy​−Uy​ Then credit favorable-year share into the fund up to the cap:

Deposity=min⁡(EPy, Fmax⁡−(Fy−1−Uy))\text{Deposit}_y = \min(EP_y,\ F_{\max}- (F_{y-1}-U_y))Deposity​=min(EPy​, Fmax​−(Fy−1​−Uy​)) Any excess beyond filling the fund is distributed:

Distributiony=EPy−Deposity\text{Distribution}_y = EP_y - \text{Deposit}_yDistributiony​=EPy​−Deposity​ Fund recursion:

Fy=min⁡(Fmax⁡, Fy−1−Uy+Deposity)F_y = \min\big(F_{\max},\ F_{y-1}-U_y + \text{Deposit}_y\big)Fy​=min(Fmax​, Fy−1​−Uy​+Deposity​) Green profit each year (profit-sharing with fund):

• Green retains the target margin, less any net excess loss not covered by the fund:

Πyfund=0.04Py−ELynet\Pi^{\text{fund}}_y = 0.04P_y - EL^{\text{net}}_yΠyfund​=0.04Py​−ELynet​

• If the policy terminates after 20X3, add the retained fund balance as additional profit:

Πfund,total=∑yΠyfund+F20X3\Pi^{\text{fund,total}} = \sum_y \Pi^{\text{fund}}_y + F_{20X3}Πfund,total=y∑​Πyfund​+F20X3​ Interpretation: reduces refund payouts in early good years, creates a buffer against future bad years, and (because Green keeps the balance at termination) materially improves Green’s expected value—though it may be viewed as less favorable/less transparent to the customer.

1. Net premium PyP_yPy​ and developed claims CyC_yCy​ for 20X1–20X3

1. For the stop-loss option: the list of Hy,iH_{y,i}Hy,i​ (annual claim totals by claimant for those ≥$1M)

If you paste those figures, I’ll compute the exact totals and show the full arithmetic.

User: Question 7:

Question 7:

Assistant: 7a Definitions in Total Risk Assessment TRA

7(a) Definitions in Total Risk Assessment (TRA)

(i) Starting Value Risk

Risk that the baseline best estimate of expected claim cost (e.g., PMPM) is wrong before applying future adjustments, due to issues such as:

• incomplete/immature claims, IBNR/lag, or claim development error
• data quality/coding or eligibility errors
• credibility limitations / non-representative experience period
• mix changes not recognized (plan, network, geography, demographics) In short: uncertainty in the starting point of expected cost.

(ii) Assumption Risk

Risk that model assumptions used to project from the starting value are wrong, e.g.:

• medical and Rx trend (price vs utilization), seasonality
• leverage from benefit changes, cost-share behavior, network changes
• vendor program impacts (care management, PBM guarantees)
• large-claim frequency/severity assumptions In short: uncertainty in the projection assumptions applied to the baseline.

7(b) Random Variation Risk

(i) Describe Random Variation Risk

Random Variation Risk is process/stochastic risk: even if the expected cost and assumptions are correct, actual annual claims will vary due to the randomness of:

• incidence (who gets sick, how many events occur)
• severity (how expensive events are, catastrophic claims)
• timing (when services occur, seasonality) It is typically modeled with a probability distribution around the mean; it generally shrinks with larger covered lives (roughly proportional to 1/N1/\sqrt{N}1/N​ for many aggregate measures) but remains meaningful because healthcare severity is heavy-tailed.

(ii) Two sketches that illustrate Random Variation Risk (in table form)

Graph 1: Distribution of annual cost around expected A simple “bell/right-skewed” shape: most outcomes near the mean, with a right tail.

| Annual cost outcome | Probability (illustrative) | | ----------------------------- | -------------------------- | | Very low | Low | | Low | Moderate | | Near expected | Highest | | High | Moderate | | Very high (catastrophic tail) | Low |

Graph 2: Volatility vs group size Random variation decreases as covered lives increase.

| Covered lives (N) | Relative volatility of annual PMPM (illustrative) | | ----------------- | ------------------------------------------------- | | 500 | High | | 2,000 | Medium | | 10,000 | Low | | 50,000 | Very low (but not zero) |

(Conceptually: standard deviation of aggregate PMPM often scales roughly like 1/N1/\sqrt{N}1/N​, while the tail remains influenced by catastrophic risk.)

7(c) Risk measures (method and formulas)

Your prompt references a “table below” that is in the Excel file (not visible here). Without the scenario/probability table, I cannot compute numeric values, but the required calculations are:

Let:

• SiS_iSi​ = total annual claims (or total annual cost) under scenario iii
• pip_ipi​ = probability of scenario iii (sums to 1)
• BBB = annual budget (in dollars)
• MMM = member months in the year (members × 12)

(i) Expected excess or shortfall PMPM

• Expected excess (above budget) PMPM:

Excess PMPM=∑ipimax⁡(0, Si−B)M\text{Excess PMPM}=\frac{\sum_i p_i\max(0,\ S_i-B)}{M}Excess PMPM=M∑i​pi​max(0, Si​−B)​

• Expected shortfall (below budget) PMPM:

Shortfall PMPM=∑ipimax⁡(0, B−Si)M\text{Shortfall PMPM}=\frac{\sum_i p_i\max(0,\ B-S_i)}{M}Shortfall PMPM=M∑i​pi​max(0, B−Si​)​ (Some exams accept “expected deviation” as ∑pi(Si−B)/M\sum p_i(S_i-B)/M∑pi​(Si​−B)/M; clarify which is intended.)

(ii) Chance of exceeding the budget

P(S>B)=∑ipi1(Si>B)P(S>B)=\sum_i p_i\mathbf{1}(S_i>B)P(S>B)=i∑​pi​1(Si​>B)

(iii) Chance of exceeding the budget by $12M or more

P(S≥B+12,000,000)=∑ipi1(Si≥B+12,000,000)P(S\ge B+12{,}000{,}000)=\sum_i p_i\mathbf{1}(S_i\ge B+12{,}000{,}000)P(S≥B+12,000,000)=i∑​pi​1(Si​≥B+12,000,000)

7(d) PAD adequacy and risk-reduction actions

(i) Assess adequacy of current PAD assumption of 5%

A 5% PAD is adequate only if it meaningfully reduces the probability and severity of budget overruns to the CFO’s tolerance level.

How to assess (what a grader wants):

• If the budget is set as B=E[S]×(1+0.05)B = E[S]\times(1+0.05)B=E[S]×(1+0.05), then test whether: - P(S>B)P(S>B)P(S>B) is acceptable (e.g., <10% or whatever threshold governance uses), and - tail exposure (e.g., P(S>B+12M)P(S>B+12M)P(S>B+12M), expected excess PMPM) is acceptable.
• If P(S>B)P(S>B)P(S>B) remains high or the expected excess PMPM is material, then 5% is not adequate—either because: - assumption risk is larger than 5%, and/or - random variation / catastrophic tail dominates and PAD alone is the wrong tool (needs risk transfer).

Bottom line: PAD is meant to cover assumption/model uncertainty; if exceedance risk is largely driven by random variation/catastrophic claims, a PAD increase may be inefficient versus stop-loss or pooling.

(ii) Actions ABC can take to reduce chances of exceeding budget

Practical levers fall into risk transfer, budgeting/capital, and cost control:

1. Risk transfer / financing - Purchase or tighten specific stop-loss and/or aggregate stop-loss - Implement pooling/captive strategy for catastrophic claims - Introduce a stabilization reserve/fund (explicit contingency)
2. Budgeting / governance - Increase PAD (if assumption risk is the driver) or set budget to a chosen percentile (e.g., P75/P90) - Improve forecasting cadence (monthly monitoring, emerging experience triggers)
3. Cost and utilization management - Strengthen UM: prior auth, step therapy, site-of-care management - High-cost claimant management: case management, centers of excellence - Network strategies: steerage, reference-based pricing (where appropriate), narrow/high-performance networks - Rx management: formulary optimization, specialty management, biosimilar adoption - Benefit design changes (higher member cost share, deductible/OOP adjustments) if consistent with HR goals

These actions directly reduce either the mean, the variance, or the right-tail of claims—each of which can reduce budget exceedance risk.

If you provide the scenario/probability table from the spreadsheet (even pasted as text), I will compute the numeric answers for 7(c) and evaluate PAD=5% quantitatively against those results.