Editing Openai/695d4253-5060-8005-95db-586e777927f4 (section)

=== 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∑ipimax(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∑ipimax(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∑pi1(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∑pi1(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:
# 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)
# 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)
# 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.