This memo demonstrates the pricing models of manual base premium for Attaboy Basic, and required premium for Attaboy Plus at issue age 0, 5 and 10. Further analysis will be provided regarding to concerns raised from resulted premiums and their impact on company’s profitability and asset adequacy.
Attaboy Basic
The pricing model is built to calculate the monthly manual premium for Attaboy Basic, aiming to meet company’s target loss ratio. Below assumptions used in the model are generated from company’s cleaned data, or estimated by others, deemed reliable:
- $18.98 as base year billed PMPM (gross estimated amounts billed to customers by veterinarians without cost sharing)
- Annual trend of 10.7% of increase in PMPM
- Policy has a length of 16 months of trend based on projected sales date
- Benefit plan provides a 20% of coinsurance and estimated $1 of the PMPM cost of the deductible and limits
- Estimated $1.25 as fixed expense, 10% of premium as variable expense
The calculation starts from applying trend factor and trend length to the based year PMPM. The trended billed PMPM is estimated to be $18.98 x (1+10.7%)^(16 months / 12 months) = $21.73
Next, with coinsurance factor and deductible and limits, the cost sharing is estimated to be ($21.73 – $1) x 20% + $1 = $5.15
Thus, the claim cost after Benefit Plan is projected to be $21.73 – $5.15 = $16.58
Finally, to achieve company’s targeted loss ratio of 79.9%, the monthly premium should be equal to projected claim cost / loss ratio = $16.58 / 79.9% = $20.76.
Concern is raised since the profit level under manual premium of $20.76 turs out to be 4.1%, which is 2% short from company’s required profit level of 6.1%. In situation like this, various strategies through changing product feature, business operation or company policy could be considered to increase the profit level:
- Decrease Coinsurance or Cost of the deductible and limits
By changing these product features, insurer will cover more claim cost, and thus increase the premium. However, the higher premium may result in losing market competitiveness and customers. Moreover, the higher claim cost will further decrease the profit level, offsetting the effect from the premium.
For Attaboy, it is possible to lower the coinsurance factor. However, an decrease of 10% coinsurance factor only increases profit level by approximately 0.6%. Meanwhile, Attaboy can also lower $100 annual deductible since, according to the new data just received from Vet3 and Vet6, majority of the annual claims are less than deductible. However, decreasing deductibles, although increases premium, would not make effective impact on overall profit level since the company has to cover more claim amount. Therefore, this strategy is not recommended.
- Decrease expense
A lower fixed or variable expense will directly increase company’s profit level. Fixed expense such as rent cost, utilities cost or licenses cost are relatively difficult to cut. Employees’ fixed compensation can be cut by replacing labor with technology. Variable costs such as agents’ commission can also be decreased through adopting online sales platform. However, the cost of implementing new technology and training cost show also be considered.
If Attaboy can lower the variable expense by 2%, or the fixed expense per dollar PMPM by $0.4, the required profit level would be achieved. Discussion with business operation and management team is necessary to analyze the potential risk on business continuity.
- Increase investment income
Due to the long-term nature of insurance product, most insurance companies invest the reserve into financial market for an investment income, depending on companies’ risk appetite and tolerance level.
Based on Attaboy’s pricing model, an investment income of $0.4 per dollar PMPM would help reach the required profit level. However, there will be extra cost on time and labor in order to determine the investment strategy or setup investment projection model. Scenario testing should also be conducted to assess market risk.
- Reinsurance
With reinsurance, part of the claim will be covered by reinsurer, and thus decrease insurer’s claim cost, resulting in higher profit level. However, insurer needs to pay premium to reinsurer, resulting in less profit. Therefore, scenario testing should be performed to assess the effectiveness of the reinsurance.
Insurance companies are usually benefited through reinsurance for severe claim such as catastrophic events. However, most of Attaboy’s claims are high frequency but low severity. Therefore, this is not recommended for Attaboy.
- Lower target loss ratio
If companies set premium based on target loss ratio, it is possible to lower the loss ratio to set higher premium, and thus increase profit level. For Attaboy, this means lowering target loss ratio by 1.9%, from 79.9% to 78%. This is recommended only if prudent analysis has been performed based on company’s historical claim data as well as industry’s experience, proving that a 78% loss ratio is a plausible result.
Attaboy Plus
Since the premiums for Attaboy Plus, which pays a lump sum death benefit, vary by issue age but level for lifetime, the pricing model is built to project the cashflow for the 16 policy years, targeting a 20% internal rate of return (IRR) on distributable earnings. Below assumptions are implemented in the pricing model:
- Annual lapse rate of 1.1%
- 20% of first year premium as acquisition expenses, and $5 maintenance expenses per year per policy
- 3% of reserves as target surplus
- 35% income tax, and no DAC tax
- 5% rate of return on average reserves and beginning of year surplus balances
- 5% GPV DR (discount rate)
- Mortality rate by attained age from 0 to 30 years old
- End of year reserves per $1 of insurance by issue age and duration, determined by management
The number of policies EOY (end of the year) is first estimated as number of policies BOY (begin of the year) multiplied by survival rate, which is (1 – mortality rate of current attained age) x (1 – lapse rate). Each EOY Reserve, or BOY Reserve of the next year, is then calculated as the EOY reserves per $1 of insurance, multiplied by death benefit of $250, times EOY policies number. The TS (target surplus) for each year is, by requirement, 3% of the EOY reserve.
The distributable earnings for each policy year is subject to three components: after-tax income, change in TS and after-tax Inv Inc (Investment Income) on TS. With policy counts, After-tax income per policy is determined as the sum of (premium – expense) with 5% of GPV return, Inv Inc on average reserve, change in reserve, less total death benefit and income tax. In mathematical terms, this is represented as:
Distributable Earnings = After-tax Income + Change in TS + (Inv Inc on TS) x (1 – income tax)
Where
After-tax Income = ((Premium– Expense) per BOY policies x (1+GPV DR) + Inv Inc on (BOY Reserve + EOY Reserve)/2 + Change in Reserve – Death Benefit x number of deaths) x (1 – income tax)
After fitting assumptions and formula into the pricing illustration model, in order to achieve a 20% IRR on distributable earnings, the company requires a level annual premium at issue age 0, 5, and 10 are
| Issue Age | Annual Level Premium | Monthly Premium
(assuming UDD between integer ages) |
| 0 | $57 | $4.77 |
| 5 | $73 | $6.06 |
| 10 | $123 | $10.25 |
Gross premium valuation is one of the most prevalent methodologies to achieve asset adequacy for insurance companies, because reserves are calculated by directly discounting each Income Statement item, ensuring a positive cashflow in projected period. Based on a dissection of Attaboy Plus’s Income Statement items, holding gross premium reserves instead of the reserves given by management is equivalent to achieving a gross premium valuation discount rate, namely 5%, as IRR of distributable earnings. Comparing with the distributable earnings under 20% IRR, those under 5% IRR would be higher for each policy year, with the largest difference in the first policy year and gradually decreasing until termination.
