Required equity is determined based on a standard formula at the product level given a target risk based capital as outlined at the corporate level. Return on this equity is actually a recursive calculation using the following formula:
Return on Required Equity = Present Value of (After Tax Operating Income / Required Equity) over product lifetime.
The most efficient way to calculate this is to determine your required equity first, then use that as part of the after tax operating income at each point in time over the product’s life. Component wise this works according to the bullets below.
Required Equity Components
- C1-C4 Risk Amounts: these amount to percentages of projected statutory reserves and premium as determined by legal and corporate needs. For example the C2 risk amount might be 1% of premium and 6% of statutory reserves at a given time.
- RBC Target: this equals the desired RBC ratio for the product as set at a corporate level, for example 350%.
- Covariance: the trickiest component, this represents the discount that should be applied to the C1-C4 factors due to the fact that they are somewhat correlated, it could be 90% for instance.
- Deferred tax asset or liability: Given the timing of premiums and difference between statutory and best estimate reserve a given product will be paying taxes ahead of or behind schedule. As a proxy to a larger calculation many products could take the product of the tax rate and reserve difference between the statutory and best estimate values as the tax deferment.
The total required equity is equal to the sum of the C1-C4 amounts multiplied by the RBC Target and Covariance, plus the deferred tax asset.
Adjusted Operating Income Components
- Premium – Simply the amount of premium paid over time
- Benefits – Expected benefits each year, this is going to be a function of the reserve projection done for the C1-C4 equity calculation and should basically fall out of that.
- Expenses – Can be projected simply using fixed and variable percentages of premium by product or this could be an additional projection.
- Investment income on cash flows – As cash comes in there will be some return for holding it, this is equal to the product of the investment return on cash and the net cash flow (Premium – Benefits – Expenses – Change in Reserve).
- Investment income on reserves – Reserves are not stuffed under the mattress either but are invested, the projected reserve multiplied by an investment rate of return yields income as well.
- Investment income on required equity – Even the equity held in the steps above is invested and similarly can be multiplied by a projected investment return to estimate income.
- Corporate tax rate – Finally, the corporate tax rate is a factor in calculating adjusted operating income.
Note that several components of adjusted operating income are based on required equity and the reserves projected to get it! The formula for the final adjusted operating income over time is
Total adjusted operating income = (1-Corporate tax Rate)(Premium-Benefits-Expenses+Investment Income).
Yearly, the return on equity is equal to that year’s total adjusted operating income divided by the required equity as of the end of the year.
Overall the return on required equity is equal to the present value of future adjusted operating income divided by the present value of required equity, discounted at the corporate hurdle rate.