CH 23 - 24 (Supervisory Reserves and Capital Requirements) Flashcards
Two Approaches to Liability Valuation
- Gross Premium
(*unit linked business is special case of gross) - Net Premium
Two Methods to Liability Valuation
- Discounted cash-flow
- Formula approach
Gross Premium
RESERVES = PV of Expected Future Benefits \+ PV of future expenses - PV of expected future office premiums
- Explicit allowance for…
> Expenses
> Bonuses - Future premiums are actual (office) premiums expected
- Differences between pricing and valuation bases will be taken as profit/loss (prudence would mean slower realisation of profits)
- Reserves may initially negative for non-linked business
(partly due to initial expenses, partly to capitalising expected future profit) - Reserves tend to quite sensitive to changes in basis
Net Premium Formula Method
RESERVES
PV of Expected Future Benefit Outgo (incl. prev declared bonuses)
-
PV of future NET (risk) premiums (based on initial guaranteed benefits only)
- Simple model (+simple data requirements)
- Only implicit allowance for…
> Future expenses
…assumption made implicitly by assuming difference between net and office premium is greater than future annual expenses
> Future bonuses
(only includes benefits previously declared)
…assumption made implicitly through difference between net premium and office premium; or through low valuation rate
- Reserves are relatively insensitive to changes in valuation basis
Market Consistent Valuation
aka “Fair Valuation”
Investment returns:
Risk free rate of return
Discount rates:
Risk free rate of return
Assets:
Market Value
Liabilities:
Replicating portfolio
or
Discounting CFs by RFR
Certain elements
(mortality/persistency/expenses)
don’t have a deep and liquid enough market to trade/hedge such risks.
Risk margin added to best discounted estimate liability as compensation for uncertain aspects
Risk Free Rate Determination
> Based on govt bond yields or swap
> May need to remove credit risk on these proxies (deduction)
> Sometimes can take credit for illiquidity premium
Risk Margins Methods
- CoC Methods:
Cost of Capital
=
Difference between actual interest and opportunity interest
Calculate capital required at each future period in excess of liabilities
- -> Multiply amounts by CoC
- -> Discount using market consistent rates for overall risk margin
- Assumption Method:
Margins on each assumption
Methods of solvency capital requirement
- VaR
- Simple formula
Passive vs Active Valuation Definitions
Passive:
- Relatively insensitive to changes in market conditions
- Updated relatively infrequently
Active:
- Based more closely on market conditions
- Assumptions updated on frequent basis
Passive vs Active Valuation Pros
SESI
Passive:
- Easier to implement
- less Subjective
- relatively Stable profit emergence
Active:
1. more Informative for understanding the impact of market conditions
Passive vs Active Examples
Passive:
Book value (assets),
Net premium valuation (liabilities),
Fixed % of liabilities (capital)
Active:
Market consistent valuation (assets + liabilities),
Risk-based approach (capital)
Two purposes for calculating reserves
1. Demonstrate Solvency (regulator) 2. Quantify realistic position of the company (shareholders + management: profitability, sustainability info)
Conditions that Regulator may require before allowing for negative reserves
- Total reserves (unit + non unit) > guaranteed surrender value
(Ensures company holding enough money if policy surrenders) - Future profits arising on policy with negative non-unit reserve need to emerge in time to repay ‘loan’ effectively made from other contracts with positive non-unit reserves
- No future valuation strain, after taking account of future non unit reserves
- In aggregate, sum of all non-unit reserves should not be negative (including reserves even from non unit contracts)
- Note even if negative non unit reserves allowed, for prudential valuation, safer to assume
» future CFs are lower than best estimates
» interest rate used is higher than best estimate
» survival rates are lower than best estimates
Value of the Unit Reserve (for Unit-Linked)
Number of units x Bid value
i.e. price at which life company is contractually obliged to buy the units from the policyholders at
Value of the Non-Unit Reserve (for Unit-Linked)
- The calculation process starts with the last projection period in which the net cashflow becomes negative.
- An amount is set up at the start of that period which is sufficient, allowing for earned investment return over the period, to “zeroise” the negative cashflow.
- This amount is then deducted from the net cashflow at the end of the previous time period.
- The process continues to work backwards towards the valuation date, with each negative being “zeroised” in this way.
- When the process has been completed, if the adjusted cashflow at the valuation date is negative then a non-unit reserve is set up equal to the absolute value of that negative amount
Calculation of NEGATIVE Non-Unit Reserve
(1) Project the expected future non-unit cashflow from the policy, ie income from charges less outgo.
(2) Identify the last (most distant) cashflow (whether positive or negative).
(3) Set the reserve as an amount needed to meet that cashflow at that point in time (even if the cashflow is positive set the non-unit reserve as a negative amount).
(4) Check that the total reserve (ie unit plus non-unit) is greater than the surrender value (ie unit reserve less surrender penalty).
(5) Move back to the next previous cashflow, discount the reserve and then subtract from the reserve the new cashflow at the earlier time period. Repeat step (4).
(6) Carry on repeating the process working backwards over time to the valuation date.
(7) This will give the required non-unit reserve.
