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
