Chapter 11-Analysis of Surplus

Question 1

Outline the reasons for the change in surplus over a year? (10)

Answer 1

• Shows the financial effects of divergence of the valuation assumptions from the actual experience
• Furthermore it disclose the impact of new business volumes
• Various elements of the analysis of surplus can be used as checks for valuation data and results
• Assist in surplus distribution by indemnifying non-recurring elements in the surplus emerging
• Trends in elements of surplus may provide the company/management important information
• New items identified in the surplus may be used to inform risk identification process
• Assist in setting future assumptions
• Analyse the impact of policy alterations
• Assist in decision making e.g. de-risk the portfolio
• Required as part of statutory returns

Question 2

Outline the sources of surplus? (16)

Answer 2

o Change in valuation assumptions

o Release of compulsory/discretionary margins (IFRS only)
o Release of risk margin (prudential supervision basis only)
o Expected profit margin on group products (IFRS)

o Actual vs. expected investment return

o Actual vs. expected expenses

o Actual vs. expected mortality
o Actual vs. expected morbidity
o Actual vs. expected other risk benefits (e.g. retrenchment)

o Actual vs. expected withdrawals

o Actual vs. expected changes in unit-linked and with profit contracts
o Actual vs. expected tax

o New business

o Other policy alterations/changes

o Changes in maturity guarantee reserves

o Exercise options and guarantees

Question 3

outline the two approaches for determining the source of surplus? (3)

Answer 3

• An approach that involves the use of formula to build up the valuation liability over the year usually based on without profit products using net premium valuation method
• The second approach is the projection of assets and liabilities over the valuation year which can be applied to different types of business (requires recalculation of assets and liabilities on various bases)
• Even though the formula approach is not often used it can be used as a check for the projection approach

Question 4

If performing the analysis of surplus on a prudential basis what will influence the change in the risk margin? (4)

Answer 4

• Changes in the size of non-hedgeable components of SCR
• Assumptions regarding the run-off of non-hedgeable components of SCR
• Changes in the allowance of diversification within risk margin calculation
• Changes in business decisions that affect the risk margin such as reinsurance

Question 5

outline how to determine the surplus arising from valuation assumptions? (1)

Answer 5

• The effect of a change in the basis can be calculated by considering the value of liabilities at the beginning or end of the year

Question 6

outline the formula approach to calculating invetsmnet return surplus? (3)

Answer 6

• Actual investment income allocated to contracts (I) less
• Valuation interest rate (is this a simple rate?) accumulating reserves at the beginning of period to the end l (V0xi) less
• Net income (gross premium less actual claims less actual expenses) accumulated at valuation interest rate on assumption that cashflow is received halfway throughout the year 0.5i(P-E-C)

Question 7

outline the formula approach to calculating expense surplus? (4)

Answer 7

• Expected expenses as per the valuation assumption(E’) less
o This is the difference between office premium and net premium’
o Can be determined based on average number of contacts and proportion of premium that makes up expenses

• Part of actual expenses for business inforce at the start of the year (RE)
• Accumulated at the expected valuation interest rate assuming the payments occurred halfway through the year on average
• (E’-RE)(1+ix0.5)

Question 8

outline the formula approach to calculating mortality surplus? (4)

Answer 8

• Expected death strain less actual death strain (EDS-ADS)

• Expected death strain (approximation) consists of two components
o Capital at risk multiplied by expected mortality q(S-V)xk_1
o Loss of net future premium due to death q(P-E’)xk_1

• Actual death strain approximation is calculated as death payments plus premium not received due to death
• Accumulated to the end of the year assuming payments occur halfway throughout the year on average
• Less reserve held at the end of the year for contracts that existed due to death

Question 9

outline the formula approach to calculating morbidity surplus? (4)

Answer 9

Manchester Unity Method
• Expected sickness payment less actual sickness payment accumulated at valuation rate assuming payments are made half way throughout the year

Inception annuity method
• This is done in two parts
• Expected inceptions less actual inceptions multiplied by the annuity factor
• Actual terminations less expected terminations multiplied by the annuity factor

Question 10

outline the formula approach to calculating withdrawal surplus? (4)

Answer 10

• This is essentially calculated as reserves held accumulated to the end of the year plus
• Premium less withdrawal benefits accumulated to the end of the year assuming that timing occurs halfway throughout the year less
• Contribution from withdrawals to death strain

Question 11

outline the formula approach to calculating New business surplus? (3)

Answer 11

• Premiums (net of expected renewal expenses) less actual new business expenses
• Accumulated at valuation rate assuming new business occurring halfway throughout the year on average less
• Contribution of new business to expected death strain
• Less reserve at the end of the year for new business

Question 12

outline the calculation of surplus using a projection approach? (6)

Answer 12

i. Assets are allocated to contracts equal to the value of liabilities at the beginning of the year
ii. The assets and liabilities are projected to the end of the year using beginning of the year assumptions as expected experience over the year
iii. Calculate assets and liabilities at the end of the year using beginning of the year valuation assumptions
iv. Step (ii) and (iii) are repeated changing one item of the experience to its actual value
v. The recalculated surplus at the end of the year less the previous surplus calculated gives contribution of the item to surplus
vi. Steps (iv) and (v) are repeated for each item in the experience

Question 13

ouline actions that can be taken given the results from an analysis of surplus? (3)

Answer 13

• The results of an analysis of surplus may indicate that the design of a contract can be altered e.g. risk charges for a unit linked contract
• Result may also indicate that a change in basis assumptions are required
• Need to consider this in conjunction with the experience investigation and possibly industry experience