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GPV for Takaful

6 April 2012

Hassan Scott Odierno, FSA

Kuala Lumpur

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Actuarial Work in Takaful

• Pricing / Product

Development

• Risk Management /

Corporate Governance

• Valuation and Projections

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8 Step Process for Performing an Actuarial Valuation

• Data Accuracy

• Data Consistency

• Data Completeness

• Assumptions

• Methodology

• Calculations

• Results

• Report generation

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Why do we care about GPV?

With fair value accounting being implemented worldwide, our

actuarial reserves must be at best estimate plus padding.

With the old standard net premium valuation (NPV) basis it is

not clear if this is the case. Also, we must strive for fairness

with respect to surplus sharing, which can only be achieved if

assets and liabilities are using a best estimate approach

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How do we calculate GPV?

In GPV we estimate all cash flows including bonuses and take

their present value using best estimates plus padding

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How do we determine the padding?

Padding can be defined by a regulator as a certain increase

from base assumptions such as in South Africa or determined

at a percentile such as 75th percentile in Malaysia

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How do we determine the 75th percentile reserve?

We analyze the experience of each assumption getting the

mean, standard deviation, other descriptive statistics and fit to a

distribution such as normal or lognormal

Scenario 1 Scenario 2

Assets 1000 1000

VRBE 500 500

VRLCC 800 800

VR75 550 650

TCR 250 (800-550) 150 (800 – 650)

TCA 450 (1000-550) 350 (1000-650)

CAR 180% (450 / 250) 233% (350 / 150)

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Expense Analysis

Accuracy of the GPV reserves depends on accurate splits of

expenses of the operators fund between family and general

Takaful, group and individual, first year and renewal and

percent of contribution and per policy. Simplified methods such

as all expenses assumed to be at inception for single

contribution plans results in under reserving

Year Actual Expense Pricing

1 100 150

2 10 0

3 10 0

4 10 0

5 10 0

6 10 0

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Expense Overruns

If operations are still in the growth stage then expenses as well

as new business can be projected several years into the future

to determine expense assumptions. In this case there will be

expense overruns in the first few years which must be reserved

for

2011 2012 2013

A. Policies 2 4 8

B. Actual Expenses 1,000 1,100 1,200

C. Assumption (B/A) 500 275 150

D. Expense Assumptions 2011 2,000 4,000

E. Overruns / (Underruns) (900) (2,800)

F. Long Term Expense Assumptions (50) 200 400

G. Overruns / (Underruns) 900 800

H. Expense Assumptions 2013 600 1,200

I. Overruns / (Underruns) 500 0

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Expense confidence levels

One approach to confidence levels is to compare actual

expense levels versus those projected from management the

prior year to estimate managements ability to predict expense

levels

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Mortality experience splits

Potential splits in experience:

• Agency versus bancatakaful

• Level of underwriting

• Age or age band

• Males versus females

• Select versus ultimate period

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Mortality confidence levels

We need credibility (at least 64 deaths) in using subsets of data,

but the question is whether volatility is expected to vary by the

subsets. Collecting industry data by industry associations or

retakaful operators would be useful here, but need to account

for higher expected volatility of experience on an individual

basis

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Critical illness experience

There is very little critical illness experience available, company

or industry wide. As actuaries we are also much less confident

of how experience will emerge. Thus confidence interval

estimation will be a challenge. This is also where industry

associations or retakaful operator could assist

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Lapse / surrender analysis

Lapse experience is at minimum split by duration and single /

regular contributions. When calculating confidence levels we

need to test both high and low lapsation, which might change

over time even for the same policy. At issue is whether volatility

varies by duration.

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Projecting investment returns / discount rates

Two methods are used for investment return / discount rate

assumptions for the risk fund, best estimates plus padding or

the risk free yield curve. When using best estimates it is

important to have benchmarks by asset classes to allow

comparisons of volatility of benchmark versus actual experience

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Savings fund investment returns / discount rates

In GPV reserving for plans with savings accounts we need to

assess the probability of the savings fund to run out of money

and don’t allow for Tabaru’ drips in the risk fund once it does run

out. Padding would need to be included here

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Risk free yield curve

To calculate the risk free yield curve we obtain the yields to

maturity for key durations, interpolate by six month period, then

use bootstrapping in excel and goal seek to get the zero

coupon yields. This is difficult to obtain in most countries

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Operators fund GPV methodology

This is dependent on the model, but we take the present value

of outgo minus income:

• Outgo

• Management Expenses

• Commissions

• Taxation / Zakat

• Income

• Wakalah fees in whatever format

• Mudharabah investment sharing

• Risk fund surplus sharing

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Sterling Reserves

GPV is similar to sterling reserves, but sterling reserves are

slightly more conservative as some offsetting is not allowed

Year Cash Flow

1 (100)

2 50

3 50

Ignore discounting:

GPV = 0

Sterling = 100

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Risk fund GPV methodology

• Outgo

• Benefit payments

• Expenses (some models)

• Mudharabah investment sharing (some models)

• Retakaful contributions

• Income

• Tabarru’ drips (some models)

• Gross contributions net of wakalah fees (some models)

• Retakaful surplus sharing (some models)

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Following the bigger picture

Where we build conservatism into tabarru’ rates as a buffer we

must also build this into the valuation assumptions. If not the

buffer is completely released at inception

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Illustration of GPV

A mortgage reducing term Takaful (MRTT) drip plan is taken as

an example to show the changes from NPV to GPV in terms of

the reserve itself as well as on first year strain and overall

profitability

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MRTT Under NPV

Cash Flow NPV NPV Mort Change

NPV Reserving

Rate Change

GPV

A. Wakalah Fee 2,594 2,594 2,594 2,594

B. Mudharabah share Investment income from PIA

31 31 31 31

C. Investment Income of Operators Fund

4 4 4 9

D. Surplus share from Risk Fund 0 44 0 44

E. Management Expenses 210 210 210 210

F. Commission 1,038 1,038 1,038 1,038

G. Increase in expense reserve 0 0 0 139

H. Increase in solvency margin 0 0 0 802

I. Surplus after solvency and corporate tax (A+B+C+D-E-F-G -H) * (1-corporate tax)

1,036 1,069 1,069 367

J. Qard 2,738 0 0 0

K. Total Capital Available (H – I) 1,702 1,069 1,069 367

L. Reserves at end of year 1 2,874 0 0 0

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MRTT under NPV

Reserves and thus Qard under NPV drops tremendously once a

best estimate plus padding mortality table is used, but not much

of a change due to using the risk free yield curve. The final GPV

includes lapsation as well as solvency margin and expense

reserve.

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Conclusion

GPV in Takaful follows the same

processes and general methodology

as conventional insurance, but the

actuary must keep in mind both the

detail level issues specific to Takaful

as well as the big picture of how and

where reserves should be held.

Questions

hassan.odierno@actuarialpartners.com