Asset/liability Management for Universal Life

Grant PaulsenRimcon Inc.

November 15, 2001

Step 1: Split the product in two

InsuranceFund

Policyholderfund

Premiums

Return of fund ondeath or surrender

Risk chargesExpense charges

MER/spreadSurrender charges

Net death benefit(face value)

ReinsurancePremiums Benefits

Expenses

Taxes

Step 2: Match the policyholder fund

• For index linked accounts, buy the underlying index• Track liability balances on at least a weekly basis• Compare asset returns with index returns and

identify sources of tracking error– asset/liability mismatch– transaction costs– backdating– tracking of assets to index (i.e. exchange traded funds,

index futures)– tax effects

Step 3: Match the insurance fund (the hard part)

Reserve components of a typical UL policy:

Present value Duration

Risk charges 6,488,404 10

Net benefits (4,881,908) 21

Ceded premiums (2,157,152) 20

Ceded benefits 2,435,406 19

Expense charges 693,615 10

Expenses (566,236) ??

Surrender charges 248,522 ??

Commissions (1,641,296) 2

Investment income tax (455,153) ??

Crediting rate margin 304,609 ??

Net total 468,811

Note: figures vary (a lot) depending on age of policyholder, age of policy, policy features, fund types, MER levels, modeling assumptions.

If interest rates fall 1%

Present value

Risk charges 6,488,404 7,163,944

Net benefits (4,881,908) (6,475,137)

Net 1,606,496 688,807

A 1% rate decline removes $917,689 worth of profitability from the line of business. Reserves will increase by roughly this amount.

The largest risk is in the risk (COI) charge vs. net benefit cash flows

Annual Risk Charge Cash Flows

0

200,000

400,000

600,000

800,000

1,000,000

1,200,000

1,400,000

0 10 20 30 40 50 60

Annual Death Benefit Cash Flows (net of fund)

(1,400,000)

(1,200,000)

(1,000,000)

(800,000)

(600,000)

(400,000)

(200,000)

0

0 10 20 30 40 50 60

Combined Cash Flows for 1000 Policies($1 million of annual premium)

(1,500,000)

(1,000,000)

(500,000)

0

500,000

1,000,000

1999 2009 2019 2029 2039 2049 2059

Combined COI Charge +Death Benefit Cash Flows

ALM Problem: How do we lock in the reinvestment rate at time of issue

Reinvestment is assumed at product pricing rate

Combined Risk Charge + Benefit Cash Flows

(1,500,000)

(1,000,000)

(500,000)

0

500,000

1,000,000

1999 2009 2019 2029 2039 2049 2059

Inter-segment Notes

Annuity Asset & Liability Cash Flows

-800,000

-600,000-400,000

-200,000

0

200,000400,000

600,000

800,000

1999 2009 2019 2029 2039 2049 2059

1. “Sell” this cash flow to annuities.

2. Sell the asset that the inter-segment note replaces and transfer the cash from Annuities to Universal Life

$

3. Use the cash to buy long-dated assets that better match the liability profile.

Other cash flow components• Ceded cash flows

– premiums and benefits usually have similar durations– small positive cash flow (pricing vs. reserving assumptions)– long duration – offsets some death benefit cash flows

• Expense charges– generally fixed – same duration as premiums

• Expenses– interest rate theoretically = inflation + real interest rate– higher interest rates => higher inflation– theoretical duration is zero– how does valuation model treat inflation?

• Surrender charges– short term (generally 5 years or less)– surrenders (fund depletion) fall when interest rates rise

“Problem” cash flow components• Crediting rate margin

– depends on fund size => higher fund returns mean larger

fund and more crediting rate cash flows– when equity markets fall, future MER cash flows decline too– movement from equity linked to GICs reduces MERs– in high-return scenarios, fewer policies lapse– effective duration very sensitive to model assumptions and can

only be determined through scenario testing– do you believe the current 2-3% MERs will hold up for 40 years?

• Investment income tax– based on a 5-year moving average of 10-year Cda bond yields– you have to pay IIT even if equity returns are negative

• Expenses– interest rate theoretically = inflation + real interest rate

Summary• UL is far more complicated than most other insurance products – interest rate risk is potentially huge.• Cash flow dynamics are complex, and don’t depend only on interest rates. Duration (including key rate duration) is not sufficient.• Assumptions (including policyholder behavior) have a large impact on cash flow dynamics (and reserves).• You need a well thought out model.• You need to understand the valuation software well enough to be sure it is implementing the model correctly.• You need to sensitivity test the key assumptions.