Universal Life Insurance

Study guides: Exam ALTAM, Exam DISC-IA

Universal Life Insurance (UL) is a flexible-premium permanent life insurance policy built on a transparent account value: premiums are credited to the account, expense and cost-of-insurance charges are deducted, and interest is credited at a declared rate. The death benefit is either level (Type A) or the account value plus a fixed amount (Type B).

$AV_t = \left(AV_{t-1} + P_t - EC_t - CoI_t\right)\left(1 + i_t^{c}\right)$

$CoI_t = q^{*}_{x+t-1}\,v_q\,\left(DB_t - AV_t\right)$

$P_t$ is the premium (the policyholder chooses it, within limits), $EC_t$ the expense charge, $i^c_t$ the credited rate, $q^{*}$ the cost-of-insurance mortality rate and $v_q = 1/(1+i_q)$ the CoI discount factor. $DB_t - AV_t$ is the additional death benefit, the insurer's net amount at risk
Type A: $DB_t = FA$ , the face amount, so $CoI_t$ depends on $AV_t$ and the recursion is solved for $AV_t$ . Type B: $DB_t = FA + AV_t$ , so $CoI_t = q^{*}_{x+t-1}\,v_q\,FA$ directly
Corridor: to keep its tax status as insurance, the death benefit must be at least $c_t\,AV_t$ , where $c_t$ is the corridor factor; when this binds, $DB_t = c_t\,AV_t$ replaces $FA$ . A surrender pays the cash value $AV_t - SC_t$ , after a surrender charge
As a product: Universal life is a cash value policy whose premiums and face amount are both flexible. The owner may pay on any pattern, so long as enough is paid to keep the policy in force: if the account value falls too low to cover the charges, the coverage ends unless the owner pays more or reduces the benefits. Increasing the face amount may require new evidence that the insured qualifies. This flexibility is the key difference from whole life, whose premiums follow a set schedule.
The insurer's own profit test projects the account alongside its own interest, mortality and expense assumptions; a no-lapse guarantee keeps the cover in force when the account value runs out and needs a reserve of its own

One Year of a Type B Account A Type B UL policy has face amount $100{,}000$ and account value $5{,}000$ at the start of the year. The policyholder pays $2{,}000$ . The expense charge is $50$ plus $3\%$ of premium, $q^{*} = 0.004$ , $i_q = 4\%$ and $i^c = 4.5\%$ . Find the account value and death benefit at year end.
Answer $EC = 50 + 0.03(2{,}000) = 110$ .
 $\begin{align*} CoI &= 0.004(100{,}000)/1.04 \\ &= 384.62 \end{align*}$ 
 $\begin{align*} AV_1 &= (5{,}000 + 2{,}000 - 110 - 384.62)(1.045) \\ &= 6{,}505.38(1.045) \\ &= 6{,}798.13 \end{align*}$ 
The death benefit is $100{,}000 + 6{,}798.13 = 106{,}798.13$ : under Type B the amount at risk stays at the face amount, whatever the account does.

Type A Account Value With the Corridor Check A Type A UL policy has face amount $150{,}000$ and $AV_{t-1} = 20{,}000$ . The premium is $3{,}000$ , the expense charge is $100$ plus $2\%$ of premium, $q^{*}_{x+t-1} = 0.006$ , $i_q = 5\%$ , $i^c = 4\%$ and the corridor factor is $c_t = 2.5$ . Find $AV_t$ and $CoI_t$ .
Answer $EC = 160$ and $k = q^{*}v_q = 0.006/1.05 = 0.0057143$ . Assuming the corridor does not bind, $CoI_t = k(150{,}000 - AV_t)$ , so
 $\begin{align*} AV_t &= \frac{(20{,}000 + 3{,}000 - 160 - 150{,}000k)(1.04)}{1 - 1.04k} \\ &= \frac{22{,}862.17}{0.994057} \\ &= 22{,}998.85 \end{align*}$ 
 $\begin{align*} CoI_t &= 0.0057143(150{,}000 - 22{,}998.85) \\ &= 725.72 \end{align*}$ 
Check: $2.5(22{,}998.85) = 57{,}497 < 150{,}000$ , so the death benefit stays at the face amount and the assumption holds. Had the corridor bound, $DB_t = 2.5\,AV_t$ and the CoI would have been recomputed on $1.5\,AV_t$ .

How it appears on the exam

ALTAM gives the charges, credited rate and premium pattern and asks for the account value, cost of insurance, death benefit and cash value year by year for a Type A or Type B policy, including the corridor test, usually in a spreadsheet layout.

ALTAM then profit tests the policy: the insurer's cash flows (premium less charges is not profit — the account is the policyholder's), profit vector and signature, NPV, IRR, profit margin and discounted payback period, under best-estimate or stress assumptions, and reserves for a no-lapse guarantee.

DISC-IA asks for the features of universal life against whole life: flexible premiums, the visible account, the death benefit options and the cash value.

Exam traps

Charging Type A CoI on the face amount: the amount at risk is $FA - AV_t$ , and $AV_t$ appears on both sides, so the recursion has to be solved, not simply evaluated.

Using the credited rate $i^c$ to discount the CoI. The CoI discount is at $i_q$ , and the two rates are often different in the same question.

Skipping the corridor check, or doing it on $AV_{t-1}$ . It applies to the year-end account value, and when it binds the answer changes.

Treating policyholder charges as the insurer's mortality cost: in the profit test the insurer earns the CoI charge but pays the actual death claims on its own mortality basis.