ALTAM SOA EXAM QUESTIONS AND
ANSWERS
Justify the assumption of no lapses for this new policy - Correct Answers -Since this is a
single premium product, after the premium is paid, the only potential cash flow will be
the benefit payment from the insurer to the insured. Thus, the insured would have no
reason to lapse this policy; lapsing could only be detrimental to the policyholder, it could
never be beneficial in terms of the possible future cash flows. This is opposed to the
case where the policyholder pays an annual premium; in this case, the insured might
decide that the potential future benefit from the insurer is not sufficient to continue to
pay the annual premium.
Explain why the expected present value of the death benefit is greater for this new
policy than for the original policy (original policy has decrement 2 as lashes, new policy
has no lapses) - Correct Answers -Because lapses have been eliminated, mortality will
act on a larger portion of the population, resulting in a larger number of deaths and
hence a greater EPV of death benefits.
Explain why we use the q's calculated in part A (q without ') for the EPV(benefit) but the
q(')'s given for the EPV(prem)? - Correct Answers -The EPV of premiums requires
surviving. It is easier to calculate the surviving probability by using p, which is the
product of surviving the independent p's. But, for the death benefit, it is failing and it is
easier to get the failing probability from the dependent model since that is what we
ultimately need. In other words, we only pay the death benefit if it "beats" the competing
lapse decrement.
Explain in words difference between q^(j) and q^'(j) and why q^(j) <= q^'(j) - Correct
Answers -q^(j) is the probability that a life age x fails due to decrement j under the
multiple decrement model. q^'(j) is the probability that a life age x fails due to decrement
j under the associated single decrement model.
Under the multiple decrement model, all other decrements besides j are also competing
as the cause of failure. Under the associated single decrement model, each decrement
is considered in isolation.
Since the multiple decrement model has all decrements competing as the cause of
failure, the life is less likely to fail due to decrement j, relative to the associated single
decrement model, where decrement j does not compete with other decrements.
Describe two ways that dependency is incorporated in this model (joint life). The middle
has both alive (state 0). That can go left to both dead(state 4) or right where (x) is alive
,and (y is dead) (state 1), or where (x) is dead, (y) is alive. Also has a path from state 1
to state 3 which has both dead. Can also go from state 2 to 3. - Correct Answers -
Common shock: The lives can transition from State 0 (both alive) to State 4 (both dead)
directly, which means there is a positive probability of simultaneous deaths. Because
the lives can die at the same time, they are dependent.
Broken heart syndrome: A condition where the mortality of a person is higher after the
death of another person due to a "broken heart." Both lives in this model exhibit the
possibility of a broken heart syndrome. The mortality for (x) after the death of (y), mu13
x+t:y+t = 1.2mu* x+t , is higher than the mortality for (x) when (y) is alive, which is mu02
x+t:y+t = mu* x+t - .0005. Similarly, the mortality for (y) after the death of (x), mu23
x+t:y+t = 1.05mu* y+t , is higher than the mortality for (y) when (x) is alive, which is
mu01 x+t:y+t = mu* y+t - .0005.
Without further calculation, state whether the change in the normal contribution rate
would be greater or smaller under Projected Unit Credit funding. Justify your answer. -
Correct Answers -TUC contribution starts smaller than the PUC contribution since TUC
uses salary based on current age rather than salary projected to exit dates. However,
TUC contribution rises more steeply than the PUC contribution, as TUC funds the
increase in salary from year to year. The TUC contribution will end at a higher level than
the PUC contribution.
This means that the PUC contribution for 35-year-olds is larger than the TUC
contribution, and the PUC contribution for 60 year-olds is smaller than the TUC
contribution. Removing the PUC contributions for the 35-year-olds decreases the
numerator by a larger percentage. This should lead to a smaller change in the normal
contribution rate.
Define adverse selection - Correct Answers -Adverse selection in insurance pertains to
when a policyholder has more information than what is available to the insurer, so high
risk policyholders will buy insurance in disproportionate amounts as compared to
regular risks.
In the context of this problem, adverse section would occur when an employee would
choose the most beneficial pension plan at the time of retirement in the context of their
health among other factors.
Explain how adverse selection might impact the pension plan's costs based on the
employees' selection of annuity with guarantee, annuity without guarantee, and lump
sum. - Correct Answers -People that believe they are likely to die sooner will take the
lump sum option; only people that expect to live longer will take the annuity without the
guarantee. If the anticipated distribution of which option is selected doesn't account for
this adverse selection, the costs could be higher than anticipated.
Actuarial Accrued Liability (section 4) - Correct Answers -Accrued means "only count
earned years of service"
, What does r65/l63 mean? (Section 4) - Correct Answers -Probability person age 63 will
retire at age 65
How can you have a positive IRR but a negative NPV? - Correct Answers -The NPV is
calculated at a risk discount rate of 20% while the IRR uses a discount rate of 14.83%.
The 20% discount rate results in a negative NPV because the profits at the end of one
year and at the end of two years when discounted at 20% are not sufficient to cover the
pre-contract expenses. The NPV is positive for discount rates less than IRR=14.83%.
Policies where profits increase as the lapse rate increases are called lapse supported
policies. Explain why such policies are risky to the insurance company. - Correct
Answers -If lapses are lower than expected in the pricing, the insurer would make less
profit than expected, and possibly even a loss. Lapse rates are unpredictable. When the
policyholder is better off not lapsing, it may result in lower lapse rates. Lower lapse rates
could easily produce losses for the company. In the market today, policyholders have
the option to sell their policies to third parties. The third party will pay the policyholder
for the policy (compared to a cash value of zero if the policy is lapsed) which may result
in very low lapses.
Explain why the corridor factor requirement exists for universal life insurance. - Correct
Answers -Universal Life is regulated as an insurance product. The corridor factor
ensures that the insurance benefit is significant throughout the term of the contract, so
that the policy is correctly classified as insurance, not pure investment.
Corridor factor Purpose: Policy must have a large enough DB component to qualify as a
life contract. For UL contracts, this is tested using corridor factor by ratio of total DB to
AV at death.
SOA: candidates were required to explain, coherently, that a significant insurance
benefit has to be maintained throughout the term of the contract for regulatory
purposes.
ADB (Addit. DB) - Correct Answers -excess of the total death benefit over the account
value
=DB-AV
Why the income does not include the premium in profit vector calculation (section 7)? -
Correct Answers -For equity-linked insurance policies, the policyholder's premiums are
deposited into the policyholder's fund, which is separate from the insurer's account. The
expected profits are the income minus outgo in the insurer's account only. Since the
premiums are not an income to the insurer's account, we do not include it in the
expected profit calculation.
ANSWERS
Justify the assumption of no lapses for this new policy - Correct Answers -Since this is a
single premium product, after the premium is paid, the only potential cash flow will be
the benefit payment from the insurer to the insured. Thus, the insured would have no
reason to lapse this policy; lapsing could only be detrimental to the policyholder, it could
never be beneficial in terms of the possible future cash flows. This is opposed to the
case where the policyholder pays an annual premium; in this case, the insured might
decide that the potential future benefit from the insurer is not sufficient to continue to
pay the annual premium.
Explain why the expected present value of the death benefit is greater for this new
policy than for the original policy (original policy has decrement 2 as lashes, new policy
has no lapses) - Correct Answers -Because lapses have been eliminated, mortality will
act on a larger portion of the population, resulting in a larger number of deaths and
hence a greater EPV of death benefits.
Explain why we use the q's calculated in part A (q without ') for the EPV(benefit) but the
q(')'s given for the EPV(prem)? - Correct Answers -The EPV of premiums requires
surviving. It is easier to calculate the surviving probability by using p, which is the
product of surviving the independent p's. But, for the death benefit, it is failing and it is
easier to get the failing probability from the dependent model since that is what we
ultimately need. In other words, we only pay the death benefit if it "beats" the competing
lapse decrement.
Explain in words difference between q^(j) and q^'(j) and why q^(j) <= q^'(j) - Correct
Answers -q^(j) is the probability that a life age x fails due to decrement j under the
multiple decrement model. q^'(j) is the probability that a life age x fails due to decrement
j under the associated single decrement model.
Under the multiple decrement model, all other decrements besides j are also competing
as the cause of failure. Under the associated single decrement model, each decrement
is considered in isolation.
Since the multiple decrement model has all decrements competing as the cause of
failure, the life is less likely to fail due to decrement j, relative to the associated single
decrement model, where decrement j does not compete with other decrements.
Describe two ways that dependency is incorporated in this model (joint life). The middle
has both alive (state 0). That can go left to both dead(state 4) or right where (x) is alive
,and (y is dead) (state 1), or where (x) is dead, (y) is alive. Also has a path from state 1
to state 3 which has both dead. Can also go from state 2 to 3. - Correct Answers -
Common shock: The lives can transition from State 0 (both alive) to State 4 (both dead)
directly, which means there is a positive probability of simultaneous deaths. Because
the lives can die at the same time, they are dependent.
Broken heart syndrome: A condition where the mortality of a person is higher after the
death of another person due to a "broken heart." Both lives in this model exhibit the
possibility of a broken heart syndrome. The mortality for (x) after the death of (y), mu13
x+t:y+t = 1.2mu* x+t , is higher than the mortality for (x) when (y) is alive, which is mu02
x+t:y+t = mu* x+t - .0005. Similarly, the mortality for (y) after the death of (x), mu23
x+t:y+t = 1.05mu* y+t , is higher than the mortality for (y) when (x) is alive, which is
mu01 x+t:y+t = mu* y+t - .0005.
Without further calculation, state whether the change in the normal contribution rate
would be greater or smaller under Projected Unit Credit funding. Justify your answer. -
Correct Answers -TUC contribution starts smaller than the PUC contribution since TUC
uses salary based on current age rather than salary projected to exit dates. However,
TUC contribution rises more steeply than the PUC contribution, as TUC funds the
increase in salary from year to year. The TUC contribution will end at a higher level than
the PUC contribution.
This means that the PUC contribution for 35-year-olds is larger than the TUC
contribution, and the PUC contribution for 60 year-olds is smaller than the TUC
contribution. Removing the PUC contributions for the 35-year-olds decreases the
numerator by a larger percentage. This should lead to a smaller change in the normal
contribution rate.
Define adverse selection - Correct Answers -Adverse selection in insurance pertains to
when a policyholder has more information than what is available to the insurer, so high
risk policyholders will buy insurance in disproportionate amounts as compared to
regular risks.
In the context of this problem, adverse section would occur when an employee would
choose the most beneficial pension plan at the time of retirement in the context of their
health among other factors.
Explain how adverse selection might impact the pension plan's costs based on the
employees' selection of annuity with guarantee, annuity without guarantee, and lump
sum. - Correct Answers -People that believe they are likely to die sooner will take the
lump sum option; only people that expect to live longer will take the annuity without the
guarantee. If the anticipated distribution of which option is selected doesn't account for
this adverse selection, the costs could be higher than anticipated.
Actuarial Accrued Liability (section 4) - Correct Answers -Accrued means "only count
earned years of service"
, What does r65/l63 mean? (Section 4) - Correct Answers -Probability person age 63 will
retire at age 65
How can you have a positive IRR but a negative NPV? - Correct Answers -The NPV is
calculated at a risk discount rate of 20% while the IRR uses a discount rate of 14.83%.
The 20% discount rate results in a negative NPV because the profits at the end of one
year and at the end of two years when discounted at 20% are not sufficient to cover the
pre-contract expenses. The NPV is positive for discount rates less than IRR=14.83%.
Policies where profits increase as the lapse rate increases are called lapse supported
policies. Explain why such policies are risky to the insurance company. - Correct
Answers -If lapses are lower than expected in the pricing, the insurer would make less
profit than expected, and possibly even a loss. Lapse rates are unpredictable. When the
policyholder is better off not lapsing, it may result in lower lapse rates. Lower lapse rates
could easily produce losses for the company. In the market today, policyholders have
the option to sell their policies to third parties. The third party will pay the policyholder
for the policy (compared to a cash value of zero if the policy is lapsed) which may result
in very low lapses.
Explain why the corridor factor requirement exists for universal life insurance. - Correct
Answers -Universal Life is regulated as an insurance product. The corridor factor
ensures that the insurance benefit is significant throughout the term of the contract, so
that the policy is correctly classified as insurance, not pure investment.
Corridor factor Purpose: Policy must have a large enough DB component to qualify as a
life contract. For UL contracts, this is tested using corridor factor by ratio of total DB to
AV at death.
SOA: candidates were required to explain, coherently, that a significant insurance
benefit has to be maintained throughout the term of the contract for regulatory
purposes.
ADB (Addit. DB) - Correct Answers -excess of the total death benefit over the account
value
=DB-AV
Why the income does not include the premium in profit vector calculation (section 7)? -
Correct Answers -For equity-linked insurance policies, the policyholder's premiums are
deposited into the policyholder's fund, which is separate from the insurer's account. The
expected profits are the income minus outgo in the insurer's account only. Since the
premiums are not an income to the insurer's account, we do not include it in the
expected profit calculation.
