CM1 Actuarial Mathematics

WHY DO WE PAY INTEREST?
Since, lenders provide borrowers with money for a specified period of time, lender will not be able to use that money during that time, so to make up for this inconvenience along with protecting lenders from the risk of default by the borrower, lender demands interest which may either be fixed in monetary terms or in percentage with respect to the principal amount.

WHAT IS FORCE OF INTEREST?
If we consider a nominal interest rate convertible very frequently (e.g. every second), we are no longer thinking of a fund that suddenly acquires an interest payment at the end of each interval, but of a fund that steadily accumulates over the period as interest is earned and added. In the limiting case, the amount of the fund can be considered to be subject to a constant ‘force’ causing it to grow which is known as force of interest.

WHAT DO YOU MEAN BY DISCOUNTING?
When we are interested in finding out the present value of any amount by pulling it back to the present time at a given rate of interest, it is known as discounting of the cash flows.

WHAT IS A TREASURY BILL? WHO ISSUES IT?
Treasury bills are short-term loans made by the government, these are generally issued at discount and redeemed at par value.

STATE THE EQUATIONS OF VALUE?
An equation of value equates the present value of money received to the present value of money paid out: ‘PV income = PV outgo’

HOW DO WE CALCULATE PROSPECTIVE LOAN OUTSTANDING?
Calculating the loan prospectively involves looking forward and calculating the present value at the current point in time of future cash flows, the loan outstanding at time t is the present (or discounted) value at time t of the future repayment instalments.

HOW DO WE CALCULATE RETROSPECTIVE LOAN OUTSTANDING?
Calculating the loan retrospectively involves looking backwards and calculating the accumulated value of past cash flows, the loan outstanding at time t is the accumulated value at time t of the original loan less the accumulated value at time t of the repayments to date.

WHAT IS DISCOUNTED PAYBACK PERIOD?
The DPP tells us how long it takes for the project to move into a position of profit. Other things being equal, a project with a shorter discounted payback period is preferable to a project with a longer discounted payback period because it will start producing profits earlier.

WHAT DO YOU UNDERSTAND BY INTERNAL RATE OF RETURN?
In economics and accountancy terms, the yield per annum is often referred to as the ‘internal rate of return’ (IRR) or the ‘yield to redemption’. The internal rate of return for an investment project is the effective rate of interest that equates the present value of income and outgo, i.e. it makes the net present value of the cash flows equal to zero.

WHAT IS NET PRESENT VALUE OF A PROJECT?
Net present value is defined as the difference between the value of the positive cash flow and the value of the negative cash flow. The net present value is similar to the accumulated profit, the only difference being that we are now looking at the value at the outset (which, by definition, is a fixed date), rather than the value at the end of the project. A higher net present value indicates a more profitable project.

WHAT IS PAYBACK PERIOD?
Payback period refers to the amount of time it takes to recover the cost of an investment. It is calculated by dividing the initial investment by the average cash flows.

WHICH IS BETTER: PAYBACK PERIOD OR DISCOUNTED PAYBACK PERIOD?
Since the discounted payback period factors in the time value of money, it shows how long it will take to recoup an investment based on observing the present value of the project’s projected cash flows. Thus, DPP is better than PP.

IS TREASURY BILL A PART OF MONEY MARKET OR CAPITAL MARKET?
Treasury bills or T-bills, which are money market instruments, are short term debt instruments issued by the Government of India and are presently issued in three tenors, namely, 91 day, 182 day and 364 day. Treasury bills are zero coupon securities and pay no interest.

WHERE EQUATIONS OF VALUE IS USED?
Equations of value are used throughout actuarial work. For example:  the ‘fair price’ to pay for an investment such as a fixed-interest security or an equity (ie PV outgo) equals the present value of the proceeds from the investment, discounted at the rate of interest required by the investor.  Also, the premium for an insurance policy is calculated by equating the present value of the expected amounts received in premiums to the present value of the expected benefits and other outgo.

WHAT ARE THE MAIN COMPONENTS OF LOAN SCHEDULE?
The loan schedule usually consists of original loan amount, the loan balance at each payment, the interest rate, the amortisation period, the total payment amount, and the proportion of each payment that is made up of interest vs. principal, and also includes due dates, payment frequency and remaining balance over time.

HOW IRR IS CALCULATED?
IRR is calculated as a discount rate where NPV is equal to zero. It represents the effective annual return generated by the project.

STATE THE BENEFITS OF USING NPV FOR PROJECT APPRAISAL?
The most important advantage of NPV is that it takes into account time value of money. Along with this, it makes adjustment for cost of capital the risk inherent in making projections about the future. Also, NPV is easy to calculate with its additive nature where multiple projects’ NPV can be added up to get the actual view of wealth creation.

WHAT DO YOU MEAN BY CONVEXITY OF A BOND?
Convexity gives a measure of the change in duration of a bond when the interest rate changes. Thus, ‘Convexity’ refers to the shape of the graph of the present value as a function of the interest rate.  For a series of cash flows with the same discounted mean term, a series consisting of payments paid close together will have a low convexity, whereas a series that is more spread out over time will have a higher convexity.

HOW VOLATILITY OF BOND IS DETERMINED?
The effects of changes in interest rates on the cash flows generated by an asset or required by a liability can be quantified by calculating the volatility. Both the volatility and the discounted mean term provide a measure of the average ‘life’ of an investment. This is important when considering the effect of changes in interest rates on investment portfolios since an investment with a longer term will in general be more affected by a change in interest rates than an investment with a shorter term.

WHAT IS DISCOUNTED MEAN TERM OF AN INVESTMENT?
One measure of interest rate sensitivity is the duration, also called Macaulay duration or discounted mean term (DMT). This is the mean term of the cash flows weighted by present value.

WHAT IS IMMUNISATION OF A PORTFOLIO?
Immunisation refers to the selection of an asset portfolio that will protect this surplus against small changes in the interest rate. It aims to match asset and liability duration and convexity to stabilise surplus.

WHAT ARE THE CONDITIONS IN REDINGTON THEORY OF IMMUNISATION?
In the 1950s, the actuary Frank Redington derived the three conditions that are required to achieve immunisation. The conditions for Redington’s immunisation may be summarised as follows: 1. the value of the assets at the starting rate of interest is equal to the value of the liabilities. 2. The volatilities of the asset and liability cash flow series are equal. 3. The convexity of the asset cash flow series is greater than the convexity of the liability cash flow series.

WHAT IS INDEX LINKED BONDS?
An index-linked bond is a bond which has payment of interest income on the principal that is related to a specific price index, usually the Consumer Price Index (CPI) or Wholesale Price Index (WPI).

EXPLAIN RUNNING YIELD OF A BOND?
The running yield of a bond is the yield generated by the payment of the coupons alone ignoring the redemption payment.

HOW RUNNING YIELD IS DIFFERENT FROM GROSS REDEMPTION YIELD OF A BOND?
A redemption yield is the yield obtained by an investor who holds the bond until redemption whereas the running yield is the yield generated by the payment of the coupons alone (ignoring the redemption payment).

WHAT IS PAR YIELD? IS IT ALWAYS POSITIVE?
Par yield, also referred to as the par rate, is when the coupon rate and the yield of a bond are equal and the bond price will be the same as its nominal value, also called its par value. A par yield curve represents bonds that are trading at par. Also, Par yields are usually positive, but can theoretically be zero or negative under extreme market conditions (though rare)

WHAT IS ANNUITY IN PERPETUITY?
‘In perpetuity’ means that the payments continue forever.

WHAT IS SPOT RATE? HOW IS IT DIFFERENT FROM FORWARD RATE?
The n-year spot rate is a measure of the average interest rate over the period from now until n years’ time whereas the discrete-time forward rate is the annual interest rate agreed at time 0 for an investment made at time t for a period of r years.

CAN FORWARD RATE BE NEGATIVE?
Forward interest rates are negative whenever the yield curve is negatively sloped.

WHAT IS TERM STRUCTURE OF INTEREST RATE?
Term structure of interest rates refers to the relationship between interest rates and different terms or maturities of bonds.

WHY I IS GREATER THAN I12?
Due to the effects of accumulation, i is greater than i12.

WHY D IS LESS THAN D12?
Due to the effects of compounding,  we are ‘annualising’ a pthly effective discount rate i.e. d12.  For example, to ‘annualise’ an effective discount rate of 0.5% per month, we would make it twelve times it to get 6% pa. This is not the correct annual effective discount rate. The 6% we have obtained is referred to as a nominal discount rate convertible monthly.

WHAT IS TIME VALUE OF MONEY?
The time value of money is the concept of recognising the earning potential of money over time where a sum of money is worth more now than the same sum will be at a future date. The time value of money is also referred to as the present discounted value.

DESCRIBE THE PROCESS OF DATA ANALYSIS?
The data analysis process starts with clearly defining the objective or decision the analysis needs to support. Relevant data is then identified, collected, cleaned, and validated to ensure quality. Exploratory analysis is performed to understand patterns and relationships, followed by building and validating appropriate models. Finally, results are communicated clearly to stakeholders, and the process is monitored and refined as new data becomes available.

DIFFERENCE BETWEEN REPRODUCIBILITY AND REPLICATION.
Reproducibility is linked to the concept of replication which refers to someone repeating an experiment and obtaining the same (or at least consistent) results. Due to the possible difficulties of replication, reproducibility of the statistical analysis is often a reasonable alternative standard.

DIFFERENCE BETWEEN CENSORING AND TRUNCATED DATA.
Censored data occurs when the value of a variable is only partially known. Truncated data occurs when measurements on some variables are not recorded so are completely unknown.

WHY MODELS ARE USED?
A model is an imitation of a real-world system or process. Models of many activities can be developed, for example:  the economy of a country, the workings of the human heart, and  the future cash flows of the broker distribution channel of a life insurance company.

DIFFERENCE BETWEEN DETERMINISTIC AND STOCHASTIC MODELS.
A stochastic model is one that recognises the random nature of the input components. A model that does not contain any random component is deterministic in nature. In a deterministic model, the output is determined once the set of fixed inputs and the relationships between them have been defined. By contrast, in a stochastic model the output is random in nature like the inputs, which are random variables. The output is only a snapshot or an estimate of the characteristics of the model for a given set of inputs. Several independent runs are required for each set of inputs so that statistical theory can be used to help in the study of the implications of the set of inputs. A deterministic model is really just a special (simplified) case of a stochastic model.

WHAT IS SCENARIO BASED TESTING? HOW IS IT DIFFERENT FROM SENSITIVITY TESTING?
A scenario-based model would take into consideration a particular scenario; that is a series of input parameters based on this scenario. Different scenarios would be useful in decision analysis as one can evaluate the expected impact of a course of action. Whereas, sensitivity testing refers to the approach of using a deterministic model with changes in one or more of the assumptions to see the range of possible outcomes that might occur.

WHAT IS ANNUITY CERTAIN?
An annuity-certain provides a series of regular payments in return for a single premium (i.e. a lump sum) paid at the outset.

WHAT IS A PURE ENDOWMENT PLAN?
A pure endowment is an insurance policy which provides a lump sum benefit on survival to the end of a specified term usually in return for a series of regular premiums. For example, a payment of £50,000 is made if a life now aged 30 survives to age 60, but no payment is made if this life dies before age 60.

WHAT ARE VARIOUS ASSURANCE PRODUCTS?
whole life assurance, term assurance, pure endowment & endowment assurance.

WHAT ARE SOME FEATURES OF ANNUITIES?
An annuity is a regular series of payments. An annuity-certain is an annuity payable for a definite period of time: the payments do not depend on some factor, such as whether a person is alive or not. If payments are made at the end of each time period, they are paid in arrears. If they are made at the beginning of each time period, they are paid in advance. An annuity paid in advance is also known as an annuity-due. Where the first payment is made during the first time period, this is an immediate annuity. Where no payments are made during the first time period, this is a deferred annuity. If each payment is for the same amount, this is a level annuity. If payments increase (decrease) each time by the same amount, this is a simple increasing (decreasing) annuity.

RATE ON BASIS OF PREMIUM: TERM ASSURANCE, ENDOWMENT POLICY AND WHOLE LIFE ASSURANCE?
On the basis of decreasing order: Endowment>whole life>term assurance

HOW NOMINAL RATE OF INTEREST IS DIFFERENT FROM EFFECTIVE RATE OF INTEREST?
Effective rates have interest paid once per measurement period whereas nominal rates are paid more frequently than once per measurement period.

WHAT IS ACCUMULATED PROFIT?
Accumulated profit is the accumulated value of the net cash flows as at the time of the last payment.

WHAT IS SELECT MORTALITY?
Policyholders with a duration of one year, say, will have recently satisfied the company about their state of health. We would therefore expect their mortality to be better than that of policyholders of the same age with duration of, say, 3 years who passed the medical underwriting hurdle several years ago. Thus, the mortality of the recently joined policyholders is called select mortality, and we expect it to be better than that of longer duration policyholders, whose mortality we call ultimate mortality.

HOW UDD IS DIFFERENT FROM CFM?
Under uniform distribution of deaths(UDD) assumption, for an individual aged exactly x , the probability of dying on one particular day over the next year is the same as that of dying on any other day over the next year whereas under constant force of mortality(CFM), for integer ages, we suppose that the force of mortality is constant.

HOW ARE GROSS PREMIUMS CALCULATED?
The gross premium is the premium required to meet all the costs under an insurance contract, and is the premium that the policyholder pays.  It is also sometimes referred to as the office premium which contains impact for loaded profits, cost of capital, adjustments for competition and other loadings.

WHEN PROSPECTIVE AND RETROSPECTIVE RESERVES ARE EQUAL?

Prospective and retrospective reserves are equal at any duration t if calculated using the same basis of interest, mortality, expenses, and premiums. Both approaches represent the same policy value at time t, just derived from different perspectives.

WHAT IS JOINT LIFE ANNUITY?
A joint life annuity covers two lives, where the regular payments are contingent on the survival of one or both of those lives.

WHEN LAST SURVIVOR POLICY BEGINS PAYMENT?
Two common types of policy are: an annuity payable to a couple while at least one of them is alive, and  an assurance payable on the second death of a couple. These are both examples of last survivor policies, where the payment is contingent on what happens to the second life to die, rather than the first.

WHAT IS MORTALITY PROFIT?
The mortality profit is defined as the difference between Expected Death Strain & Actual Death Strain where EDS is the amount the company expects to pay out, in addition to the year-end reserve for a policy and ADS is the amount it actually pays out, in addition to the year-end reserve.

HOW MULTIPLE STATE MODELS IS DIFFERENT MULTIPLE DECREMENTS MODEL?
Multiple state models are well suited to valuing cash flows that are dependent on multiple transitions, such as of health insurance contracts. A multiple decrement model is a multiple state model which has:  one active state, and  one or more absorbing exit states.

WHAT IS UNIT FUND?
Unit fund is the total value of the units in respect of the policy at any time.

HOW ULIP WORKS?
With unit-linked contracts the policyholders are entitled units, which represent a portion of a fund or funds of investments managed by the life insurer referred to as the unit fund of the policy. The unit fund value moves in line with the performance of the backing investments. The non-unit fund represents the accumulation of all cash flows paid in that are not used to buy units, less all cash flows paid out that have not arisen from the cancellation of units. As such it represents the accumulation of the company’s profits from the policy at any time.

WHAT ARE THE VARIOUS CONSTITUTES OF NON-UNIT FUND?
Non-unit fund includes unallocated premiums, bid/offer spread and unit fund charges. Non-unit benefits include, for instance, any sum insured payable on death in excess of the value of the units, or any guaranteed maturity value in excess of the value of the units.

WHAT IS BID-OFFER SPREAD?
The bid price is the cash-in value of each unit and the offer price is the price that has to be paid to purchase a unit in the fund. The difference between the two (with the offer price being greater than the bid price) is called the bid-offer spread.

WHAT ARE THE STEPS OF PROFIT TESTING?
The steps in profit testing starts with deciding on the structure of the product, building a model to project cash flows for the product then deciding on a risk discount rate and profit criterion then decide on some ‘first draft’ premiums (conventional product) / charges (unit-linked product), vary the premiums / charges until our profit criterion is met, keep varying premiums until we have a product that meets the profitability criterion, is marketable, and is resilient to adverse future experience.

HOW PROFIT MARGIN IS CALCULATED?
Profit margin is the NPV expressed as a percentage of the EPV of the premium income where the risk discount rate is used to do the discounting in both the numerator and the denominator.

WHAT IS RESERVING?
Reserving is the process of determining the amount an insurer must set aside at a given time to meet future policy liabilities. It represents the present value of future expected benefits minus the present value of future expected premiums, calculated using actuarial assumptions relating to mortality, interest, expenses, and lapses. Reserving ensures that the insurer remains financially capable of meeting future obligations.

WHY DO WE NEED A RESERVE?
Insurance benefits are often payable in the future, while premiums are received gradually over time. This creates a timing mismatch between inflows and outflows. To ensure solvency and the ability to meet future claims as they arise, insurers maintain reserves as a financial safeguard.

WHAT IS A PROSPECTIVE RESERVE?
A prospective reserve at time t is the expected present value of future benefits minus the expected present value of future premiums, calculated at time t. It looks forward from time t and measures the remaining obligation of the insurer under the policy.

WHAT IS A RETROSPECTIVE RESERVE?
A retrospective reserve at time t is the accumulated value of past premiums received minus the accumulated value of past benefits paid, calculated at time t. It looks backward from time t and reflects how past cash flows have built up to the present value of the policy.

WHEN ARE PROSPECTIVE AND RETROSPECTIVE RESERVES EQUAL?
Prospective and retrospective reserves are equal at any duration t if calculated using the same basis of interest, mortality, expenses, and premiums. Both approaches represent the same policy value at time t, derived from different perspectives.

WHAT IS A NET PREMIUM RESERVE?
A net premium reserve is calculated using net premiums, where premiums are determined such that the expected present value of benefits equals the expected present value of premiums at policy inception. It ignores expenses and focuses only on mortality and interest assumptions.

WHAT IS A GROSS PREMIUM RESERVE?
A gross premium reserve takes into account actual premiums received and includes expenses. It reflects a more realistic valuation basis used in practice for financial reporting and regulatory purposes.

HOW DO YOU CALCULATE PROFIT OF A LIFE INSURER?
Profit is calculated by comparing the assets available at the end of a period with the liabilities required at that time. If assets exceed liabilities, the excess represents profit. If liabilities exceed assets, it results in a loss.

WHAT ARE THE COMPONENTS OF PROFIT?
Profit arises from differences between actual experience and the assumptions used in pricing or reserving. The key components include mortality experience, investment returns, expenses, and lapse or persistency experience. Profit emerges when actual outcomes are more favourable than expected.

WHAT ARE THE EXPENSES INVOLVED IN LIFE INSURANCE?
Life insurance expenses are broadly classified into acquisition expenses, maintenance expenses, claim expenses, and overhead expenses. Acquisition expenses occur at policy inception, maintenance expenses recur during the policy term, claim expenses arise when processing claims, and overhead expenses represent general administrative costs.

WHAT IS A TERM INSURANCE PRODUCT?
Term insurance is a pure protection product that provides a death benefit if the policyholder dies during the policy term. There is no maturity benefit if the policyholder survives. It primarily covers mortality risk and is typically low-cost compared to savings-oriented products.

WHAT ARE THE MAIN RISK DRIVERS IN TERM INSURANCE?
The primary risk driver is mortality risk. Other important factors include lapse rates, expenses, and underwriting quality. Investment risk is relatively lower compared to savings products because the benefit is payable only upon death during the term.

WHAT IS A WHOLE LIFE POLICY?
A whole life policy provides a death benefit whenever the insured dies, regardless of timing. Since the benefit is certain to be paid eventually, reserves build up over time. It primarily covers long-term mortality risk and has a savings component.

WHAT IS AN ENDOWMENT POLICY?
An endowment policy provides a benefit either on death during the term or on survival to the end of the term. It combines protection and savings features. Premiums are higher than term insurance because a maturity benefit is guaranteed.

WHAT IS A MONEY-BACK POLICY?
A money-back policy provides periodic survival benefits during the term and a final benefit at maturity or death. It offers liquidity during the policy period, with a more complex cash flow structure due to multiple payouts.

WHAT IS A UNIT LINKED INSURANCE PLAN (ULIP)?
A ULIP is an investment-linked life insurance product where premiums are invested in market-linked funds chosen by the policyholder. The investment risk is largely borne by the policyholder, while the insurer primarily bears mortality and expense risk.

WHAT IS AN ANNUITY PRODUCT?
An annuity provides regular periodic payments, usually after retirement, for a fixed period or for life. The key risk for the insurer is longevity risk, as payments may continue longer than expected.

WHAT IS A PARTICIPATING POLICY?
A participating policy allows policyholders to share in the insurer’s surplus through bonuses declared periodically. The risk is partially shared between the insurer and the policyholder.

WHAT IS A NON-PARTICIPATING POLICY?
A non-participating policy is one where benefits are fixed and guaranteed at inception. The insurer bears the full experience risk, and policyholders do not participate in surplus.

WHY ARE RESERVES SIGNIFICANT IN WHOLE LIFE POLICIES?
Reserves are significant because the insurer is certain to pay the death benefit at some point in the future. Since the claim is guaranteed to occur, sufficient funds must be built gradually over time. As the policyholder ages, mortality risk increases, increasing liability.

WHAT IS AN ANNUITY FUNCTION?
An annuity function is a mathematical function used to calculate the present value or accumulated value of a series of level payments made at regular intervals. It is widely used to value annuities, loans, and pension benefits.

WHY IS THE ANNUITY FUNCTION IMPORTANT IN ACTUARIAL WORK?
Annuity functions allow actuaries to determine the present value of future payment streams under given interest rate assumptions, forming the foundation for pricing and reserving.

WHAT IS AN ASSURANCE FUNCTION?
An assurance function calculates the present value of a benefit payable on death, incorporating mortality and interest assumptions.

WHAT IS A WHOLE LIFE ASSURANCE FUNCTION?
It represents the present value of a benefit payable at death whenever death occurs. Since death is certain eventually, it reflects the discounted value of a guaranteed future payment.

WHAT IS A TERM ASSURANCE FUNCTION?
It represents the present value of a benefit payable only if death occurs within a specified term. No benefit is paid if survival extends beyond the term.

WHAT IS AN ENDOWMENT ASSURANCE FUNCTION?
It represents the present value of a benefit payable on death within a specified term or on survival to the end of the term.

WHY ARE ASSURANCE FUNCTIONS IMPORTANT IN ACTUARIAL WORK?
They enable actuaries to quantify the present value of future death benefits under specific assumptions, forming the basis for premium and reserve calculations.

WHY MIGHT TWO ACTUARIES CALCULATE SLIGHTLY DIFFERENT PREMIUMS FOR THE SAME PRODUCT?
They may use different assumptions regarding mortality, expenses, lapse rates, interest rates, or profit margins. Even small assumption differences can affect premiums.

WHY ARE LEVEL PREMIUMS CHARGED WHEN MORTALITY INCREASES WITH AGE?
Level premiums ensure affordability and prevent anti-selection. Excess premiums collected in early years build reserves that finance higher mortality costs in later years.

WHAT HAPPENS IF LAPSE RATES ARE HIGHER THAN EXPECTED?
For protection products, early lapses may reduce future claims. For savings products, higher lapses may cause surrender strain or gains depending on product design and expense recovery.

IF INTEREST RATES FALL AFTER PRICING A WHOLE LIFE PRODUCT, WHAT HAPPENS TO RESERVES AND PROFITABILITY?
Lower interest rates increase the present value of liabilities, raising reserves. Future investment returns decline, reducing long-term profitability.

WHY ARE LONG-TERM PRODUCTS MORE SENSITIVE TO INTEREST RATE CHANGES THAN SHORT-TERM PRODUCTS?
Cash flows far in the future are heavily affected by discounting. Small rate changes significantly impact present values for long-duration products.

IF MORTALITY IMPROVES UNEXPECTEDLY, HOW DOES IT AFFECT TERM INSURANCE AND ANNUITIES?
For term insurance, claims reduce and profitability increases. For annuities, payment duration increases, raising liabilities and reducing profitability.

WHY CAN RESERVES BE NEGATIVE IN EARLY YEARS FOR SOME PRODUCTS?
High acquisition expenses at inception may exceed early premiums. Under gross premium valuation, reserves can temporarily be negative if costs are expected to be recovered later.

WHY DOES LEVEL PREMIUM NOT CREATE ANTI-SELECTION ISSUES EVEN THOUGH MORTALITY INCREASES WITH AGE?
Underwriting occurs at entry and premiums are fixed. Early excess premiums build reserves to cover later mortality, preventing selective behaviour.

IF LAPSE RATES INCREASE UNEXPECTEDLY, WHY MIGHT PROFITS INCREASE INITIALLY BUT REDUCE LATER?
Early lapses may reduce future claims and allow expense recovery. Later, profitable policies may lapse, reducing long-term income.

WHY IS ANNUITY PRICING MORE SENSITIVE TO LONGEVITY IMPROVEMENTS THAN LIFE INSURANCE PRICING?
Annuities involve repeated survival payments, so longer lifespans increase liabilities significantly. Life insurance pays once at death, so the timing shift is less impactful.

A PRODUCT SHOWS POSITIVE EXPECTED PROFIT BUT LARGE INITIAL STRAIN. WOULD YOU LAUNCH IT?
I would assess capital availability, solvency impact, payback period, internal rate of return, and sensitivity to assumptions. Excessive strain may affect liquidity and commercial viability despite positive expected profit.

IF YOU UNDERESTIMATE MORTALITY AND OVERESTIMATE INTEREST RATE, WHAT HAPPENS TO RESERVES?
Both assumptions reduce calculated liabilities, leading to understated reserves and increased solvency risk.

WHY IS PRICING NOT JUST EPV CALCULATION?
Pricing must consider capital requirements, risk margins, regulation, policyholder behaviour, competition, and profit objectives beyond expected present value.

IF INTEREST RATES SUDDENLY INCREASE, WHAT HAPPENS TO EXISTING RESERVES?
Higher discount rates reduce liability present values, lowering reserves. However, asset values may decline, so overall impact depends on asset-liability matching.

WHY ARE ENDOWMENT POLICIES MORE CAPITAL INTENSIVE THAN TERM INSURANCE?
Endowments guarantee payment on death or survival, making payout highly probable. Term insurance pays only on death within the term, requiring less capital backing.

WHY DOES PROFIT EMERGE GRADUALLY INSTEAD OF UPFRONT?
Risk unfolds over time, and accounting recognises income in line with risk exposure and uncertainty in future experience.

WHAT ARE ASSET SHARES?
Asset shares represent the accumulated value of premiums after allowing for expenses, claims, bonuses, and investment returns. They show how a policy has grown within the insurer’s asset pool.

WHAT IS THE DIFFERENCE BETWEEN PRICING AND RESERVING?
Pricing determines premiums for new business. Reserving estimates liabilities for existing policies to ensure claims can be paid.

EXPLAIN DISCOUNTING.
Discounting converts future cash flows into present value using an assumed interest rate, reflecting the time value of money.

WHAT IS THE DIFFERENCE BETWEEN STOCHASTIC AND DETERMINISTIC APPROACHES?
A deterministic approach uses fixed inputs to produce a single outcome. A stochastic approach models uncertainty and produces a distribution of outcomes.

WHY IS THE INTEREST RATE ALWAYS HIGHER THAN THE CORRESPONDING DISCOUNT RATE?
The interest rate applies to the initial amount invested, while the discount rate applies to the final accumulated amount. Since the final amount is larger, the same interest represents a smaller percentage, making the discount rate lower.

WHY IS MONEY TODAY WORTH MORE THAN MONEY IN THE FUTURE?
Money today can earn returns and provides immediate utility. Future money involves uncertainty and opportunity cost.

HOW WOULD RISING INTEREST RATES AFFECT PRESENT VALUES?
Higher interest rates increase discounting, reducing the present value of future cash flows.

WHY DO ACTUARIES PREFER CONTINUOUS COMPOUNDING IN THEORY?
Continuous compounding simplifies mathematical modelling and works naturally with cash flows that can occur at any time.

HOW WOULD YOU EXPLAIN PRESENT VALUE TO A NON-TECHNICAL PERSON?
Present value means how much a future amount of money is worth today, considering that money today can be invested or used immediately.

HOW DOES THE INTEREST RATE IMPACT ANNUITY VALUES?
Annuity values move inversely to interest rates. Higher rates reduce present value; lower rates increase it.

WHY MIGHT AN ANNUITY WITH MORE PAYMENTS BE WORTH LESS THAN ONE WITH FEWER PAYMENTS?
If additional payments occur far in the future, heavy discounting may make their present value negligible.

IF INTEREST RATES SUDDENLY BECOME ZERO, WHAT HAPPENS TO THE VALUE OF AN ANNUITY?
Without discounting, the present value equals the total sum of all future payments.

CAN AN ANNUITY EVER HAVE AN INFINITE VALUE?
In theory, a perpetuity with zero or negative interest would not converge, leading to infinite value.

WHY IS AN ANNUITY MORE SENSITIVE TO RATES THAN A BOND WITH THE SAME MATURITY?
Annuities involve multiple distributed payments, many far in the future, making them highly rate-sensitive compared to bonds with concentrated principal repayment.

HOW CAN FORWARD RATES BE HIGH EVEN WHEN SPOT RATES ARE LOW?
Forward rates reflect market expectations of future interest rates. If markets expect rates to rise, forward rates can exceed current spot rates.

Profit Testing

What is Profit Testing?
This is the process of projecting the income and outgo emerging from a policy, and discounting the results. The results can then be used for various different purposes, such as setting the premium for a life policy that will give us our required level of profitability. We can set the premiums for a product to give a desired level of profitability by projecting cash flows under a certain set of assumptions, deciding on a risk discount rate and profit criterion, and then varying the premium amount until the profit criterion is satisfied.

What are the different Decrements?
The different decrements are:
a) Healthy
b) Sickness
c) Critical Illness
d) Withdrawal
e) Retirement
f) Death

Difference between Surrender and Lapse.
Lapse refers to the termination of policies without payout to policyholders, while surrender usually indicates that a surrender value is paid out to the policyholder.
A life insurance lapse occurs when you stop paying your policy’s premium and the contractual grace period has expired, while surrender refers to the amount that the policyholder will get from the life insurance company if he decides to exit the policy before maturity.

What are dependent probabilities and independent probabilities?
The dependent probability is the probability that a life aged x in a particular state will be removed from that state within a year by the decrement alpha, in the presence of all other decrements in the population.
The independent probability xqa is the probability that a life aged x in a particular state will be removed from that state within a year by the decrement alpha, where alpha is the only decrement acting on the population.

What is mortality profit? State its formula.
That part of the profit earned during the year due to difference in expected and actual mortality is referred to as mortality profit.
The mortality profit is defined as: Mortality profit = Expected Death Strain – Actual Death Strain. The EDS is the amount the company expects to pay out, in addition to the year-end reserve for a policy. The ADS is the amount it actually pays out, in addition to the year-end reserve. If it actually pays out less than it expected to pay, there will be a profit. If the actual strain is greater than the expected strain, there will be a loss.

What is profit testing?
Profit testing is the projection of all future policy cash flows to assess whether an insurance product meets profitability objectives over its lifetime.

Why is profit testing important for insurers?
It ensures products are financially viable, appropriately priced for risk, and aligned with business, capital, and regulatory objectives before launch or repricing.

Where does profit testing fit in the product lifecycle?
It supports product design, pricing, regulatory approval, monitoring of performance, and repricing decisions.

What cash flows are included in profit testing?
Premiums, expenses, commissions, benefits, reserve movements, investment income, reinsurance cash flows, tax, and sometimes capital costs.

Why are reserve movements included as cash flows?
Because increases or releases of reserves affect the insurer’s available cash and profitability in each period.

How is investment income typically modeled?
By applying assumed interest rates to reserves and positive cash balances, reflecting expected asset returns.

What are the key assumptions in profit testing?
Mortality or morbidity, lapses, expenses, commission structure, interest rates, inflation, tax, and reinsurance terms.

Which assumptions usually drive profitability the most?
Lapse rates, expenses, and interest rates are often the most sensitive, depending on the product type.

Why are lapse assumptions so critical?
Lapses affect premium income duration, expense recovery, and timing of profits, making them a major driver of strain and breakeven.

How does mortality affect profitability?
Higher mortality generally reduces profits in protection products due to higher claims, while the impact differs for savings products.

What is a profit vector?
A year-by-year projection of profit or loss showing timing and emergence of profitability.

What is present value of profit (PVP)?
The discounted value of all future profits over the policy term.

What discount rate is used and why?
Typically the expected investment return or a risk-adjusted rate, to reflect the time value of money and risk.

What is profit margin?
The ratio of present value of profit to present value of premiums, showing profitability relative to scale.

What does IRR tell you that margin does not?
IRR captures the timing of cash flows and the speed of profitability, not just total profit.

What is new business strain?
Initial losses arising from high upfront commissions, expenses, and reserve requirements.

Why do many products show losses in early years?
Because expenses and commissions are front-loaded while premiums and profits emerge gradually.

What is breakeven analysis?
Identifying the policy duration at which cumulative profits turn positive.

Why is breakeven an important metric?
It indicates capital lock-in duration and helps assess growth sustainability.

How do lapses affect protection vs savings products?
Lapses usually reduce profits in protection products but may increase profits in savings products due to surrender charges.

How does policy term affect profitability?
Longer terms allow better recovery of initial expenses but increase exposure to long-term risks.

How does premium frequency affect results?
More frequent premiums improve cash flow timing and reduce initial strain.

What is sensitivity analysis?
Testing profitability under changes to one assumption at a time.

Why is sensitivity analysis essential?
It identifies key risk drivers and highlights assumptions requiring careful monitoring.

What is scenario testing?
Assessing profitability under combined adverse or favourable assumptions.

What risks are typically revealed through profit testing?
Mortality, lapse, expense inflation, interest rate risk, and regulatory or capital risk.

How do you check reasonableness of profit testing results?
By comparing margins, IRR, and breakeven with similar products and historical benchmarks.

What reconciliation checks are used?
Matching projected premiums, claims, and reserves against source data and expected totals.

How do you handle assumption changes?
Update assumptions, rerun projections, and clearly document impacts and rationale.

What is capital strain?
The impact of regulatory capital requirements on early profitability and growth.

How does profit testing support regulatory approval?
It demonstrates product sustainability, fairness to policyholders, and financial soundness.

How does profit testing influence pricing decisions?
It ensures premiums meet profitability targets while remaining competitive.

How is profit testing typically implemented?
Using Excel-based projection models with separate assumption, cash flow, and output modules.

How can VBA support profit testing?
By automating projections, sensitivity runs, reconciliations, and reporting.

What checks are required before finalising results?
Consistency checks, validation against benchmarks, documentation, and peer review.

What is expected vs actual analysis?
Comparing projected profits with emerging experience to validate assumptions.

Why is this comparison important?
It helps refine assumptions and improve future pricing accuracy.

How would you explain profit testing to non-actuaries?
As a way to check whether a product makes money over time while managing risk.

What makes a product viable?
Meeting profitability, risk, capital, and regulatory requirements consistently.

Why is profit testing critical for actuarial roles?
Because it connects pricing, risk management, capital, and business strategy.