Reserves

Why it matters

In the last lesson the 60-year-old paid a level premium of 1,138.46 for 5 years. But the cost of the cover is not level: the chance of dying rises every year. Early premiums are more than the cost of that year's cover, and later premiums are less. The insurer must keep the early surplus to pay the later claims. That money, set aside for future obligations, is the reserve. It is usually the largest item on a life insurer's balance sheet, and calculating it is one of the core jobs of a valuation actuary.

The prospective reserve

The reserve at time t for a policy still in force is the value of what the insurer still owes minus the value of what it will still receive:

t_V = APV(future benefits) - APV(future premiums)     (at time t, for a life now aged x + t)

This is the prospective method, the same idea as the loan balance in module 1 (the present value of the payments still to come). At issue, 0_V = 0 by the equivalence principle. At the end of the term, nothing is owed and nothing will be paid, so the reserve is 0 again.

Worked example: the 5-year term policy

Using the same life table, i = 5%, benefit 100,000 and premium 1,138.46, the reserves at the start of each policy year (just before the premium is paid) are:

The reserve rises while the early "overpayments" accumulate and then falls as they are used up. A whole life or endowment policy, by contrast, builds a large reserve that keeps growing, because a payment is certain (or very likely) eventually. Reserves per policy are small numbers, but an insurer with a million policies holds hundreds of millions.

The retrospective method gives the same number from the other direction: premiums received minus benefits paid, both accumulated with interest and survivorship. Prospective and retrospective reserves agree when the same basis is used for premiums and reserves.

Why insurers must hold reserves

• Solvency. Without reserves, an insurer could spend early premiums and then be unable to pay later claims. Regulators require reserves so that policyholders are protected.
• Accurate profit. If the whole premium were counted as income when received, profits would look high early and negative later. Setting up the reserve as a liability spreads profit over the life of the policy.
• Pricing feedback. Reserve and capital requirements tie up money, and that cost feeds back into premiums.

Reserve bases and regulation

The calculation depends on the basis: mortality table, interest rate and expenses. Different purposes use different bases:

• Statutory reserves are set by insurance regulators. In the US, life insurers follow the NAIC Valuation Manual, which includes principle-based reserving (VM-20) for many life products: reserves reflect company experience and stochastic scenarios instead of only fixed formulas.
• GAAP and IFRS 17 reserves are for financial reporting to investors.
• Outside the US, regimes such as Solvency II in Europe use a best estimate plus a risk margin.

The details change often and differ by country, so in practice you read the current rules from the regulator rather than memorising them.

Property and casualty reserves

In property and casualty (P&C) insurance (auto, home, liability), the big reserve is for claims that have already happened but are not yet fully paid:

• Case reserves: estimates on reported claims, set by claim adjusters.
• IBNR (incurred but not reported, plus development on known claims): the actuary's estimate of what the case reserves will grow to, usually from loss development triangles with methods such as the chain ladder. You will build one in module 4.

Common mistakes

• Thinking a reserve is a pile of profit. It is a liability: money already committed to future claims.
• Assuming reserves are always positive and growing. Term reserves are small and return to zero; some product designs can even produce negative reserves, which regulators usually floor at zero.
• Mixing timing. State whether the reserve is just before or just after the premium due at time t.
• Ignoring the basis. A reserve is only meaningful with its mortality, interest and expense assumptions.

Quick recap

• Level premiums for rising costs create early surplus that must be held for later claims.
• Prospective reserve = APV(future benefits) - APV(future premiums); 0 at issue under the equivalence principle.
• Reserves protect solvency and spread profit; the basis and the rules depend on the purpose and the regulator.
• P&C reserves cover claims already incurred: case reserves plus IBNR.

This lesson has no activity: check your understanding with the quiz on the Do tab.