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IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Non-unit reserves for unit-linked contracts (zeroisation)

An actuary holds a non-unit reserve at time 1 that is larger than the zeroisation reserve, leaving all other reserves and assumptions unchanged. The non-unit funds earn interest at rate i, and profits are discounted at the risk discount rate r. Which statement about the effect on the profit signature and its net present value is correct?

The year 1 profit falls and the year 2 profit rises, and the net present value rises only if the earned rate exceeds the risk discount rate. The extra reserve is deferred profit that grows at the earned rate while being discounted at the risk discount rate.

  1. AThe year 1 profit falls and the year 2 profit rises, and the net present value rises only if i is greater than rCorrect
  2. BThe net present value is unchanged, because the extra reserve is released in full at time 2
  3. CThe year 1 profit falls and the net present value falls whatever the relation between i and r
  4. DThe year 1 profit rises, because the extra reserve is an asset, and the net present value rises
  5. Only the year 2 profit changes, and the net present value rises whatever the relation between i and r

Explanation

The extra reserve is a strain at time 1, which reduces the year 1 profit. It is released at time 2 with interest at rate i, which raises the year 2 profit. Per unit of extra reserve, the change in NPV is proportional to (1+i)/(1+r)^2 - 1/(1+r), which is positive only if i exceeds r. So the NPV is not unchanged in general.

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