Actuarial Analyst Screen

How it works

The sitting is a single section, "Life contingencies & reserving" - 20 items in 30 minutes, drawn from mortality and survival mechanics (qx to px conversion, compounding multi-year survival), annuity valuation (annuity-due timing, the effect of mortality improvement on EPV), loss development (volume-weighted link ratios, chain ladder versus Bornhuetter-Ferguson), and the Cramer-Lundberg ruin model. The instructions ask for probabilities to four decimal places, matching the precision the underlying formulas are checked against.

Items are served one at a time - a mix of numeric-entry and four-option multiple choice - and the 30-minute clock runs continuously with no per-item limit. allowBack is false, so once an item is submitted or left blank it cannot be revisited and the palette cannot jump backward; flagging an item surfaces it, with the correct answer and explanation, on the marked script at the end, but does not let you return to it mid-run.

The section ends when the clock reaches zero or all 20 items have been used, whichever comes first; anything left over is scored as skipped.

How scoring works

Each of the 20 items is worth 1 mark and the section's penalty is 0 - a correct answer scores +1, a wrong answer scores 0 (not negative), and an unanswered item scores 0 as well. The net section score is correct minus wrong times the penalty, which collapses to the raw count correct since the penalty is zero.

Numeric items are checked against the exact stored answer within a fixed tolerance (for example the survival-probability items are checked to within 0.0005 or 0.0006), so an answer correctly rounded to four decimal places as instructed is what the tolerance is built around. Since a wrong answer and a blank score the same, there is no scoring reason to leave an item unanswered.

The review screen reports the score out of 20, percentage of maximum, and per-skill accuracy across the tagged skills - distributions, expected-value, selection-bias, optional-stopping - from items you actually answered, and states directly that no percentile is reported because there is no comparison population behind this assessment yet.

Life contingencies & reserving

The survival-probability items compound multiplicatively - px = 1 - qx for one year, and k-year survival is the product of k consecutive one-year survival probabilities, never a sum or an average. Carry every intermediate product to at least four, ideally six, decimals before rounding the final answer; the tolerances (0.0005-0.0006) are tight enough that early rounding pushes a correct method to a wrong number.

On the annuity-due item, the trap is timing: the k = 0 term is the payment itself, undiscounted and unconditional on survival, because an annuity-due pays at the start of each period. On the loss-development items, use the ratio of sums (not the average of the individual year-over-year ratios) for the volume-weighted link ratio, and recognize the one situation - a thin, barely-developed origin year with a large cumulative development factor - where Bornhuetter-Ferguson is the safer method, precisely because chain ladder would multiply a single noisy figure by that large factor.

The ruin-theory and mortality-improvement items are pure reasoning, no arithmetic: ruin probability falls with a larger safety loading and a larger initial surplus, and rises with claim frequency and tail heaviness; a mortality improvement always raises a life annuity's EPV, because the writer is short longevity and every improvement means more expected payments, never fewer.

Pacing across the whole sitting

30 minutes across 20 items is about 90 seconds each on average, but the reasoning items (annuity-due timing, ruin theory, mortality direction) take well under that once known, so spend the time saved there on the compounding-arithmetic items, where the actual bottleneck is careful multiplication, not conceptual difficulty.

Because allowBack is false, flag anything you are unsure of rather than re-deriving it - a flagged item's explanation shows up on the marked script afterward regardless, and re-checking arithmetic in place costs time the clock is taking from the remaining items.

With no negative marking, always submit a computed answer rather than leaving a numeric item blank - even an answer you are not fully confident in has a chance of landing inside the tolerance, while a blank guarantees zero.

A worked example

1. The item gives one-year mortality rates for three consecutive ages and asks for the probability of surviving all three years, to four decimal places.

   $$q_x = 0.012, \quad q_{x+1} = 0.013, \quad q_{x+2} = 0.016$$

2. Convert each to a one-year survival probability.

   $$p_x = 0.988, \quad p_{x+1} = 0.987, \quad p_{x+2} = 0.984$$

3. Surviving three years means clearing all three hurdles in sequence, so the probabilities multiply rather than add.

   $${}_3p_x = p_x \cdot p_{x+1} \cdot p_{x+2}$$

4. Multiply stepwise, keeping six decimals until the final rounding.

   $$0.988 \times 0.987 = 0.975156, \qquad 0.975156 \times 0.984 \approx 0.959554$$

5. Round to four decimal places and enter 0.9596 - already visibly below any single year's survival (0.984 to 0.988), the compounding cost of clearing three hurdles instead of one.

   $${}_3p_x \approx 0.959554 \ \Rightarrow\ 0.9596$$

Common mistakes

• Adding or averaging the one-year survival probabilities instead of multiplying them. k-year survival is a product of k one-year survivals - any additive shortcut fails the tight decimal tolerances.

• Rounding each one-year survival probability to two or three decimals before multiplying. The compounding amplifies early rounding error well past the 0.0005-0.0006 tolerance; carry at least four decimals through the multiplication.

• Treating the annuity-due's first payment as discounted or contingent on survival. The k = 0 term is exactly the undiscounted payment - v^0 = 1 and the probability of surviving zero years is 1 by definition.

• Averaging the individual link ratios instead of taking the ratio of the column sums for the volume-weighted development factor - the sum-then-divide estimator is the standard one precisely because it weights large, credible years more than small, noisy ones.

• Concluding that improved mortality helps an annuity writer. It is the opposite - a longer expected payment stream from lower mortality raises the liability, which is exactly what the item is testing.

Why interviews test this

Entry-level actuarial interviews and the exams themselves both live in this exact notation - qx, px, kpx, EPV sums - so being fluent enough to convert and compound survival probabilities without hesitation is table stakes, not a differentiator. What actually separates candidates is whether they can also state, without prompting, which side of a mortality change (better or worse survival) helps which type of product - an annuity writer and a life insurer are affected in opposite directions by the same table.

On the reserving side, "when would you not use chain ladder?" is a standard follow-up question in P&C actuarial interviews, and the answer this section tests for is specific: an immature origin year where a single noisy data point gets leveraged by a large cumulative development factor, at which point Bornhuetter-Ferguson's credibility blend toward an independent a-priori estimate is the safer call. Being able to name that situation, not just compute both methods, is what the item is checking for.