Why Product Mix Is a Risk Decision
A product can be attractive on its own and still change the risk profile of the business in an undesirable way. A launch may broaden the portfolio, but it may also expose several products to the same event. An expansion may increase contribution while making one line too dominant. A withdrawal may reduce one large exposure yet leave the remaining portfolio more concentrated.
A risk-informed product portfolio decision therefore compares the before-and-after mix, not just the proposed product in isolation. Concentration measures, common scenarios, and strategic fit each answer a different question. None is a complete measure of risk or a substitute for judgment about the business’s objectives and constraints.
Measuring Concentration Without Mistaking It for Risk
One simple screening measure is the Herfindahl-Hirschman Index (HHI). Select a consistent measure of portfolio size, such as annual premium, and calculate each product’s share of the total. The HHI is the sum of the squared shares. In this tutorial, shares are expressed as decimals, so the HHI ranges from values near zero for a broadly distributed portfolio to one when a single product represents the entire total.
Here \(w_i\) is the selected size measure for product \(i\), and \(s_i\) is its share. Squaring gives greater weight to larger shares. The measure is useful for comparing portfolio mixes on the same basis, but it does not capture product volatility, severity, shared exposures, or the quality of risk controls. Premium is only a proxy for portfolio size; if products have materially different risk per premium dollar, a premium-weighted HHI can give an incomplete picture.
The basic effect of an expansion follows directly from the definition. If product \(k\) grows by \(x\), its numerator changes from \(w_k^2\) to \((w_k+x)^2\), while the portfolio total changes from \(W\) to \(W+x\). Thus:
The denominator must be recomputed because every product’s share changes when the total changes. The resulting HHI can rise or fall: the direction depends on the existing product’s share and the expansion’s size. This is why it is safer to calculate both portfolio values than to assume every expansion increases concentration.
Worked Example: Expanding a Dominant Product
A hypothetical insurer has annual premiums of $65 million for property, $30 million for casualty, and $20 million for life. It is considering adding $15 million of property premium. The company uses a premium-weighted HHI screening limit of 0.43. Under a specified severe event, the expanded property portfolio is estimated to incur a $10 million loss, casualty a $5 million loss, and life a $2 million loss. Determine whether the proposal meets the HHI and scenario-loss limits, where the loss limit is $18 million.
Method. Recalculate the shares using the post-expansion premium total, then separately add the losses for the stated event.
After expansion, property premium is \(65+15=\$80\) million. Total premium is \(80+30+20=\$130\) million. The shares are \(80/130\), \(30/130\), and \(20/130\). Therefore:
The HHI of 0.4556 exceeds the 0.43 limit, so the proposal fails the concentration screen. The specified scenario loss is \(10+5+2=\$17\) million. Since $17 million is below the $18 million limit, it meets the scenario-loss limit. The proposal meets one limit but not both.
Check. The post-expansion premium components sum to $130 million, and the scenario losses sum to $17 million. The HHI is \(7700/16900\), not a value based on the old $115 million total. A common mistake is to calculate the enlarged property share but leave the denominator unchanged; the correction is to recalculate every share using the new total.
Shared Exposures and Scenario Aggregation
Portfolio choices should also be tested against events that may affect more than one product. A shared exposure might arise from products covering the same locations, relying on the same critical service, or responding to the same external event. A portfolio can appear diversified by product name while remaining vulnerable to a common cause.
For a specified scenario, let \(L_i\) be the loss attributable to product \(i\), measured on a consistent basis. If the product losses are distinct components of the total loss, the portfolio loss in that scenario is their sum. This is not an assertion that the product losses are independent; it is an accounting identity for the stated scenario.
The justification is direct: if the event produces separate losses \(L_1,L_2,\ldots,L_n\), the total is the amount paid or incurred across those components. A shared cause does not make the components disappear; it makes it especially important to include all affected products. Conversely, if one underlying loss has already been counted in a product-level estimate, it must not be added again as a separate “shared” loss.
Worked Example: Two Launch Options With Different Shared Exposures
A hypothetical insurer has products A, B, and C with annual premiums of $50 million, $30 million, and $20 million. A portfolio rule requires an HHI no greater than 0.35, a loss no greater than $20 million under a defined wind event, and a strategic-fit score of at least 3 on a five-point scale. Existing wind-event losses are $8 million for A, $5 million for B, and $2 million for C. The insurer is considering either product D, with $25 million of premium and a wind-event loss of $7 million because it covers locations already exposed through A, or product E, also with $25 million of premium and no loss in this particular wind event. The strategic-fit scores are 4 for D and 3 for E. Compare the options against the stated tests.
Step 1: Calculate the existing concentration. Total premium is \(50+30+20=\$100\) million. The existing HHI is:
Step 2: Calculate concentration after either launch. Either option increases total premium to \(100+25=\$125\) million. For D, the HHI is:
E has the same premium and therefore the same HHI, 0.2832. Both options meet the 0.35 concentration limit.
Step 3: Compare the wind-event losses. Existing portfolio loss is \(8+5+2=\$15\) million. With D, the total is \(15+7=\$22\) million, above the $20 million limit. With E, it remains \(15+0=\$15\) million, below the limit. D’s loss is added because the scenario specifies that its covered locations are exposed to the same wind event; adding this product changes the portfolio result even though the HHI is identical.
Step 4: Apply the strategic-fit test. D scores 4 and E scores 3, so each meets the minimum score of 3. Under these stated tests, E meets all three; D meets the concentration and strategic-fit tests but fails the wind-event limit. This does not establish that E is preferable under every business consideration: the result is limited to the selected measure, scenario, and fit assessment.
Check. Both post-launch totals are $125 million, and \(4425/15625=0.2832\). The event losses are $22 million for D and $15 million for E. The common trap is to infer that equal premium and equal HHI imply equal risk; the scenario calculation shows why they do not.
Withdrawals, Rebalancing, and Strategic Fit
Withdrawing a product can reduce total losses in a particular scenario, but it can also increase the concentration of the remaining portfolio. The change in HHI depends on the shares left behind, not merely on the size of the withdrawn product. A withdrawal decision should therefore identify both what risk is removed and what capabilities, contribution, or diversification may be lost.
Likewise, a replacement launch should be assessed as part of the proposed new mix. Comparing “withdraw” with “withdraw and replace” makes the consequences visible. Strategic fit should be stated against the organization’s objectives—for example, whether a product uses capabilities the business intends to build or creates a material mismatch with its chosen direction. A fit score can help structure discussion, but it is a judgment, not a physical risk measure. The basis for the score and any minimum threshold should be clear.
Worked Example: Withdraw or Replace a Large Product
A hypothetical insurer has annual premiums of $60 million for product A, $25 million for B, and $15 million for C. Its specified regional-disaster losses are $11 million, $4 million, and $1 million, respectively. Annual contribution is $6 million for A, $3 million for B, and $2 million for C. Management is considering withdrawing A. A proposed replacement, D, would have $20 million of premium, a $2 million loss under the same disaster scenario, and annual contribution of $2.5 million. Compare the existing portfolio, withdrawal alone, and withdrawal with D.
Existing portfolio. Total premium is $100 million. Its HHI is:
The scenario loss is \(11+4+1=\$16\) million, and total annual contribution is \(6+3+2=\$11\) million.
Withdrawal alone. After removing A, total premium is \(25+15=\$40\) million. The remaining shares are \(25/40=0.625\) and \(15/40=0.375\), so:
The scenario loss falls to \(4+1=\$5\) million, while contribution falls to \(3+2=\$5\) million. The event loss is lower, but the remaining portfolio is more concentrated than before.
Withdrawal with replacement D. The new total premium is \(25+15+20=\$60\) million. The HHI is:
The scenario loss is \(4+1+2=\$7\) million, and contribution is \(3+2+2.5=\$7.5\) million. Relative to withdrawal alone, the replacement increases the scenario loss by $2 million and contribution by $2.5 million, while reducing the HHI from 0.53125 to about 0.3472. Relative to the original portfolio, it has lower scenario loss, lower contribution, and lower HHI. Those comparisons expose the trade-offs; they do not by themselves determine whether the change is strategically desirable.
Check. The replacement portfolio’s components total $60 million, its scenario loss is $7 million, and its contribution is $7.5 million. A common mistake is to report that removing the largest product necessarily lowers concentration. Here withdrawal reduces the scenario loss but raises HHI from 0.4450 to 0.53125.
A Practical Comparison Sequence
A disciplined comparison keeps the inputs and decision tests visible. It also prevents a favorable result on one measure from obscuring a failure on another.
Specify the products, business unit, time horizon, and whether the choice is a launch, expansion, reduction, or withdrawal.
Choose a consistent size basis for concentration and a consistent loss basis for scenario comparisons. Explain when premium is only a proxy for risk exposure.
Update the total and every affected share. For each selected scenario, include losses from all products affected by the event and avoid counting the same underlying loss twice.
State the relevant objective, the basis for any qualitative assessment, and which limits are binding. Do not treat a fit score or concentration threshold as a complete risk assessment.
Compare before and after results, identify what risk or capability is added or removed, and state what remains uncertain or outside the selected tests.
Common Exam Traps
- Using an old denominator. After a launch or expansion, recompute total premium and every share before calculating HHI.
- Calling HHI a risk measure. It summarizes concentration on the chosen size basis; it does not measure severity or identify common causes.
- Assuming different product names mean independent exposures. Check whether products may respond to the same event, region, service provider, or other common factor.
- Counting a shared loss twice. Aggregate distinct product-level loss components, but do not add an exposure again if it is already included in a component estimate.
- Letting one favorable result settle the decision. A proposal can meet a scenario limit and fail a concentration limit, or fit strategy while creating unacceptable exposure. Report each test separately.
Check Your Understanding
For each problem, calculate or compare the requested portfolio results before checking the final answer.
- A hypothetical portfolio has annual premiums of $40 million, $35 million, and $25 million. A proposed expansion adds $20 million to the first product. Calculate the HHI before and after the expansion, using decimal shares. (Answer: Before: 0.3450; after: \(5450/14400\approx 0.3785\).)
- A portfolio has scenario losses of $6 million, $4 million, and $3 million across three products. A proposed launch adds $5 million of loss under the same scenario because it covers an exposed site already insured through one existing product. The portfolio limit is $17 million. What is the total scenario loss, and does it meet the limit? (Answer: $18 million; no, it exceeds the limit by $1 million.)
- Products A, B, and C have premiums of $50 million, $30 million, and $20 million. Product A is withdrawn. Calculate the HHI before and after withdrawal. (Answer: Before: 0.3800; after: \((30/50)^2+(20/50)^2=0.5200\).)
- A portfolio has event losses of $9 million for product A and $4 million for product B. A new product C adds a distinct $3 million loss under the same event, but an additional $2 million “shared event adjustment” is already included in A’s $9 million estimate. What total should be reported? (Answer: $16 million: \(9+4+3\); do not add the $2 million again.)
- A proposed launch reduces premium-weighted HHI from 0.40 to 0.31, but increases a specified common-event loss from $14 million to $21 million. The concentration limit is 0.35 and the event-loss limit is $18 million. State whether each limit is met and what conclusion follows from these tests. (Answer: The HHI limit is met; the event-loss limit is failed by $3 million. The proposal does not meet both limits, despite the lower HHI.)