Welcome to Expense Assumptions and Expense Allocation!

In the world of actuarial work, we spend a lot of time worrying about interest rates and when people might die or get sick. But there is a silent "profit-killer" that every provider of financial products must master: Expenses. If you don't accurately estimate and allocate the cost of running the business, even the most brilliantly designed product will lose money.

In this chapter, we explore how to categorize costs, how to decide which product pays for which lightbulb in the office, and how to set the assumptions that go into our financial models. Don't worry if this seems a bit "accountancy-heavy" at first—we will break it down into simple, logical steps!

1. The Types of Expenses

Before we can model expenses, we need to know what they are. In CP1, we generally classify expenses by when they happen and what they are for.

A. Timing-Based Classification

  • Initial (Acquisition) Expenses: These are the costs incurred when selling a new contract. Examples include commission to agents, marketing costs, and the cost of underwriting (assessing the risk).
  • Renewal (Maintenance) Expenses: These are the ongoing costs of keeping a contract on the books. Examples include premium collection, sending out annual statements, and general policy administration.
  • Termination (Claim) Expenses: These are the costs incurred when a contract ends, whether because of a claim (e.g., death or a general insurance loss) or because the customer cancels (surrenders) the contract.
  • Investment Expenses: The costs of managing the assets that back the liabilities. This includes brokerage fees and the salaries of the investment team.

B. Nature-Based Classification

  • Fixed Expenses: Costs that don't change regardless of how many policies you sell (e.g., the rent for the head office).
  • Variable Expenses: Costs that vary directly with the volume of business (e.g., a \$50 medical fee for every new life insurance applicant).

Quick Tip: Think of a coffee shop. The rent is a fixed expense. The cost of the coffee beans is a variable expense. To be profitable, the price of one latte must cover its beans plus a tiny slice of the rent!

2. Expense Allocation

Expense allocation is the process of deciding how much of the total company spending should be "charged" to each specific product or policy. This is vital for pricing and valuation.

How do we allocate?

Actuaries usually express expenses in the model in one of the following ways:

  • Per Policy: A flat dollar amount per contract (e.g., \(E_{per\_policy} = \$100\)). This is common for renewal admin.
  • Percentage of Premium: Common for commissions or premium taxes (e.g., \(5\%\) of every premium paid).
  • Percentage of Sum Assured/Benefit: Sometimes used for underwriting or claim costs.
  • Percentage of Fund Value: Standard for investment management expenses (e.g., \(0.5\%\) of assets under management).

Direct vs. Indirect Costs

It is easy to allocate direct costs (like commission on a specific sale). It is much harder to allocate indirect costs (overheads like the CEO's salary or the legal department). Usually, these overheads are spread across all products based on a reasonable "driver," such as the number of policies or the total premium income.

Key Takeaway: If you allocate too many expenses to a product, the price will be too high and no one will buy it. If you allocate too few, the company will report a loss because the actual costs weren't covered.

3. Setting Expense Assumptions

When we build a model to value provisions or price a product, we need to predict what expenses will look like in the future. Here are the factors we must consider:

A. Expense Inflation

This is a major exam point! Expenses (like salaries and rent) usually increase over time. Important: Expense inflation is often higher than general price inflation (CPI) because insurance companies are labor-intensive, and salary inflation often outpaces price inflation.

In our models, if the current expense is \(E\), the expense in year \(t\) will be: \(E \times (1 + i_{exp})^t\) where \(i_{exp}\) is the assumed rate of expense inflation.

B. New Business Volumes

If a company expects to grow rapidly, it can spread its fixed costs over more policies, reducing the "per policy" expense. However, if the company is shrinking, the expense per policy will go up (this is known as expense diseconomies of scale).

C. One-off vs. Recurring Costs

When looking at historical data to set assumptions, actuaries must strip out "one-off" costs (like a one-time IT system upgrade) so they don't accidentally assume those high costs will happen every year forever.

Did you know? Technological changes can radically change expense assumptions. Moving from paper-based claims to an automated app can turn a high-cost termination expense into a very low one!

4. Living with the Solution: Monitoring Expenses

Once the product is launched, the Actuarial Control Cycle tells us we must monitor what actually happens. This is part of "Living with the solution."

Analysis of Surplus/Profit

Companies perform an analysis of surplus/profit to see why they made more (or less) money than expected. If Actual Expenses < Expected Expenses, the company makes an expense profit. If Actual Expenses > Expected Expenses, it suffers an expense loss.

Management Actions (Syllabus 5.1)

If expenses are too high, providers may:

  • Outsource administration to a cheaper third party.
  • Invest in automation to reduce staff head-count.
  • Review commission structures.
  • Close a product line if it is no longer "expense-efficient."

Quick Review: Key Concepts

Common Mistakes to Avoid:

  • Forgetting to include inflation on future renewal expenses.
  • Assuming all expenses are variable; remember that some costs stay the same even if sales drop.
  • Ignoring investment expenses when calculating the net investment return.

Summary Checklist:

  1. Identify the expense type (Initial, Renewal, Termination, Investment).
  2. Decide on the allocation basis (Per policy, % of premium, etc.).
  3. Adjust for future expense inflation.
  4. Consider economies of scale based on expected business volumes.
  5. Monitor experience via analysis of surplus/profit.

This concludes the notes on Expense Assumptions and Allocation. Remember: in CP1, always think about the commercial impact—how does a change in expenses affect the provider's ability to meet the needs of its stakeholders?