There are plenty of actuary jokes out there that play on the stereotypes of those that work in the life insurance field. Carrying around a calculator or mortality table may seem to be the definition of a joke, but these are actually supplies that actuaries do carry around! Actuaries are the insurance mathematicians who do the calculations for the insurance products – mainly determining what a policyholder pays for their insurance, and determining the liability reserve that the company needs to hold in order to be able to pay out projected death benefits in death claims for a policy.
Most of the general public is familiar with term life insurance as this is the most commonly sold product. Policyholders shop around for term life insurance, and they are given a quote for their premium to pay (typically monthly or annually) based on the desired death benefit (often known as the face value). Factors that go into determining what their rate will be include the age at purchase, male or a female, and smoker or non-smoker. (Note that I am not accounting for smoking in this example.) The actuarial calculations for the rates also do not include expenses and pricing the product to make money.
How are term life insurance premiums calculated?
- Use the mortality table, the face value, and the interest rate to determine the net present value of the death benefit (in other words, for each policyholder that purchases a term life insurance policy what is the cost of their death benefit). Keep in mind that for a term policy over say 30 years, the policyholder (or rather their benefit recipients), do not receive any of the face value unless the policyholder dies! Often people will buy life insurance for the value of their home in case they die for example. In the 2001 CSO life mortality table, the interest rate used for calculations is 6%.
- Net Present Value of Death Benefit = sum of the Present Value of Death Benefits for each year in the policy (
- Present Value of Death Benefit = (probably of dying in a given year) x (probability of surviving to that year) x (discount factor)
- Net Present Value of annuity due = sum of Present Values of annuity due payments
- Present Value of annuity due = (probability of surviving to that year) x (discount factor)
- To determine the premium, set up the equation NPV of Death Benefits = (Premium) x (Net Present Value of annuity due), and solve for the Premium at year 0 since premiums are level over the policy duration.
- Keep in mind that premiums are paid a the BEGINNING of the period, and the death benefit is paid out at the END of the period (in this theoretical example at least)!
Breaking down the Present Value of Death Benefit by year (note that this example uses 5.5% interest, not 6% interest!)
What are reserves and how are they calculated?
- Insurance premiums are level every year, and likelihood that the death benefit will be paid to the policyholder increases over time – therefore insurers need to hold a reserve for each policy on their books to account for the difference between the NPV of the premiums and the NPV of the death benefit
- Reserves go into an insurer’s financial statement a liability because this is extra money they need to set aside and hold to pay out the death benefit for claims
- Note the humpback curve. The reserve for a policy starts at 0 (because this is when the policy premium is calculated) and also ends at 0, and reaches its highest amount in the middle of the policy duration. This is where the mortality path intersect the level premium amount.
Use this visualization to understand the components of their financial statements and also how to use the reserve liabilities for corporate finance decisions. Understanding what actuaries do is just part of the complex structure of an insurance company!
Want to create this view yourself? Check out the link to the article, including steps to set up the dashboard. https://www.codemag.com/Article/2001091/Financial-Modeling-with-Power-BI-and-DAX-Life-Insurance-Calculations
-HW