concept about equity and policyholder surplus...

[victorandjenny]

In the Werner&Modlin Ratemaking 4th edition, on page 138, the book talks about investment income.
I believe the authors do not use two words, "equity" and "policyholder surplus", very accurately. In fact, the insurer can invest capital, which equals asset minus reserve. Here the capital is bigger than equity or policyholder surplus, because equity or policyholder surplus equals asset minus liability, and liability should be bigger than reserve.
For example, if the insurer cellected premium for a 2-year policy, which is $100. The projected loss is $75 in the following 2 years. Assuming the total expense, including the projected future expense, on this policy is $15, and the profit is thus $10 if we do not consider investment income. The equity is only $10, right?
This insurer does not need to set the loss reserve of $75 at the beginning. Maybe the loss reserve for the first half year is $30 and then increase the reserve to $50 at the end of the first year, assuming there is no claim reported in the first year.
So at first, it is not risky for the insurer to invest more than $10 at first. Right?

Thanks.

[Vorian Atreides]

If the insurance company is a "stock company"--that is, it's publically traded (like Allstate)--its assets less liabilities is called "equity".

If the insurance company is a "mutual company"--that is, it's technically owned by the policyholders (like State Farm)--its assets less liabilities is called "policyholder surplus".

Allstate might have a supplemental "policyholder guarantee fund" to ensure that the stockholders are not taking all of the equity in the event of insolvency, but this isn't what's being refered to in W&M.

It's in this context that the two terms are treated the same.

[victorandjenny]

Thanks for your answer.
My main point is that in the W&M paper, they write that the insurer can invest equity, but I think it can invest more than equity, because the liability is for a long policy period and at first, you do not want to put all projected loss aside as reserve.


If the insurance company is a "stock company"--that is, it's publically traded (like Allstate)--its assets less liabilities is called "equity".

If the insurance company is a "mutual company"--that is, it's technically owned by the policyholders (like State Farm)--its assets less liabilities is called "policyholder surplus".

Allstate might have a supplemental "policyholder guarantee fund" to ensure that the stockholders are not taking all of the equity in the event of insolvency, but this isn't what's being refered to in W&M.

It's in this context that the two terms are treated the same.