P&C Insurance Economics 102: ROE drivers

I recently spend some time thinking and thinking about the ROE drivers of insurance companies. It was not a constant process but the understanding came to me as returns do: chunky and non smooth …

(Insurance Economics 101 can be found here)

Return on equity or ROE indicates an insurance company’s profitability in relation to its capital with ROE = net profit / equity. One can take annual (or ltm) net income or comprehensice income. I prefer to look at net income as it is a more smoot return measure, but over time, comprehensive net income should not deviate too much, and more importantly, be higher in the long run. This and other important factors is reflected in the important measure and growth of book value per share. (see a tweet regarding PGR)

ROE drivers. An insurance company has a certain amount of equity in t=0 (EQ₀), that allows for certain business and investments. Within its opportunity set, regulations, markets, and strategy the company:

• Insurance companies write (and earn) premiums in the amounts of GPW/NPW/NPE. Equity must and should be provided for higher business volume due to regulations and/or internal risk managment.
  • Regulators use a simple measure of Premiums-to-surplus (below) to determine the maximum level of business undertaken.
  • These premiums generate a technical result of TR = (1-CR) x NPE = underwriting margin x NPE.
• Insurances hold total investments from parts of its equity and float in the relation Inv/EQ.
  • These investments generate investment income or total returns on investments (ROI).
  • Float refers to premiums received but not yet earned (or paid back).
  • Float, in general, develops with premiums and is higher the more long-tail insurance is written, and thus, premium growth might be very valuable.
  • Skilled investment managmenet might result in higher (risk-adjusted) investment returns.
• The technical result (TR) and investment result (IR) or invesmtnet income, together result in Earnings before Tax (Ebt=TR+IR) which, after tax, translates into earnings after tax or net income (NI).
  • (Comprehensive) Net income over Equity results in ROE=NI/EQ.
• Depending on the dividend payout-ratio (Dividends/NI) the company retains a certain amount of net income which increases the book value of equity for the next period (EQ₁) and enables higher business volumes.
  • Over many periods the above process results in a compounding book value, and together with P/B multiples at initial point of investment (t₀) and when we exit the investment (t_T) and paid dividends, results in total investment performance.
    • P/B should positively correlate with profitability (ROE).
• Higher equity allows for
  • more business (GWP/NWP growth) which can be pursued by sales/marketing teams (otherwise premium can be ceded to re-insurance commissions), and
  • more investments with potentially a higher allocation to high-return investments carrying more risk
• (there are some other PnL items like re-insurance commissions and other income/costs, interest expenses, etc…)

(pls excuse my poor handwriting)

Premiums-to-surplus definition is for NPW/EQ, which is close to NPE/EQ if growth is at modest levels. It is a simple risk measure without taking into account the level or neither the variability of profitability (1-CR). Simple measures can have their benefits*. When we think about insurance ROEs it is helpful to think of premiums-to-surplus as NPE/EQ.

A ratio to measure the insurer’s ability to take in losses that are above the average as well as his financial power is called the premium to surplus ratio. It can be computed through dividing the net premiums written by the surplus. A lower ratio depicts greater financial strength for the company. As a rule, state regulators set up less than 3-to-1 premium surplus ratio to be adhered by insurance companies. Aus <https://www.usacoverage.com/agents/premium-to-surplus-ratio.html>

*) The sector or country allocation within an investment portfolio, based on invested capital or current market values, does not take into account the probability distribution of returns, it simply states what portion of capitla is invested. Or, said in another way: what can be lost in a worst case (worst case for equity stocks is losing 100%). The benefits of such a simple (risk) measure were probably never more obvious and relevant than after watching quotes for most Russian stocks or ADRs/GDRs approaching zero.

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