Insurance
Insurance is an interesting business. No, I'm serious. For one thing, if a company is writing unusual kinds of insurance, it has a lot of room for fudging numbers -- even more so than in most industries. When the insurer signs a contract and collects a premium, it incurs a liability equal to the expected pay-out. For an unusual contract, an insurer can easily misestimate this liability, either deliberately or honestly.

Correlation of risk is an important danger to avoid. You have to expect some claims to come in, but you don't want them all to come in at the same time. If the risks a company takes are independent of each other -- for example, 50,000 different auto insurance policies -- the company can estimate relatively well that they will have to pay, say, $30 million a year in claims. They won't know exactly which customers will have claims, and which won't, but if the company knows the odds, and if car accidents are not strongly correlated¹, the payout will be pretty predictable. On the other hand, if you write flood or hurricane insurance for 50,000 homeowners in the same town, the chances are good that either a lot of them will be hit or none of them will be. The correlation is high, and the risk to the insurance company is high.

If a small insurance company is taking on strongly-correlated risks -- or is wise enough to realize that any collection of risks will abruptly auto-correlate at the worst possible moment -- it can often buy "reinsurance" from a larger insurance company. Reinsurance will compensate the company if and only if their losses exceed a certain amount.

You might assume that the main way an insurance company makes money is to charge a premium high enough to cover the costs of insuring its risks, and that the difference is its profit. That's not quite right -- most insurance companies regularly operate with underwriting losses. You might see an insurance company refer to its "combined ratio". This is the sum of the company's "loss ratio" -- the ratio of what it pays in claims to what it earns in premiums -- and its "expense ratio" -- overhead expenses divided by premiums earned. A typical combined ratio might be 102%.

The catch is that the insurance company gets the premiums up front, and pays the claims substantially later. What the company is doing, in essence, is borrowing money from policyholders at a rate of 2%. The amount of money being borrowed is called "float", and is recorded as liabilities called "unearned premiums" and "unpaid losses". What an insurance company tries to do, then, is essentially the same thing a bank does -- it borrows money at one rate, and tries to invest it at a higher rate. Banks are more restricted in the risks they can take, and they know with more certainty what rates they will be paying. Insurance companies generally invest more in equities, and don't know precisely what combined ratios they'll get until after they see their losses come in.

The P/E ratio is a terrible valuation metric to use for an industry in which earnings fluctuate with the stock market. A back-of-the-envelope calculation I like to use to value an insurance company is book value, minus non-investment assets, plus a percentage of float. Let me explain my reasoning: if the combined ratio is consistently exactly 100%, the company can invest the float and keep the profits. If the float never shrinks -- as old claims are paid off, they're replaced with new premiums -- this is essentially equivalent to owning the float. So if the investment manager can earn a fair return on both the company's investment assets and its float, the company is worth book plus float, minus any assets used in generating the float, which I assume is all non-investment assets. If the combined ratio is 102%, and a fair interest rate is 5%, I might suppose that three fifths of the float counts as equity. This isn't a very sophisticated model -- you have to assume that the float won't evaporate, that there aren't negative surprises upcoming, that the investment manager is good, etc. -- but if I think a company is growing its float and can maintain its combined ratio, I like the model for its simplicity.

My car insurance company, Commerce Group, has been growing float and earning a consistent underwriting profit, with a combined ratio of around 98-99%. According to their latest financial reports, reflecting the end of September '03, they had non-investment assets (i.e., "bad" assets) of about $998 million, equity of $857 million, unpaid losses of $953 million, and unearned premiums of $853 million. If we sum the last three figures and subtract the first, we get a value of $1.665 billion, or about $52/share. The stock closed yesterday at $43.65.

If you buy and lose money on it, I take no responsibility for your loss². But it looks interesting to me.


1. I would guess that the main source of correlation for car accidents is the weather -- i.e., if the weather is really bad, a lot of people will crash, or cars will experience hail damage, or whatnot. I don't know how big a factor this is, but I assume it's not huge.

2. If you make money, feel free to give me credit, though I should acknowledge that my attention was drawn to the stock -- and its impressive combined ratio -- by a fellow BU student.

- posted by Steven @ 8:22 AM