I have been thinking for a while about how much umbrella liability coverage someone should have. The rule of thumb that people should carry an amount equal to their net worth seemed wrong a few ways:

- Warren Buffett needs a $85 billion dollar policy?
- Assume a $2mm claim where the insureds used the rule of thumb:
- The person with $1mm net worth is wiped out
- The person with $2mm net worth is fine

I think I have solved the problem though. To simplify the analysis, assume for the moment that:

- The insurance is priced at the pure cost of insurance. In other words, the magnitude of the claims times the probability of the claims. Thus, there is no profit margin, expenses, etc. for the insurance company.
- The insured is essentially risk neutral. In other words, we don’t care about being insured, and given the previous assumption we are indifferent to carrying the insurance. (Because
*on average*we lose the same amount either way – through claims or through premiums.)

Because the odds of a claim go down with the size of the claim the initial amount (the first $1mm say) will cost more than additional amounts (the second $1mm should be cheaper, the third $1mm cheaper still, etc.).

Since the insurance is accurately priced, it might seem that there is no way to determine how much to buy. The first $1 million is fairly priced, but so is the second, etc. and we are indifferent. BUT *we don’t actually get that amount of coverage.* Imagine I have a net worth of $1mm and I buy a $1mm policy. I have paid (in my idealized example) *exactly *the right amount for it. But suppose I have a net worth of $50k and I buy a $1mm policy. It costs the same amount (it’s still a $1mm policy after all), but it is only “saving” me $50k – I can’t lose more than my net worth! So in this case I am paying 20x the amount I should for coverage. (I know I am ignoring wage garnishment, but I am keeping this simple for the moment – I’ll make this more complete below.) So I should buy the amount that matches my net worth so as to match the cost to the value to me.

Of course my example above is too simplistic, so here are the other considerations:

- Reasons to buy
*less*than net worth:- Insurance companies charge more than the expected losses (of course) to cover their overhead, direct expenses, and to profit.
- There is likely an adverse selection problem where if you are buying out of an abundance of prudence, you are likely in a risk pool that includes at least some people who know they are prone to problems. I.e. the premium covers the average person and you are likely less risky than average if buying this as part of a well-thought-out and prudent financial plan rather than because you know you sometimes drive while impaired.
- Much of your net worth may not be attachable by creditors (which is what the folks suing become if they win). “Net worth” should be reduced by retirement plans, insurance and annuity cash values, spendthrift trusts, etc. In short, anything that isn’t available to satisfy a judgment.
- Competition (and lack thereof) probably makes small amounts correctly priced, but larger amounts less so. In other words, there are so many companies that will write a $1mm policy the prices are probably not too much above the expected claims. A $20mm policy is probably priced well above the expected claims. (I have no data on this, I am merely speculating – but I am pretty sure I am right.)

- Reasons to buy
*more*than net worth:- Since we are in fact risk averse, having extra (to avoid our $1mm net worth being wiped out by a $2mm claim) can make sense. Since wealth has decreasing marginal utility, the small amount we pay for premiums costs much less in utility (happiness) than then large possible losses in utility – even adjusted for the differing probabilities (100% chance of paying a small premium vs.
*much*less chance of a large claim). - To the extent your wages can be garnished (even after going through bankruptcy) the PV of future wages (i.e. human capital) should be insured too.

- Since we are in fact risk averse, having extra (to avoid our $1mm net worth being wiped out by a $2mm claim) can make sense. Since wealth has decreasing marginal utility, the small amount we pay for premiums costs much less in utility (happiness) than then large possible losses in utility – even adjusted for the differing probabilities (100% chance of paying a small premium vs.

So, here’s how to determine the appropriate amount of coverage:

- Compute your net worth.
- Add the PV of your future wages to account for 2b above.
- Subtract any protected amounts (retirement plans, PV of protected portion of wages, home equity that has homestead exemption, etc. – see here for a comprehensive list) to account for 1c above.
- Round up by $1mm (or more depending on risk aversion) to account for realistic risk aversion. In other words, I think 2a trumps 1a, 1b, and 1d for most folks.