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:

1. Reasons to buy less than net worth:
   1. Insurance companies charge more than the expected losses (of course) to cover their overhead, direct expenses, and to profit.
   2. 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.
   3. 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.
   4. 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.)

2. Reasons to buy more than net worth:
   1. 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).
   2. 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.

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

1. Compute your net worth.
2. Add the PV of your future wages to account for 2b above.
3. 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.
4. 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.

My latest quarterly ramblings to my Financial Professionals list are out: Financial Professionals Spring 2019

This will start a little technical (and seemingly off-topic), but should quickly get relevant and may cause you to see some things in a new light.

To begin, we need to discuss synthetic securities, and I will use stocks as the easiest one to understand. Suppose you have a non-dividend-paying stock that is trading at $50 (we could use any security that has options on it but for simplicity I will use the term “stock” throughout this piece, but you could replace it with the generic term “the underlying” with no loss of applicability if you like). If you wanted to “own” (replicate) the upside of that stock over the next three months, you could buy a call with a $50 strike price maturing in three months. If you wanted to “own” the downside of that stock over the next three months (I know it sounds weird – why would you want to do that? – but stay with me) you would sell a put with a $50 strike price maturing in three months. You could also purchase a t-bill that matured in three months at $50. (You’ll see why that matters shortly.)

Now, the interesting thing is that we can create any one of these instruments with any three of the others. For example, the stock we have been discussing is exactly equal to being long the call, short the put, and long the t-bill. Mathematically, it looks like this:

S = C – P + T

Any value that the left of the equation goes to in three months the right side will match perfectly. These relationships must hold because if there were an inequality, it would allow a risk-free arbitrage opportunity. For example, if the stock was too expensive you could short the stock and go long the instruments on the right and arbitrage the difference.

The interesting part is that with simple algebra we can rearrange this equation. For example, we can move the call option to the other side like this:

S – C = T – P

The left side of this equation is covered call writing (long the stock, short the call) which is widely considered a relatively safe “widows and orphans” type strategy. Perhaps you have noticed though that it is exactly the same as buying T-bills and selling naked puts on stocks – a strategy that most folks would consider insanely risky!

We can also rearrange to remove the risk of the stock. Suppose we are long the stock, short the call (we sold the upside), and long the put (we bought protection against the downside):

S – C + P = T

This is a really tight collar and as you can see gives you T-bill returns. (Before you get clever ideas, the tax laws would consider this a constructive sale of a stock position.)

Now in real life there are complications like dividends and the fact that the options are usually purchased out of the money. These changes make the math complicated but don’t change the underlying reality – when you do covered call writing, you are effectively buying bonds and selling naked puts, or, as the saying goes, picking up nickels in front of a steamroller.

I don’t think it changes the overall point that this “conservative” strategy is actually extremely risky, but there are two reasons that selling calls can add a little value. (The same holds for selling puts for that matter – because of the equation above I can make puts out of calls or calls out of puts by combining with stocks and T-bills – just rearrange the equation – and “put/call parity”, as it is called, exists.) First, the price of the option is based on expected volatility and historically the expected volatility is higher than the volatility that is actually realized. In short, options are probably a little bit too expensive on average (though Nassim Taleb, of Black Swan fame would argue the opposite and I’m not sure he’s wrong) so selling them (as in a covered call writing strategy) might earn a small premium. Second, there is a well-known effect called the “volatility smile” where if you graph the strike prices of the option on the x-axis and the volatility of the stock implied by the market prices on the y-axis it should be a straight line, but it generally forms a “smile” which just means that the further away from the current market price the strike price is (i.e. the more out-of-the-money or in-the-money an option is), the more expensive it is (options on stocks with higher volatilities are more expensive). Thus, out-of-the-money options are potentially too expensive. There isn’t a clear reason why this should be so, but it may be related to people’s preference for lottery-type payoffs and willingness to insure against catastrophic losses even at higher prices. Here is a graph of the volatility smile:

In short, I would caution against using covered-call-writing as a strategy unless you were also comfortable with owning a bond portfolio and writing naked puts – it’s the same thing!

By default we set up every taxable (i.e. non-retirement) account to have margin but we almost never use it. (You don’t want retirement accounts to have debt at the account level because it gives rise to UBTI – unrelated business taxable income – which is taxed at the high trust rates, but you get no basis in the IRA for it. In essence you end up getting taxed twice on the income. Leverage in the underlying investment – debt that a company holds, or a leveraged ETF – is This is why leveraged ETFs are sometimes used (but not y us): leverage in the underlying investment is fine from a tax perspective.)

If you have a diversified portfolio with both stocks and bonds (as almost everyone should) and then you add leverage through margin interest you are essentially long fixed-income and short fixed-income but almost certainly paying on the spread. It is far better to liquidate bonds (for temporary needs) or a portion of the portfolio as a whole (for longer-term needs). Nonetheless we occasionally have clients in margin for the following reasons:

1. The client needs/wants funds right away and it is worth a few days of margin interest expense to them rather than waiting for the trade to settle.

2. The client needs/wants funds and all the positions in the account have large short-term gains. This usually only happens when it has been less than a year since the client came on board or tax loss harvesting was done and the market subsequently moved up nicely. If the gain will be long-term in 10 days (for example) it might make sense to send them the funds, putting the account into margin for the 10 days, and then liquidate the position to repay the margin loan after the taxes are more favorable. For example, assume a 10% unrecognized gain, a 20% differential in long and short term tax rates, and 7% margin interest rate, and a need for $100,000. 20% of the $10,000 gain is $2,000. 7% of $100,000 for 10/365 of a year is $192. Obviously the larger the gain and the shorter the period until it becomes long-term the more this makes sense.

3. Similar to the previous item, if it is December and the client’s tax rate will be lower the following year it might make sense to use margin. For example, suppose the gains are long-term, but they are in the 15% LTCG bracket this year, but will be in the 0% LTCG braket next year. There is a 15% difference in the rate by waiting until the next year to sell.

4. The client anticipates putting the funds back before too long and doesn’t want to disturb their asset allocation (paying transaction fees to sell and then repurchase later) and paying taxes on gains. For example, suppose a client has a bonus coming (with very high probability)  in 60 days, but they find the “perfect” house to buy now and don’t want the opportunity to get away. It might make sense to take funds out of the account (causing it to go into margin) to purchase it and then replace the funds shortly when the bonus arrives.

In most cases, there are even better sources of short-term funds than margin interest – a HELOC (Home Equity Line Of Credit) for example – but sometimes it does make sense to use margin, temporarily.

My latest quarterly ramblings to my Financial Professionals list are out: Financial Professionals Winter 2019