Prices for insurance coverage changed as follows:
Value up to $50 is $1.65.
$50.01 to $100 is $2.05.
$100.01 to $200 is $2.45.
$200.01 to $300 is $4.60.
The price per additional $100 of insurance, valued over $300 up to $5,000, is $4.60 plus $0.90 per each $100 or fraction thereof.

Crudely taking the mid-point of each bracket up to $300, we get implied loss rates of 6.6%, 2.73%, 1.63%, 1.84%, respectively. The rate converges asymptotically to $0.90/$100, or 0.9% implied loss. The numbers have such a wide range that it’s worth taking a closer look.

On page 1 of this 2011-2012 report, it is stated that “lost mail volume is estimated at 1.79 percent.” At these 2007 rates (compare gray and orange lines of below figure), paying for insurance is surely uneconomical for anything under ~$100, but has potentially arbitrageable positive expectation for items valued at ~$300 or more. This is surprising.

Interestingly, some of these underpricings have been rectified according to this 2017 document:

Amount for Merchandise Insurance Coverage Desired
$0.01 to $50: $2.10
50.01 to 100: 2.65
100.01 to 200: 3.35
200.01 to 300: 4.40
300.01 to 400: 5.55
400.01 to 500: 6.70
500.01 to 600: 9.15
600.01 to 5,000 (maximum liability is $5,000): $9.15 plus $1.25 per $100 or fraction thereof over $600 in declared value.

These (again, gray and orange lines of below figure) align much more with actual loss rates; still, there is an asymptotic positive expectation for paying for insurance, and in amounts closer to upper bracket limits. Amounts at the lower bracket limits, though, now hug the actual loss rate line, and that may be a part of the pricing decision after all.

What about the high rates on low-value items? That’s probably the result of an embedded per-incidence fixed cost. We can back this out by assuming $50 is the target insured amount for the $0 to $50 bracket for the purpose of pricing fixed costs. One model is to obtain an implied loss rate at $50 to match the asymptotic rate, i.e. insurance cost at $50 = asymptotic loss rate * $50 + fixed cost (*), though this can be used (as we do later) at any target insured amount.

At 2007 prices, this gives $1.2 per insured item as the fixed cost portion, or $1.2/0.9% = $133.33 per incidence. Similarly, at 2017 prices, this gives $1.475 per insured item or $1.475/1.25% = $118 per incidence. These costs seem plausible. Implied loss rates adjusted for such costs are plotted as the blue lines in previous figures.

The last oddity is that Express Mail insurance rates have built-in insurance up to $100. Let’s find out how much that is worth. Using the same, older 2007 document that quotes for Express Mail, we have:

Prices for Express Mail insurance:
The first $100 of value is still provided. Values above $100 are now priced differently than for regular insurance.
Value over $100 up to $200 is $0.75.
$200.01 to $500 is $2.10.
$500.01 to $5,000 is $2.10 plus $1.35 per each $100 or fraction thereof.

The asymptotic loss rate is priced at 1.35% — interesting that Express Mail should have significantly more implied losses than domestic mail overall. Assuming the same $133.33 per incidence fixed cost as for all domestic mail in 2007, but substituting $100 as the target insured amount into (*), we obtain an insurance cost at $100 of $3.15. So there you go, the “true” price table might be:

$0-$100: $3.15
$100-$200: $3.90
$200-$500: $5.25
$500-$5000: $5.25 + $1.35 per each additional $100

This is rather favorable for insured values just under the $500 mark!

I place an order from the location of the red square to the green and purple exchanges on which trades occur. My communication capability on the gray “public” channel is slower than the communication capability of some competing agent on the blue “private” channel. Therefore, triangle inequality notwithstanding, the competing agent observes my actions at the green exchange and reacts at the purple exchange before my order arrives there. It appears to me exactly like I have been scooped by somebody acting anti-causally, so what happened?

Well, somebody (the competing agent) did see the future, in some sense. Simultaneity does not exist at this time scale, just like in special relativity. The competing agent is simply taking advantage of this fact.

This is of course old news, but it’s nevertheless interesting to hear the two perspectives — one that considers this as front-running and one that considers this as fair competition. After all, all that the competing agent had was a more capable channel, which no one is prohibited from obtaining. This “difference of opinion” is of course nothing of the sort, but rather the symptom of a much deeper problem.

Consider this question: Do we assume there is a single market on which all trades occur? The SEC certainly did when it promulgated Regulation NMS, which among other things blithely assumed the existence of a “National Best Bid-Offer” (NBBO), basically a market-wide best price among numerous exchanges. In the days when communication delays were short compared to the interval between market transitions (i.e. low-frequency trading), there was indeed a single market. But when communication delays are now long compared to the interval between market transitions (i.e. high-frequency trading), the assumption breaks down. The exchanges, if they are some distances apart, represent different partial markets, each with a local price. There is no way at all to pretend there is a single market with a single price, despite the frantic latency arbitrages that high frequency strategies employ to synchronize prices across exchanges. (Yes, they are actually performing this service.) It’s futile. There will always be this inefficiency to exploit, and it is an inherent frictional cost of this kind of market structure, to speak nothing of the information asymmetry caused merely by different locations of agents and their communication capabilities. In other words: bad system design; bad, because nobody actually “designed” it and probably nobody thinks of it as one “system.”

So let’s recap. It seems that there are several problems with today’s trading system. Due to the improvement in technology, many assumptions that were approximately correct, such as the existence of a law of one price and simultaneity, are no longer valid. In other words, a single NBBO is not even well defined. Instead we have point-to-point information propagation that cross at certain geographic midpoints.

What to do? Actually, this problem has been solved before. As logic components in computer systems became faster, propagation delay became important and if it weren’t for clocks, systems would enter ambiguous states and become unstable. The solution was latched clocking: allow state changes only at quantized intervals of time, and in the intervening time, the changes would have the opportunity to propagate across the entire system so that the overall system state was once again consistent. The same thing works for trading markets, i.e. allow the market state (trades and incoming orders) to update only at quantized intervals of time, and allow enough time to pass between for these information to be received by all exchanges forming the same market. The goal is to get back to the regime where communication delays are short compared to the interval between market transitions.

Elaine Wah of the University of Michigan has a paper on this, with analysis showing the actual financial benefits of removing the inefficiency inherent in continuous trading. Generally, market performance should improve when we clock at speeds relevant to the underlying information generating and decision feedback processes. Any faster and we are introducing noise and also by not allowing signals (trading interests) to fully mix into a steady state, end up introducing large transients (volatility, worse executions) into the system.

This besides, it is great to see EECS getting involved in solving what is essentially an information and engineering problem, using methods that have been tried in digital computer circuits.

I am surprised that this happens. The distribution of closing prices should be sharply cut off at the lower end, because any good selling at substantially below the mean is subject to arbitrage on the price distribution. This works best for abstract goods like gift certificates, where there is no shipping cost to complicate matters. For example, a gift certificate sells for $100 on average, so you bid on all auctions for it at $95. If there is enough price fluctuation, you will get a few at that price. Now you relist them. There are more sophisticated options but let’s say you just relist them as auctions. Then on average, you will get $100. So you make $5 for each one sold.

If everybody thinks this can be done, they will all go do this and there will be no auctions that close below $95.

This shows closing prices of equally valued amazon gift certificates sold on ebay within the last two days. There are a lot of “buy it now” transactions listed, and those tend to be at the higher end. It seems like an excellent arbitrage opportunity right here to bid on auctions selling at below $80 and relist as “buy it now” for, say, $88. Ebay and paypal fees will eat about $6, so there is still a profit of at least $2 each time this happens.