In my first article, "Legerdemath: Tricks of the Banking Trade," I made brief mention of Treasury-rate locks:

"Most brazenly, we taught clients phony math that involved settling Treasury-rate locks by referencing Treasury yields rather than prices."

A number of readers expressed doubt that using a settlement method based on Treasury prices was appropriate. What follows is an abridged explanation of a Treasury-rate lock deception. I offer it not in the misguided hope of stamping out abuses in Treasury-rate lock transactions. Rather, I seek to give a detailed example of a certain *type* of behavior -- hoping it carries more weight coming from an ex-insider speaking onymously.

There are two basic ways to describe the value of a Treasury bond, either by price or by yield. Price answers a simple question: How much would it cost you to purchase a bond? This price will change over time, in much the same way that the price of a stock changes over time. Playing counterpart, yield expresses the return that will be earned by purchasing this bond at a certain price.

It is similar to how one can describe the speed of a car either by the average number of miles per hour it is traveling at or by the time it takes it to travel one mile -- if you know one you can solve for the other, and if one goes up the other comes down.

To belabor the point, either "1 mph" or "a 60-minute mile" provides you access to the same knowledge about the speed of a car. And, just as traveling at 1 mph allows you to complete a mile in 60 minutes, purchasing a bond at a certain price "allows" you to earn a certain return (i.e. a certain yield) on your investment.

Now back to Treasury-rate locks. When a company puts on a Treasury-rate lock, it is putting on a bet that will pay off for the company if Treasury prices go down and go against them if prices go up. I ask that you accept on faith that sometimes this bet, rather than being a gamble, reduces risk and uncertainty for a company.

When the time comes to settle this bet, the change in value of the bond must be calculated. This should be a simple matter of subtracting the bond price at the time of settlement from the price agreed to when the rate lock was put on.

However, when it comes to bonds, corporate clients do not think in terms of price; they think in terms of yield because yield is expressed in the language of interest rates, the same language companies are familiar with from business concepts such as rates of return and borrowing costs.

And so the client is conveniently never shown how to settle based on prices. Instead they are taught a nonsensical and more complicated method called yield settlement. The sole purpose of this settlement method is to trick the client into allowing the bank extra profit. Unaware that they should even take a second look at what they assume is procedural, the client does not question.

Whereas price settlement asks, "By how much did Treasury prices change?" yield settlement asks, "By how much did Treasury yields change?" But how does one convert a change in yield (i.e. a change in an interest rate) into a dollar value that can be paid out? The short answer is that one cannot.

But why not? If price and yield are both valid ways of expressing the value of a bond, shouldn't you be able to measure the change in value of a bond by looking at either the change in its price or the change in its yield? Resorting to hyperbole, teaching a client yield-based settlement is akin to selling them on skipping through time.

Return to our car analogy. In this analogy, "mph" will play the role of "yield" and "travel time" will play the role of "price." And, rather than calculating the difference between two bond values, we will calculate the difference in travel time between each of two laps by our car around a 1-mile track:

If lap 1 is completed at a speed of 120 mph and lap 2 at a speed of 1 mph, how would you calculate the difference in travel time between the two laps?

If you were using yield-settlement logic, you would first imagine a car that speeds up from 1 to 2 mph. The time required to travel a mile would decrease from 60 to 30 minutes -- a 30-minute change. Then you would assume that for all 1-mph changes in speed, travel time per mile would also change by 30 minutes. This logic implies that lap 2 would take 3,570 minutes longer to complete than lap 1 ((120 - 1) x 30). Short of a DeLorean and some lightning, this is not possible.

For makes and models without a flux capacitor, correctly calculating the decrease in travel time means converting each speed from mph to travel time per mile, then taking the difference between the two travel times. As a 120-mph lap takes 30 seconds to complete and a 1-mph lap takes 60 minutes to complete, the difference in travel time between the two laps would be 59.5 minutes. Similarly, for rate-lock settlements, yields must be converted to prices, with the correct settlement value being the difference between those prices.

Yet we at Citigroup, and in my experience our peers at other banks, almost always instructed clients to use the yield-based settlement method. And so a product that is meant to return the difference between two Treasury prices, a matter of elementary subtraction, is perverted for profit.

If yields change by very little, this profit does not amount to much. Fortunately, depending on one's point of view, banks have other tricks for profiting from rate locks and do not rely solely on yield-based settlement. In fact, miseducating clients with yield-based settlement is almost an afterthought, just a bonus that pays off with large movements in yield.

And, in behavior that might be considered yet more sinister, sometimes banks had to agree with one another to miseducate clients with yield settlement. This transpired if a client decided to divvy up a single rate-lock transaction, with each bank getting a piece of the deal and each bank knowing that settlement of the rate lock would have to be a coordinated affair.

All this mathiness is hidden in plain sight. Some examples of yield settlement can be found online. Or you can just ask a company that put on a rate lock to dig up some trade confirmations and see what settlement methodology was used. There are hundreds, if not thousands, such documents in corporate offices around the country, each one part of an unwarranted transfer of millions of dollars from clients to banks.