This analysis came out of a discussion on whether trading in a zero-sum market like precious metals or corporate securities can occur in full compliance with the Second Great Commandment, which Jesus quoted from the Law of Moses:

"Love the Lord your God with all your heart and with all your soul and with all your mind." This is the first and greatest commandment. And the second is like it: "Love your neighbor as yourself." All the Law and the Prophets hang on these two commandments. Matt.22:37-40

It was suggested to me that the analysis might be more easily understood if arranged in the form of a syllogism. I have no particular reason to believe that is true, but here it is anyway.

P1  Love the Lord your God with all your heart and with all your soul and with all your mind. Moral Axiom

This is not a key component of the syllogism, but is included to make the numbering more esthetic.

With very few or no exceptions, this is the sense of "love" in the Bible.

This could also be argued from P1 and the authority of God and Jesus.

We further note that while there are many people in the world we can do something to help, this moral axiom commands us to serve their best interests in like measure with our own, which is not accomplished by giving everything to the poor. P2 is essentially the Golden Rule, whatever we would want from somebody in like circumstance, we should do to others.

The point of this definition is to assign a numerical value to the buy/sell decision. Most people implicitly make this calculation, as in "You want $5 for this widget? That's a good price, I'll buy it." -- meaning, their evaluation formula returns a value for the widget substantially higher than $5 -- or perhaps "You couldn't pay me to take it" -- meaning that their evaluation formula returns a large negative number.

The seller also computes an evaluation formula for the same widget, and is willing to sell it when the formula returns a value less than the price. Note that the buyer and seller usually (but not necessarily) use different formulas. It is a requirement for the transaction to take place, that the buyer's formula returns a value higher than the price, and the seller's formula returns a value lower than the price. See below for examples of evaluation formulas.

The point of this definition is to find some basis for all of the information available to a particular party in the transaction to yield a buy or sell decision based solely on what properly distinguishes the buyer from the seller, and not on private or unfair information. This is codified incompletely in the SEC proscriptions against "insider trading".

Proof:  To be in compliance P2 requires that the compliant party sees the transaction as serving the interests of the buyer and seller (approximately) equally. Recognizing the different stations in life, we do not require that the price be exactly in the middle between the buyer's and seller's formula valuation, but that both buyer and seller have a basis for believing that the transaction is profitable. This much is necessarily true, or the transaction wouldn't take place at all. P2 brings to the analysis the additional requirement that the "You" (the person in compliance) knows that the "neighbor" (the other party, from D2) is being fairly served, that is, that the information available to the compliant party does not put the other party at a disadvantage. This is accomplished by using a single evaluation formula applied separately to the two different parties, so that when it is applied to the seller's skills and assets it yields a valuation below the sell price, and when applied to the buyer's skills and assets yields a valuation higher than the price.

Using any formula less than a D4 DDF to determine the buy/sell decision fails to comply with P2. If the compliant party is not knowingly applying the DDF, then it is not love as defined in D1. If the compliant party reasonably assumes (from the fact that it is a willing transaction) that the other party's (presumably different) formula informs his decision, then it is not loving him "as yourself" (P2) because the other party is not able to use the same information in that decision. If the other party were using the same information, then it would necessarily be a DDF from the definition D4.

Note that we do not require that both parties actually use a DDF unless both parties wish to be in compliance with P2. Nor do we require that both parties use the same formula (whether DDF or otherwise). Thus one party could use a DDF and be in compliance with the Commandment, while the other party (perhaps using private information) can believe he screwed the first party. Since there is also nothing in D3 requiring the formulas to be accurate, it is further possible to be compliant but mistaken about the benefit to the other party (or oneself, for that matter) -- although of course we encourage due diligence to mitigate that risk.

Note further that the fact of using a DDF to inform one party's decision ensures that the other party's interests are being served, even if that other party does not have all of the information available for that DDF. Thus the DDF can be applied in an anonymous transaction (such as a stock market buy or sell), assuming that a DDF can in fact be formulated for that transaction.

The examples below show how these different possibilities play out.

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Evaluation Formula Examples

F1  (Wal-Mart trinket) The shelf-price of the trinket at Wal-Mart.

This formula is not DDF, since it returns the same value regardless of whether it is being considered for the buyer or seller.

This would give a valuation of $5 for red trinkets, and $3 for predominately blue ones. It is not DDF.

F3 is a DDF (assuming a shelf price higher than $4 and less than $120), because the cost to the seller, who had it made in China for $1, is substantially less than the $100 cost the housewife would have to pay in the USA to have it custom-made. Furthermore, the $20 esthetic value is divided by 10 identical trinkets on the Wal-Mart shelf, but by only 1 on the housewife's mantle. On the other hand, Wal-Mart paid $0.10 in shipping for the trinket from China to Texas, while the housewife's marginal transportation cost is $0 because she was in the store already for other purchases, and it took no extra gasoline to get it home. Therefore the valuation for the buyer, B=100+0+20, which is substantially greater than for the seller, S=1+0.1+2.

F4 is a DDF for a contract price $800, because while the materials and tool rental are the same (total $400), the handyman labor is $15/hour for 12 hours, while the homeowner's labor might be $40/hour for 25 hours. Thus for the buyer, B=$1400, while for the seller, S=$580, nicely straddling the contract price.

F4 is a DDF, but that's not the formula the handyman used to calculate his quote. Instead he used a rather simple formula:

He might figure he screwed the owner because the price paid is much greater than his formula F5 calculates it to be. All that is pure profit for him. Thus, while the owner may have used a DDF to decide to accept the contractor's bid, the contractor did not use a DDF in deciding to offer it. By F5 it was a win-lose transaction. If the owner were to calculate his decision on F5, he would surely have refused the bid and found another contractor who was not so eager to gouge the customer.

Suppose instead the owner used a different formula to calculate whether he was being offered a reasonable bid,

As this is much greater than the price the contractor bid, the owner got the best of him (that is, it was a win-lose transaction in the owner's favor). The contractor did not make as much on this job as he could have on other jobs he passed up to do this fence, and the owner got off with a much cheaper fence than his calculations showed it should cost. F6 is not DDF, but caveat emptor! The owner made out OK. The fact that the contractor used F5 (which is also not DDF -- he grins all the way to the bank) makes it "win-win" by the normal use of that term, but neither F5 nor F6 is DDF, and neither party is compliant with the Second Commandment, since both are of the (unspoken) opinion that they screwed the other party.

F7 is a DDF if the buyer is wealthy and the seller is poor. It is not DDF if the personal wealth of the two parties is the reverse or else if one or both is unknown. This may be a silly example, but it shows that it is possible to find a DDF in the stock market.

Extended example:

Two recent events could affect the stock price: (a) The freeze over most of the USA is likely to result in massive crop failures, and (b) FarMac just hired the brilliant chief technical officer away from their major competitor.

Two different investors look at this information and come up with different evaluation formulas:

F8  Investor X figures that the farms are covered by catastrophic weather insurance, resulting in extra cash on hand for buying additional farm machinery, and the new CTO will boost the technical innovation over the competitors, resulting in better products and better profitability. Investor X calculates that the increased sales and profitability should raise stock prices 20% over the next year, which he determines to yield a NPV of +15%, that is, the stock is actually worth $115 today. F8 makes no distinction between buyer and seller, so it is not DDF.

F9  Investor Y was raised on a farm, and he knows insurance does not cover the full force of the losses, so the farmers will be hurting and unlikely to buy new machinery. Furthermore, he knows that the new CTO was getting old and about to retire, so he is unlikely to contribute much to corporate profitability. Investor Y figures that the down market will depress the stock prices this year by about 15%, yielding a NPV -10% or $90 in today's dollars. F9 also makes no distinction between buyer and seller, so again it is not DDF.

Scenario 1: The market is slow to react. In investor Y's formula F9, the calculated valuation V<P, so he decides to sell his 100 shares at market price ($100) and buy them back at the end of the year, for a net profit estimated to be $2000. Investor X's formula F8 yields a calculated valuation V>P, so he decides to buy 100 shares at market price and expects to realize a $2000 profit when he sells then at the end of the year. X ends up buying Y's shares for $100.

From D4, the definition of DDF, we can see that neither F8 nor F9 are DDF. Consider instead,

Scenario 2: The market over-reacts to the weather, and the share price drops overnight to $70. This is below the value determined by F9, so investor Y decides to buy 200 shares instead of selling, because he knows that when the market recovers its senses by the end of the year, the price will rise back up to $85 he has calculated, so selling his shares at that time will yield a net profit. Notice that calculated valuation V for investor Y's F9 is the same for buyer and seller. When V>P he buys, and when V<P he sells. That is the nature of an evaluation formula.

I leave as an exercise to the reader, to come up with a DDF for a typical stock market transaction, or else to explain why that might not be possible. comments and criticisms for the purpose of better understanding what kinds of transactions serve the Golden Rule.
 

Tom Pittman
First draft 2007 February 12

The fellow who invited me to present this analysis tells me that everybody else disagrees with me on the outcome. Those people are obviously smarter than I am: they know that if they tell him the truth, he will blow them off with exceeding great hostility and venom, so they only tell him what he wants to hear. sigh