A Business is a Customer

Our title “A Business is a Customer” is an inspired conclusion attributed to the management guru, Peter Drucker (1909 -2005) and the urgency of that thought is further enhanced by the recent Rap lyric “If you’re not a businessman, why are you living?” (author unknown). We are all, of course, “business persons” all of the time because everything that we do can be fully described as a “negotiation” and an “exchange” with a “customer” and with a customer there comes a hopefully never ending stream of “payables” and “receivables” (a “relationship”, so to speak) that are ultimately, and possibly immediately or never, closed out with a “payment” and a “receipt” in what passes for cash. The object of the negotiation and exchange is irrelevant and all goods and services (and relationships) are simply reduced to streams of payables and receivables which may or may not include “payments” and “receipts” now or in the future.

We are again, of course, in our “mathematical mode” (please see these Letters, Stock Prices Are The New Pink, June 2012) and we’re going to consider what it means to define “payables” and “receivables” as options in order to understand their properties as a currency or “money”.

A “payable” is a promise to pay in some “specie” (which we will define with a  great deal of generality) and it is, therefore, a contract that can be terminated by the payment of the contract or “strike price”, K, on or before a certain date which is defined in the contract. Between then and now, the contract has the properties of a “security” or “underlying” with a time varying value, S=S(t) such that S(0)=0, that is, the “value” of  the contract S now is zero if the face amount of the contract is paid now but there’s no reason, and it’s generally not true, that the value of the contract,  S(t), is zero thereafter even if the payment of K is made some time in the future to terminate the contract. Whatever profit there is in the deal, paid now and terminated, it’s in K and the deal amounts to a mere exchange in economic terms (although there is more to say on that in the Epilogue).

The “specie” can be thought of as “cash money on its face amount” that is common to both the debtor and the creditor (the “parties” to the contract) but can be, basically, anything that the parties agree to including objects, favours, concessions, commitments or, for example, in some “contracts”, our very lives. The terms of finance such as the “strike price”, “discounted”, “appreciated”, “in good faith” or “bankruptcy” have, indeed, ancient meanings that are far from obsolete or archaic in the traffic of business, then and now.

Similarly, a “receivable” is a promise or commitment to receive under the terms of the contract and simply affirms that the contract is made by both parties and neither has an exclusive ownership of it, to do with as they please. There are always consequences.

It is also correct to assert that all such contracts are “liquid”, that is, transferable by negotiation or force majeur, with a result that can be measured by the “value” of the contract, S(t), at the time t in the future, and, therefore, that all contracts are subject to the equation of “Put-Call Parity” at all times.

The Equation of Put-Call Parity
C(t) + Payments(t) + K×exp(-k(T-t)) = P(t) + S(t)

In this equation, which is required in the absence of theft or academically risk-free returns through frictionless arbitrage (which doesn’t exist if economics does), K is the value (in money terms although we are not adverse to thinking about it in “specie” terms) that we have called the “strike price” at time T (in years) and is known or agreed upon by the both the “buyer” (borrower or lender) and the “seller” (respectively, lender or borrower, either way) and t is the time between now (time t=0) and time t=T and k=k(t) is the “force of interest” (an actuarial term) that could vary with time but might also be k=log(1+i) where i is an annualized “real rate of interest” for one year and might include an allowance for “inflation” if K does not. In any case, the “force of interest” is likely to be a “step-function”, constant for some periods of time, but with values that account for the “worth” of K at time t.

S(t) is the value of the contract and is the same for both the buyer and the seller at all times in the absence of arbitrage. It could be zero when the contract is made and must have the same “value” for both the buyer and the seller during the term of the contract although neither will have direct access to it without terminating the contract.

The right-hand side of this equation, therefore, defines a “protective put” P(t) with the value max(0, K-S(T)) at time t=T so that both sides of this equation have the value max(S(T), K) at time t=T absent “payments”, Payments(t), that could be zero, positive, or negative depending on who receives them. Payments made by the debtor to the creditor increase the value of the call and decrease the value of the put.

The left-hand side of the equation defines a “fiduciary call” and ensures that the money for the strike price K will be available at the expiration time T and the call option, in addition to the time and fundamental value, C(t), has the value max(0, S(T)-K) at time T.

We have, then, a pretty good practical grasp of K, S(t), Payments(t) and k(t), the “force of interest”, at all times t and can sensibly re-write the equation as:

The Equation of Put-Call Parity
C(t) – P(t) = S(t) – Payments(t) – K×exp(-k(T-t))

But what is C(t) – P(t)? Well, it’s the profit at time t. For example, if S(t) is “high” then the left hand side will be positive (the call has value but the put has none); whereas, if S(t) is “low”, the left hand side will tend to be negative, and the put has value but the call has none.

The “lender” or principle invariably “buys” the put, P(t), at time t=0 in order to close the deal, and “sells” the call, C(t), to the “borrower” or debtor and the only time that their values might be the same is at the time t=0 when the deal is made and there is no economic profit, S(0)=0, which is unlikely absent a gift or a simple exchange. In a cash deal for which there is no credit, the buyer or creditor will make a payment (-K) in order to make the purchase and the “profit” that is not economic or does not depend on future values is, therefore, the “value” of the contract, S(0) = C(0) – P(0) = 0, and the deal is closed by the termination of the contract. At all other times, the “profit” will depend on the ongoing relationship between the buyer and the seller and one could also say (as above) that the debtor pro-actively “sold” the put to the lender and “bought” the call because there has been a “meeting of the minds” in order to effect the deal.

Moreover, the put, P(t), and call, C(t), become negotiable financial instruments and a type of “money”. For example, the lender could obtain an early payment (of something) by selling the debt to the borrower or a third party (hypothecation) and the borrower could “sell” the debt by exchanging it for a debt of a different amount or duration. It’s also evident that one could increase the profit over time by increasing the difference between the value of the call, C(t), which is bought and owned by the customer (or debtor) and the value of the put, P(t), which is bought and owned by the “salesperson” or creditor.

The Profit Equation of Put-Call Parity
Profit(t) = C(t) – P(t)

Business, of course, provides many ways to do that (as well as many ways not to do that) but it would seem that the most enduring way would be to provide goods and services that are of increasing value to the customer, thereby increasing the value of the call and, most likely, automatically decreasing the value or “worth” of the put.

It’s also noteworthy that for such contracts of enduring value, S(0) is not necessarily zero but could be either positive or negative because the contract itself has acquired a value and cost that is not reflected in the strike price K because there is now a customer and a relationship which is a product of its enterprise (please see these Letters, The Price of Risk, August 2012).

Epilogue

“In order to carry out a market transaction it is necessary to discover who it is that one wishes to deal with, to inform people that one wishes to deal and on what terms, to conduct negotiations leading to a bargain, to draw up the contract, to undertake the inspection needed to make sure that the terms of the contract are being observed, and so on. These operations are often extremely costly, sufficiently costly at any rate to prevent many transactions that would be carried out in a world in which the pricing system worked without cost.” – Ronald H. Coase 1960, The Problem of Social Cost, Journal of Law and Economics.

For more information, please follow the Tags or Categories attached to this Letter or simply enter Search for additional references to any term that we have used. Two of our recent Letters, The Price of Risk and Maximising Shareholder Value (LOL), August 2012, may also be helpful.

Disclaimer

Investing in the bond and stock markets has become a highly regulated and litigious industry but despite that, there remains only one effective rule and that is caveat emptor or “buyer beware”.

Nothing that we say should be construed by any person as advice or a recommendation to buy, sell, hold or avoid the common stock or bonds of any public company at any time for any purpose. That is the law and we fully support and respect that law and regulation in every jurisdiction without exception and without qualification to the best of our knowledge and ability.

We can only tell you what we do and why we do it or have done it and we know nothing at all about the future or the future of stock prices of any company nor why they are what they are, now.

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