Finance According to Ecclesiasticus (Ben Sira)

Fourth instalment, after Solomon, Ecclesiastes, Wisdom and Leviticus and the talents, Jacob and Joseph. Not to be confused with Ecclesiastes: Ecclesiasticus — Sirach, or Ben Sira — was written around 190 BC in Jerusalem, translated into Greek by the author's grandson in Alexandria, and classed among the deuterocanonical books (“apocrypha” in the Protestant tradition). It is, of all the wisdom books, the most concretely financial: it quotes a recovery rate, a sizing rule for guarantees, a manual of bookkeeping. Same method: the verse, the equation, the simulation. Six claims, six tests.

I.Lending, default, and hardly the half

“Many, when a thing was lent them, reckoned it to be found, and put them to trouble that helped them. Till he hath received, he will kiss a man's hand; and for his neighbour's money he will speak submissly: but when he should repay, he will prolong the time, and return words of grief, and complain of the time.”

Ecclesiasticus 29:4-5 (KJV)

Ben Sira describes the full life cycle of a doubtful debt: flattery before, delays after, the hard times as an excuse. And in the very next verse he quantifies recovery: if the borrower prevails, the lender “shall hardly receive the half” (29:6). Lending, then, is buying a lottery: with probability \( d \) default occurs and only a fraction \( \rho \) is recovered; otherwise the lender collects \( 1 + r \). The expectation per unit lent:

\[ \mathbb{E}[\text{rendement}] = (1-d)(1+r) + d\,\rho - 1, \qquad d^{*} = \frac{r}{\,r + 1 - \rho\,}. \]

The threshold \( d^{*} \) is the default probability beyond which the loan destroys value at rate \( r \). The simulation traces the expectation as a function of \( d \), with Ben Sira's recovery — the half — as the default setting.

Expected return on a loan as a function of default probability

Interest rate r: 10% Recovery ρ: 50%

Observation. The rest of the chapter is a credit treatise in four lines: many refuse to lend “for other men's ill dealing” (29:7) — credit rationing; and yet, lend to the poor, even if it means being “content to lose thy money” (29:10) — almsgiving as an anticipated, accepted loss, outside the calculation. Ben Sira separates exactly what modern finance separates: the loan, which must cover its expected loss, and the gift, which does not pretend to be a loan.

II.Suretyship “according to thy power”

“Suretiship hath undone many of a fair estate, and shaken them as a wave of the sea: mighty men hath it driven from their houses, so that they wandered among strange nations. […] Help thy neighbour according to thy power, and beware that thou thyself fall not into the same.”

Ecclesiasticus 29:18,20 (KJV)

Ben Sira does not say: never stand surety — on the contrary, “an honest man is surety for his neighbour” (29:14). He says: according to thy power. It is a sizing rule. Suppose that over a lifetime one signs \( N \) guarantees, each committing a fraction \( f \) of one's wealth, each called with probability \( q \). After \( k \) calls, \( (1-f)^k \) of the wealth remains; being “undone” in the verse's sense — shaken as a wave of the sea — occurs when less than half is left:

\[ k_{\text{ruine}} = \left\lceil \frac{\ln \tfrac{1}{2}}{\ln(1-f)} \right\rceil, \qquad \mathbb{P}[\text{ruine}] = \mathbb{P}\bigl[K \ge k_{\text{ruine}}\bigr], \quad K \sim \mathrm{Bin}(N, q). \]

The simulation traces this ruin probability as a function of the committed fraction \( f \), for \( N = 10 \) guarantees over a lifetime. The yellow dot marks your \( f \); the red line, a prudence ceiling at 10%.

Probability of losing half one's estate over 10 guarantees

Fraction committed per guarantee f: 25% Probability of being called q: 15%

Observation. “According to thy power” is a position limit before the term existed: generosity is permitted, unbounded exposure is not. The curve is convex — doubling the committed fraction far more than doubles the risk of ruin, because calls multiply on wealth rather than add. It is the Kelly-criterion argument: what matters is not the average loss but the compounded loss.

III.The gold that drives away sleep: the point of “enough”

“Watching for riches consumeth the flesh, and the care thereof driveth away sleep. Watching care will not let a man slumber, as a sore disease breaketh sleep. […] Blessed is the rich that is found without blemish, and hath not gone after gold.”

Ecclesiasticus 31:1-2,8 (KJV)

Ecclesiastes said that money does not satisfy; Ben Sira says something else: that it costs. Each unit of wealth brings a diminishing benefit — classic concavity — but demands a share of watching, worry and guarding that grows linearly. Net wellbeing:

\[ U(W) = b\,\ln(1+W) - a\,W, \qquad W^{*} = \frac{b}{a} - 1. \]

The interior maximum \( W^{*} \) is the point of “enough”: below it, getting richer improves life; beyond it, each additional unit costs more sleep than it yields in wellbeing. The “blessed rich” of verse 8 is not the richest — he is the one who stopped on the right side of \( W^{*} \) and “hath not gone after gold”. Wealth is measured in years of income.

Net wellbeing by wealth: concave benefit, linear worry

Worry coefficient a: 0.10 Benefit intensity b: 1.0

Observation. This is not the hedonic treadmill of the second article: here preferences do not adapt — it is the cost of holding that rises. Night watches, guards, lawsuits, fear of theft — modern economics would speak of carrying costs of wealth and cognitive load. The interior optimum exists as soon as worry is linear and benefit concave; the whole question, personal to each, is the slope \( a \) of one's anxiety.

IV.“I have found rest”: the deferred feast

“There is that waxeth rich by his wariness and pinching, and this is the portion of his reward: Whereas he saith, I have found rest, and now will eat continually of my goods; and yet he knoweth not what time shall come upon him, and that he must leave those things to others, and die.”

Ecclesiasticus 11:18-19 (KJV)

This is the rich fool two centuries before the parable of Luke 12. His error is not saving: it is optimising as if the mortality rate were zero. Wealth deferred \( n \) years is worth \( (1+r)^n \) times more — but one is there to eat it only with survival probability \( S(n) \), which falls all the faster as one ages (Gompertz mortality: the hazard doubles roughly every eight years). The “expected feast”:

\[ F(n) = S(n)\,(1+r)^n, \qquad S(n) = \exp\!\Bigl(-\tfrac{\lambda_A}{g}\bigl(e^{gn}-1\bigr)\Bigr), \qquad n^{*} : \; \lambda(A+n^{*}) = \ln(1+r). \]

The optimal deferral \( n^{*} \) is reached when the risk of dying within the year catches up with the return: deferring beyond it is leaving “those things to others” in expectation. The simulation traces wealth (green), survival (red) and their product (yellow) for a person of age \( A \).

The expected feast: growing wealth × probability of being there to eat it

Current age A: 60 yrs Return r: 5%

Observation. Three chapters later, Ben Sira gives the remedy (14:11-16): “Give, and take, and sanctify thy soul” — give and enjoy one's goods during life, before the turn is past. The calculation confirms it: the older one is, the more \( n^{*} \) melts, until it turns negative — the moment for “now will I eat of my goods” has then already passed. The correct discount rate for deferred consumption is not \( r \) but \( r \) minus the mortality rate; forgetting that is the actuarial definition of miserliness.

V.Sin between buying and selling

“Many have sinned for a small matter; and he that seeketh for abundance will turn his eyes away. As a nail sticketh fast between the joinings of the stones; so doth sin stick close between buying and selling.”

Ecclesiasticus 27:1-2 (KJV)

The image has an engineer's precision: fraud does not lodge in the stone — the transaction itself — but in the joint, the gap between what the buyer sees and what the seller knows. Gary Becker turned it into a calculation in 1968: one cheats if the expected gain exceeds the expected sanction. With a fraud gain \( g \), a detection probability \( p \) and a fine of \( k \) times the gain:

\[ \mathbb{E}[\text{fraude}] = m + g\bigl(1 - p\,(1+k)\bigr) \;\gtrless\; m, \qquad p^{*} = \frac{1}{1+k}. \]

Below the detection threshold \( p^{*} \), fraud dominates the honest margin \( m \) — and its relative pull \( g/m \) is strongest where the honest margin is thin: “many have sinned for a small matter”. The simulation traces the expected profit of the honest merchant and of the cheating one, as a function of \( p \).

Expected profit per transaction: honest versus cheating (fraud gain: 5)

Honest margin m: 5 Fine k × the gain: 3

Observation. In chapter 42, Ben Sira lists the things one should not be ashamed of, and among them is exactness “of balances and weights” (42:4): honest trade is there a duty to be declared, not a given. The model says why: as long as \( p < p^{*} \), honesty costs money to whoever practises it. It becomes free only when detection is credible — hence the next section.

VI.“In number and weight, and put all in writing”

“Deliver all things in number and weight; and put all in writing that thou givest out, or receivest in.”

Ecclesiasticus 42:7 (KJV)

Two centuries before our era, Ben Sira prescribes the ledger. The model is that of till errors: over \( n \) transactions, each carries an undetected error with probability \( e \), of random sign. Without a ledger, the gap between the real till and the assumed till follows a random walk — it grows like \( \sqrt{n\,e} \) and nobody knows when it began. With a ledger reconciled every \( k \) movements, the gap is bounded by the audit window:

\[ \sigma_{\text{sans registre}} \approx \sqrt{n\,e}, \qquad \sigma_{\text{avec registre}} \approx \sqrt{k\,e}, \qquad k \ll n. \]

The simulation follows 200 transactions: the cumulative gap without a ledger (grey) drifts; with a ledger (green), each reconciliation — the yellow dots — brings it back to zero and identifies the error while it is still traceable.

Cumulative till discrepancy over 200 transactions, with and without a ledger

Error rate e: 5% Reconcile every k movements: 20

Observation. The preceding verse says: “where many hands are, shut up” (42:6) — internal control before the term existed, access separation included. Writing does not make people honest; it makes detection probable — that is, it lifts the \( p \) of section V above \( p^{*} \). The two verses form a system: the sanction deters, the ledger makes the sanction credible.

Synthesis

The first three articles in this series were about growth — geometric compounding in \( (1+r)^t \), \( s^t \), \( L^n \). Ben Sira writes about the probabilities that multiply it. Each of his six lessons is an expectation: the loan is worth \( (1-d)(1+r) + d\rho \) and recovery is “hardly the half” (I); the guarantee is sized to bound a binomial ruin probability (II); wealth has an interior optimum as soon as worry is linear (III); the deferred feast is weighted by survival, and the optimal deferral melts with age (IV); merchant fraud is an expectation that changes sign at the detection threshold (V); and the written ledger is what moves that threshold (VI). Ecclesiasticus is the practitioner's book: where Genesis and Matthew gave the dynamics, Ben Sira gives risk management — and gives it with numbers.

Iron sharpeneth iron (Proverbs 27:17): comments, objections and counter-examples welcome. Verses quoted from the King James Version Apocrypha, in the public domain; Ecclesiasticus is a deuterocanonical book and verse numbering varies slightly between editions. Parameters are illustrative; nothing here is financial advice.