The Zaccaria Deal (I) :

On modern finance and history

Eric Briys, Didier Joos de ter Beerst

Congrès AFFI Poitiers, 26 juin 2006

The last twenty years of Modern Finance : « again » !

• Miller (1986) enthusiastic paper “Financial Innovation: The Last Twenty Years and the Next” twenty years have gone by. It makes sense to see whether or not the optimistic views of Miller have been confirmed by the facts.

• Four key areas, all revived by Option Pricing Theory (OPT):

– OPT and new breed of derivative securities– Modelling of credit/default risk through OPT insights– Risk management: Var, ART– Real options and interaction with financing

• Merton frames these developments in what he calls “Functional Finance” : History “ As If” = No History

Modern Finance: Pitfalls of the silo approach

• Option pricing: Hakansson’s catch 22 paradox

• René Stulz:

“Telling students simultaneously that they should compute net present values using the

Modigliani-Miller capital budgeting paradigm, that they should optimize the firm’s capital

structure by trading off costs of distress against equity cost, and finally that they should

worry about risk management amounts to pure schizophrenia and does not have the

slightest intellectual foundation in modern finance theory.[…] It is a peculiarity of finance

that we spend so much time on teaching about a world without frictions when

everything that makes finance interesting has to do with what happens in the

presence of frictions.”

• Unfortunate outcome: “Happy people do not have a history”.

• Well, they do have one!

Key messages

• The framework we propose consists in core messages:

– Financial and real options were explicitly contracted in Late Middle-Age, and before.

– Contracts are “bricolage” of options to complete incomplete markets

– Options were “bricolage” in Late Middle-Age, they still are today!

– There is no universal theory but : “Proof is in pudding”

The original document (Archivio di Stato, Genoa, notai antichi)

A map of Zaccaria’s route (1298-1299)

Bruges

Phocea

GenovaAigues-Mortes

Cadix (Puerto San Maria)

Majorca

Sardegna

Sicily

Places mentioned in the contract

Potential calls

650 cantari of alum(= 35 tons)

3000 people working for Zaccaria in Phocea

Large fleet of a dozen of galleys, nave, cocha

Stock in key location

Call

Contracting constraints and supports

• Limited cognitive load about the future

• Lack of markets : no stock exchange, no futures, no « insurance », no limited liability

• Agency risks in long-distance maritime trade

• Trade-off between contract complexity and simplicity(incompleteness)

• Property rights in Bruges

• Usury prohibition (see under)

• Cost/time of contract to deal with business and contracting risks vs benefits

• Institutions :

• Law • Notary, Scriba (accounting),

judges, arbitrers• Standard contracting from

developped mainly in Genoa :–Commenda (equity-type)–Loca (equity-type)–Societatis (JV)–Nolis (lease)–Instrumentum ex causa cambi–...

• Private-order contracting (alberghi)

• Entrepreneurship, Innovation, knowledge

Constrain contracting efficiency Support contracting efficiency

The scenario tree : a complex web of options

First simplified model : single venture :buyback with embedded « sea loan »

120,0-(casualty)|,0)10t1Q

100-Max(100Put *t1QP casualty) (no|*

t110PCallMax t010P - 100 zV

Short asset + long cash + Long Call with Long Put « sea loan » = (compounded options)

Convention :

Vz = value of the venture, z = the indicator for Zaccaria,

T0 T1, departure, arrival

Vz = value of the venture,

P = price (with P, P *, the commodity market price in Aigues-Mortes, in Bruges),

Q = quantity,

1

A simplified tree : a put on a call on a put on a call

Call

Put

Put

Call

(red nodes = decision, white = events)

Scenario 1Scenario 1

Scenario 2Scenario 2

Scenario 3Scenario 3

Scenario 4Scenario 4

Scenario 5Scenario 5

Scenario 6Scenario 6

Timing

Arrival in Genoa, if no casualty. Payment of 3,780 G £ to

Suppa & Grillo

Contract agreement in

Genoa. Zaccaria receives 3,000 G

£.

1st November 1298 (t= 0)

1st May 1299 (t = 1)

1st November 1299(t = 3)

6 month waiting deadline

1st August 1299 (t = 2)

Arrival in Bruges, if no

casualty, and decision to

buyback alum

3 month trip Aigues-Mortes - Bruges

3 month trip Bruges - Genoa

Starting date of the venture, or repayment of

3,250 £ if Zaccaria does not

leave Genoa

Full model (2) : Zaccaria ’s payoff

p(1)1t

250-)0t

Pa-1t

650(PazV

p(1)-1t1

G)(N p(2)1 p(3) 2

αNp(4)-1 3t

Gp(3) -12t

3,780p(4)-1 3t

G2t

)d*Q*(Pp(4)

3t),0

650dQ

3,500-S(3,500 MaxPut Max CallMax Call

P = price (with P, P *, P **, respectively, price in Aigues-Mortes, in Bruges and Genoa),

Q = quantity, a = alum, d= drapery

N = transport cost for back-and-forth , G = galley (s), aN = market price of transport (nolis)

S = exchange rates

p(1) = Decision to buyback in Aigues-Mortes [1-p(1)] = Decision to Start the venture

p(2) = Casualty before Bruges (full loss) [1-p(2)] = Safe arrival in Bruges

p(3) = Decision to lease galleys (no buyback in Bruges) [1-p(3)]= Decision to buyback

p(4) = Casualty before Genoa (way back) [1-p(4)] = Safe arrival in Genoa

2

Zaccaria ’s payoff (scenario 1, …, 6)

p(1)1t

250-)0t

Pa-1t

650(PazV

p(1)-1t1

G)(N p(2)1 p(3) 2

αNp(4)-1 3t

Gp(3) -12t

3,780p(4)-1 3t

G2t

)d*Q*(Pp(4)

3t),0

650dQ

3,500-S(3,500 MaxPut Max CallMax Call

Payoff no-departure

Decisionto start

Decisionto buyback

Casualty No-Casualtyon the

way back

Decisionnot to buyback

No-Casualtyon the

way back

Upfront Investment

Buybackprice

Sea loan(indemnity)

Payoff from drapery

Rent cashGalleyrecovered

2

Decision 1 : Start the venture [1-p(1)]

01t

250-)t0Pa-1t

650(Pa1t

G)(N casualty) p(no 2t

2αN)causalty' p(no-1

t3G p

1tzE

Payoff no departure

Up frontExpenses in

transport(invest Galley +

pay salaries, food)

Cash in Nolis (transport)

if galley arrives in Bruges

Galley recovered in case of safe

arrival

Start if (Scenario 2 +Scenario 3 +Scenario 4) - (Scenario 1) > 0 Start if (Scenario 2 +Scenario 3 +Scenario 4) - (Scenario 1) > 0

2

Decision 2 : buyback [1-p(3)]

0t22

αNcasualty' p(not3

G3,780)casualty' p(no t3

Gt2)d*Q*(P)'p(casualty t3

),0650

dQ3,500-S(3,500 MaxPut p

t2 Ez

Cash in Nolis (transport)

if galley arrives in Bruges

Buyback price of 3,780 £

Payoff from drapery in Genopa

Defalult up to 3,500 Tournois

in case of casualty

Galley recovered in case of safe

arrival

Buyback if (Scenario 5 +Scenario 6) - (Scenario 3 +Scenario 4) > 0 Buyback if (Scenario 5 +Scenario 6) - (Scenario 3 +Scenario 4) > 0

2

Put/call parity

Long Put Option + Long Asset + Borrowing * Cash + Short Asset (Sales) + Long Call Option

Short Put Option + Short Asset + Lending - Cash + Long Asset (Sales) + Short Call Option

The Zaccarias

Suppa & Grillo

=

=

Protective Put Fiduciary Call

Prohibited by the Church Accetped by the Church

Back to the First model : the venture as a « sea loan »: Loan + default

,0(casualty)|,0)10T1Q

100-Max(100Put T1QP casualty) (no|T110P120Max Put t1120 - 100 zV

Long cash + short debt + Long Put on debt with Long Put « sea loan » (compounded options)

Prohibited by the Church

Conclusion :

• Pooling funds : 3,000 £ were gathered jointly from Suppa and Grillo

• Transfer funds: Zaccaria has received cash for a venture to and from Bruges

• Complete incomplete markets: innovative solution that completes market gaps

• Manage Risk. The contract spreads, through transfer and financing, the various risks among the parties to it.

• Control agency risks. agency and informational issues. • Screening/monitoring: quality of alum accounting books and scriba on board.• Incentives : ex ante selection and ex post control of parties: The option to start (“find and reveal

information”, no “cheap talk”

• Increase asymmetry of information with Competitors.

• Fostering family and business networks.

• Create Legal arbitrage (State, Church).

Empirically we have crunched numbers :

Buyback option

=

always out-of-the-money in Bruges

Conclusion : contracts as context-specific bricolage to exchange

Insurance

Contract = Options

The institutional context

The business model

CONTRACTING

CONSTRAINTS

CONTRACTING

SOLUTIONS

Debt

Equities

Sales

Management

Leasing