Product × Finance × AI: Financial Products in the Age of AIPart One From 0 to 1中文
Chapter 7

No one household can pay for a shipShares and limited liability

Someone in the village proposes building a ship to trade with other islands. A ship costs 100 portions of grain, more than any household can afford. A ship at sea has a thirty per cent chance of sinking, and no household could bear such a loss either. Borrowing to build the ship does not work: if it sinks, the borrower cannot repay and the lender loses anyway, and the interest rate a lender would demand for that is prohibitively high. And so shares appear: many households put in money together and share success and failure in proportion to their holdings. Each household puts a little grain into many ships, so that one sinking does not cripple it. Limited liability means investors can lose at most what they put in, and shares can therefore be transferred without worry. When a ship returns, debts are paid first and what remains goes to the shareholders: debt and equity are two ways of dividing the same proceeds.

1. No one household can pay for a ship

The households on the island have grown more prosperous and have more spare grain, but the most profitable trade lies across the sea. Build a ship, carry grain to other islands, and bring back salt and cloth; on its return, the cargo is worth two and a half times what the ship cost to build. But building a ship takes 100 portions of grain. A household can spare no more than 5 portions, and even the richest household in the village has only 20. Even if the grain could be found, a ship at sea has a thirty per cent chance of sinking. A household that staked everything it owned would be ruined by a single wreck.

The problem has two layers: no household can put up that much money, and no household can bear that much risk.

Today's counterpart. Building a railway, building a factory or developing a new drug requires capital and carries risks far beyond what any family can manage.

How many households does one ship take?

A ship costs 100 portions of grain, and each household can spare at most 5. Drag the number of investing households and see whether the ship gets built, and how much each household loses if it sinks.

Ship returns (70%): each gets
Ship sinks (30%): each loses

Illustrative: when the ship returns, its cargo is worth two and a half times the cost of building it; when it sinks, all the grain put in is lost.

2. Why borrowing to build a ship does not work

Could one household take the lead and borrow from the whole village to build the ship? A loan agreement requires repayment of principal and interest when due, whether or not the ship returns. If the ship returns, the borrower repays principal and interest and keeps everything else; if it sinks, the borrower cannot repay, and the lender's grain goes down with the ship. Knowing there is a thirty per cent chance of losing everything, a lender needs an interest rate of at least about 43% just to break even. Even then, the lender bears the entire loss from a sinking, while most of the gain when the ship returns goes to the borrower, so few lenders are willing to take the risk. Lending suits uses whose outcomes are fairly certain, not ventures where success and failure lie far apart.

Today's counterpart. Start-ups find it hard to get going on bank loans; most of their money comes from investors willing to share in success and failure.

Borrowing to build a ship: how high must the rate be for lenders to break even?

The captain has no grain of his own and borrows 100 portions from the village to build the ship. Drag the interest rate and see the expected gain of the lenders and of the captain.

Lenders’ expected net gain
Captain’s expected gain

Illustrative: if the ship returns (70%), the cargo is worth 250 portions; principal and interest are repaid first and the rest goes to the captain. If it sinks (30%), the captain has nothing and the lenders recover nothing.

3. Shares: sharing success and failure by holding

Try a different agreement: twenty households each put in 5 portions to build one ship together, each owning one twentieth. If the ship returns, the cargo is divided among the households by their holdings; if it sinks, each household loses its 5 portions. The investment no longer requires a fixed return; gains and losses are shared in proportion to holdings. This is a share.

Shares also make diversification possible. Rather than putting all 5 portions into one ship, a household can put half a portion into each of ten ships: if one sinks, it loses only half a portion. If whether each ship sinks is unrelated to the others, the more ships a household invests in, the steadier its returns. The reasoning is the same as for mutual insurance; only what is being shared changes, from bad luck to the success or failure of ventures.

Today's counterpart. A stock is a share in a company; hold the stocks of many companies, and the failure of one has little effect on the whole portfolio.

Spreading 5 portions across many ships

Each household invests 5 portions in shipbuilding, split evenly across a number of ships, and whether each ship sinks is unrelated to the others. Drag the number of ships and see what the 5 portions may end up as.

Illustrative: each ship returns with a 70% chance, and on return is worth two and a half times what was put in; the bars show the probability of each outcome, computed exactly from the binomial distribution.

4. Limited liability: lose at most what you put in

When a ship sinks, more than the ship is lost: the crew's wages and the goods bought on credit from others must still be paid. If the ship's investors had to answer for these debts with everything they owned, a well-off household that put half a portion into an unfamiliar ship could lose everything in a single wreck. Nor would it be willing to invest alongside households of slender means, because creditors would turn to the wealthier households to collect.

Limited liability changes this: investors can lose at most what they put in, and the ship's debts are limited to the ship's own assets. The worst outcome is known in advance. Well-off households no longer need to keep watching whether the captain is running up debts, nor to find out how much their fellow investors own, so they can safely put a small amount into each of many ships. Someone who buys a share likewise need not care how much the other investors own. The same share is worth the same in anyone's hands, so shares can be transferred, and their price depends only on the ship itself. The cost is that part of the loss is shifted to creditors, who therefore demand higher interest or collateral.

Today's counterpart. Shareholders of limited liability companies and joint-stock companies are liable only up to their capital contribution; banks lending to a company therefore look at the company's own assets and cash flow.

Limited liability: lose at most what you put in

Three households each put 1 portion into a ship built together with others. The ship sinks, still owing 30 portions in crew wages and goods bought on credit. Switch between the two kinds of liability and see how much each household loses.

Illustrative: under unlimited liability, creditors can pursue any investor for the whole debt and usually go first to the wealthiest household; under limited liability, the ship’s debts are limited to the ship’s own assets, and creditors bear whatever is left unpaid.

5. Debts first, the rest to shareholders

A ship can also borrow and issue shares at the same time. When it returns, debts are repaid first as agreed, and only what remains is divided among the shareholders. Debt pays a fixed return and carries less risk; equity has no ceiling on its return but comes last and carries more risk. Shareholders are therefore called residual claimants.

Dividing the proceeds into debt and equity does not change what the ship itself is worth. How much cargo the ship brings back depends on the winds and on trade, not on how the proceeds were divided in advance. Imagine two identical ships, one financed only with shares, the other with both debt and shares. If the debt and shares of the second together sold for more, an investor could sell their stake in the second, buy shares in the first, and personally borrow grain in the same proportion. They would get exactly the same harvest as before and pocket the price difference for nothing. When everyone does this, the difference soon disappears. So, as long as there are no taxes, a sinking brings no extra losses, everyone sees the same information, and investors and the ship can borrow grain on the same terms, the ship's total value does not depend on how its proceeds are divided.

Today's counterpart. A company's capital consists of liabilities and shareholders' equity; in bankruptcy and liquidation, creditors are paid first and shareholders come last.

Debts first, the rest to shareholders

A ship has borrowed 60 portions; the rest was put up by shareholders. Drag the value of the cargo when the ship returns and see how much the creditors and the shareholders each receive.

Creditors receiveShareholders receive

The two lines always add up to the value of the cargo: debt and equity are just two ways of dividing the same proceeds (Modigliani and Miller, 1958).

6. A permanent company with transferable shares

Early seafaring partnerships were often set up for a single voyage: the ship returned, the cargo was counted and divided, and the partnership dissolved. The Dutch East India Company, founded in 1602, went further. Its capital was originally to be liquidated after ten years, but it was later kept in the company for the long term. Investors who wanted to leave could only sell their shares to someone else, and an active trade in shares grew up in Amsterdam as a result. Gelderblom, de Jong and Jonker (2013) point out that this corporate form was not designed from the outset but took shape step by step as defects were repaired; even the limited liability of its managers was established only after years of trial and error.

Only when capital stays in the company for the long term can the company take on undertakings that span many years; only when shares can be transferred do investors avoid being locked in for those years.

Today's counterpart. The capital of a listed company stays in the company for the long term, and shareholders enter or leave by buying and selling shares on an exchange.

A partnership for one voyage, and a permanent company

Switch between the two forms of organization and see what happens to the capital from investment to exit.

The form of the Dutch East India Company took shape step by step as defects were repaired; even the limited liability of its managers was established only after years of trial and error (Gelderblom, de Jong and Jonker, 2013).

7. The village fleet: Civilization Simulator, version 7

The simulator unlocks the "Shares" rule. Each year twenty households set aside part of their grain to invest in building ships, and each ship has a thirty per cent chance of sinking. You can choose to build ships alone, have a few households build one together, or have every household hold a small share in every ship, and switch limited liability on or off. Then watch each household's wealth and the number of households ruined over twenty years.

Civilization Simulator · Chapter 7: the village fleet

Each year twenty households invest part of their wealth in building ships. Choose to build alone, have a few households build one together, or have every household hold a small share in every ship; switch limited liability on or off, and watch each household’s wealth over twenty years.

LendingCommitmentMoneyInsuranceBankSharesMarket · Ch. 8
Each household’s wealthVillage averageHouseholds ruined

Illustrative model: households start with wealth of 10 to 30 portions and earn another 4 portions a year from farming. A ship costs 100 portions and makes one round trip a year; 70% of ships return worth 1.6 times their cost, while 30% sink with nothing left and 15 portions of unpaid debts. Under unlimited liability, the investors repay a sunken ship’s debts from their own wealth in proportion to their holdings. When building together, every five households pool for one ship; a household with less than 1 portion is ruined and can only farm thereafter. The vertical axis is logarithmic.

8. What this step leaves open

With shares, large projects can be carried by many people together, but new problems follow:

  1. Shares must be saleable. When investors want to leave, they must find someone willing to take over their shares and agree on a price.
  2. The people who invest and the people who manage have separated. Twenty households invest, but only one captain goes to sea; whether the captain does his best, or keeps the gains for himself, is hard for the investors to know. Berle and Means (1932) called this the separation of ownership and control.
  3. The captain's account of the voyage may be untrue. What the cargo is worth and how great the losses were, investors can only learn from the captain.
  4. What is a share worth? The ship's prospects are uncertain, and the price of a share has to be set by the combined judgement of many people about those prospects.

What this step leaves open

Four new problems that appear once there are shares. Select one to see the assumption it hides.

The village fleetShares and limited liability

9. Implications for products

Stocks, bonds and the funds built from them all rest on the mechanisms of this chapter. Three implications follow. First, equity and debt are two ways of dividing the same proceeds: equity shares in success and failure and carries more risk; debt pays a fixed return and is paid first. A product's risk depends on which layer it holds. Second, the risk of shares can be greatly reduced by diversification; staking everything on one company means bearing risk that could have been avoided. Third, limited liability and transferable shares are what allow ordinary people to take part in large undertakings. They also shift part of the risk to creditors and separate investing from managing; the latter is where the problem of delegation begins.

Chapter summary: shares

Four conclusions, each tied to one mechanism in this chapter.

SharesSuccess and failure shared by holding

Ventures whose outcomes lie far apart do not suit lending; they suit many people investing together and sharing the losses.

DiversificationSpread the money across many ships

The average gain is unchanged and volatility falls sharply; staking everything on one ship means bearing avoidable risk.

Limited liabilityLose at most what you put in

Investors need not care about others’ wealth, and shares can be transferred; part of the risk is shifted to creditors.

Debt and equityTwo ways of dividing the same proceeds

Debts are paid first and the rest goes to shareholders; the split does not change what the ship itself is worth.

References