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Chapter 10

Ordinary people have neither the time nor the expertiseDelegation and agency

As the ships multiplied and the news grew more complicated, people who farmed had neither the time nor the expertise to judge which ship to buy. Handing their ship shares to someone who knew the trade became the natural choice: he studied shipping full time, and with many households' money pooled together, the cost of research was spread across them. Delegation saved time, and it also brought new problems. Whether the manager was any good could not be told from a few years of results; whether he was trying, the principal could not see; giving him a share of the profits made him favour risk; and even if he really was skilled, the benefit mostly went to him through the size of the money he managed and the fees he charged. The cheapest delegation was to ask someone simply to hold all the ship shares in proportion, without picking and without research.

1. Farmers have no time to study shipping

A household has to work in the fields every day. To judge which ship is worth buying, one must find out about the captain's character, the risks of the route and conditions on other islands, and keep watching prices in the market square. All this takes a great deal of time, and doing it well takes experience. For a farmer, spending that time on farming is usually a better deal than studying shipping. In The Wealth of Nations, Smith (1776) saw the division of labour as the main source of growing wealth: each person concentrates on what they do best, and then they trade with one another.

Today's counterpart. Most people have neither the time to study company accounts and industry changes nor the training to do so.

Manage it yourself, or pay someone

Drag a household's wealth and the hours per week it would take to study shipping itself, and compare the time spent managing it yourself with the fee paid each year for someone else to manage it.

Do it yourself: time spent, in grain
Pay someone: fee per year

Illustrative: each hour spent on research, if spent farming instead, would yield 0.05 portions more grain; having someone manage the shares costs 1.5% of wealth a year in fees.

2. Handing money to someone who knows the trade

One villager knows shipping well. He proposes that each household hand him its ship shares to manage together; he will distribute the returns according to each household's share and charge a small fee each year. Researching a ship is costly for a single household, but he needs to research it only once and can apply the result to all his principals' money; the more households delegate to him, the lower the research cost per household. This is the embryo of an investment fund.

The essence of delegation is handing the right to act to someone else: the manager decides for the principals which ship to buy and when to sell. The manager's aims do not fully coincide with the principals', and the principals pay a price for this, which can be divided into three components. The first is the cost of keeping watch on the manager: checking his books and finding out what he has bought. The second is what the manager spends to reassure the principals: publishing his accounts regularly and staking part of his own wealth alongside theirs. The third is the loss that remains because their interests still diverge after both have been done. More monitoring or bonding is not always better: if an extra unit of monitoring saves less than a unit of loss, it is not worth it. What the principal wants is the smallest total of the three.

Earlier, Ross (1973) had posed, as a general economic problem, how a principal should design pay so that an agent acts in the principal's interest.

Today's counterpart. A fund pools many investors' money, which a fund manager manages as a whole; returns are distributed by share, and a management fee is charged.

Research once, use it on everyone's money

Researching the fleet costs 30 portions of grain a year. Drag the number of households that hand their ship shares to the same manager to see the research cost per household.

Illustrative: the cost of research does not depend on how much money is managed; per household it is 30 ÷ number of households. The horizontal axis uses a logarithmic scale.

3. Choosing the wrong person: ability is hard to see

More than one villager is willing to manage shares for others. Whom should one choose? The most direct way is to look at past results. But a ship's success depends heavily on luck, and a few years of results say little: even if no manager had any skill, luck alone would always put a few of them at the top. Telling reliably from results that a manager is genuinely skilled often takes more years than his whole career.

Fama and French (2010) used simulations to test the performance of actively managed US funds and found that, after fees, very few funds consistently beat their benchmark in a way that luck could not explain. Other researchers argue that this method lacks statistical power and may underestimate the ability of a small number of funds (Harvey and Liu, 2022).

Today's counterpart. The funds at the top of the rankings are often replaced by a different set a few years later.

A few years cannot separate skill from luck

A hundred managers have no skill at all; whatever they earn above the average each year is pure luck. Drag the number of years observed to see their average excess returns; then drag the size of true skill to see how many years it takes to tell it apart.

Illustrative: each manager's yearly excess return fluctuates randomly by about 8 percentage points. Each dot is a manager's average excess return over the observation period; the dark dots are the top ten. To detect, with about 95% confidence, true skill that adds a per year, the number of years needed is roughly (2 × 8 ÷ a)².

4. Trying or not: invisible effort

Once a manager is chosen, there is another question: is he trying? He can go to sea every day to gather news, or sit at home and place orders carelessly. The principal sees only the result, not the effort, and the result is mixed with luck. If he receives a fixed fee each year, his income is the same whether he tries or not, and he has little reason to try. If his pay is tied to results, he has a reason, but he also bears luck risk that should not be his.

The dilemma arises because the principal sees too little. If the principal could also see other things, such as whether the manager goes to sea each day, or how other ships fared in the same year, luck and effort could be separated to some extent: if every ship had a poor harvest that year, the manager's poor result is not entirely his fault. Any information that reveals a little more about effort is worth writing into the pay agreement: pay becomes less entangled with luck while the incentive does not weaken. The more the principal can see, the cheaper it is to keep the agent in line.

Today's counterpart. Fund managers' pay usually includes a part tied to performance; funds must also disclose their holdings and trades regularly, letting investors see more.

How much pay to tie to results

The principal cannot see whether the manager is trying, only results mixed with luck. Drag the share of the manager's pay tied to results to see how hard he tries, what the principal gets, and the luck risk the manager is forced to bear.

How hard the manager tries
Luck risk the manager bears
Principal's take after pay

Illustrative: how hard the manager tries is proportional to the share tied to results; the harder he tries, the higher the fleet's return, but he must be compensated for bearing luck risk, and the compensation rises with the square of the share. When holdings and trading records can be seen, luck plays a smaller part in the result, and the same share brings less risk (Holmström, 1979).

5. Profit-sharing encourages risk-taking

Suppose the agreement gives the manager 20% of the gains while the principals bear the losses themselves. The manager is then in the position of holding an option that can only win: the more volatile the outcome, the more he expects to receive, and the more risk the principals bear. The manager therefore has reason to bet on riskier ships.

The remedies follow from this: a performance fee is charged only once net value exceeds its previous high, and the manager must invest some of his own money, sharing the principals' fortunes.

Today's counterpart. The "high-water mark" common in private funds, and requirements that fund managers invest in the products they manage, are both responses to this problem.

A share of gains without losses encourages risk

The manager takes 20% of each year's gains, while the principals bear the losses. Drag the amount of risk the manager chooses to see the expected fee he receives and the principals' expected take after the fee.

Manager's expected feePrincipals' expected take after the fee

Illustrative: yearly returns follow a normal distribution with a mean of 5% and the chosen volatility; fee = 20% × the positive part of the return. The high-water mark is simplified to a one-year version in which the previous year's loss is deducted from the fee base; the conclusion points the same way.

6. Who gets the benefit of skill

Suppose there really is a manager in the village more skilled than the others. Word spreads, and more and more people hand him their ship shares. But only a few ships are worth betting on, and the more money he manages, the harder it is for him to find equally good opportunities; his margin above the average shrinks as he grows. As long as handing shares to him is still a better deal than handing them to others, people keep moving their shares over, until, after fees, giving them to him earns no more than giving them to someone else. At that point his skill has not disappeared; its benefit has simply turned into the size of the money he manages and the fees he collects. Even if most managers are genuinely skilled, what principals get after fees is a return comparable to passive holding. People who move their money to chase performance are not foolish; it is precisely their inflows that keep performance from persisting.

The model does not assume that managers lack skill. By the authors' calibration, most managers are skilled enough at least to earn back their own fees.

Today's counterpart. Funds with outstanding performance often grow rapidly in size, and their later performance often reverts to the ordinary.

Who gets the benefit of skill

The more money a manager runs, the harder it is to find equally good opportunities, and his excess return falls as he grows. Drag his level of skill to see how large he grows before money stops flowing in, and what the principals and the manager each get.

Size reached as money flows in
Principals' excess return after fees
Manager's fees per year

Illustrative: at size q, the excess return after a 1% fee = skill − 0.03 × q − 1%; money keeps flowing in until the principals' excess return after fees falls to zero (a simplification of Berk and Green, 2004). Size is measured in units of 100 portions.

7. The cheapest delegation: hold everything in proportion

Since picking a manager is hard, and picking itself rarely beats the average, there is a simpler form of delegation: ask someone simply to hold all ship shares in proportion to each ship's share, with no research, no picking and no market timing, for a very low fee. The principals then get the average return of the whole village fleet, and save the cost of research and the risk of picking. The difference in fees looks small, but it compounds year after year: a gap of a little over one percentage point a year adds up to a large sum over several decades.

In 1976, the first index fund for ordinary investors was launched. Many people saw it as a joke at the time; it later became the default choice of millions of people.

Today's counterpart. Index funds and other products that hold all stocks in proportion to market value usually charge far lower fees than actively managed funds.

Fees compound year after year

Two identical sums of 100 portions both earn the fleet's average return of 6% a year; only the fees differ. Drag the two fees and the number of years held to see how far apart they end up.

Hold everything in proportionActive picking

Illustrative: assumes that active picking earns the average return before fees; Sharpe's (1991) arithmetic shows this holds for active investors as a group.

8. Whom to hand it to: Civilization Simulator, version 10

The simulator unlocks the rule "Delegation". Forty households can manage their ship shares themselves, hand them to a manager who picks actively, or hand them to a manager who simply holds everything in proportion. You can adjust the share of managers who are genuinely skilled, the fee for active management, and whether principals switch to whichever manager did best last year, and see each household's wealth after twenty years and the time spent each year.

Civilization Simulator · Chapter 10: whom to hand it to

Forty households each have 100 portions of wealth invested in the fleet. The three lines show the median household wealth when households manage it themselves, hand it to managers who pick actively, or hand it to a manager who holds everything in proportion; select one to see the details.

BankSharesMarketInformation in pricesDelegationRegulation & custody · Ch. 11
Do it yourselfActive managersHold everything in proportion10th to 90th percentile of households for the selected option

Illustrative model: the fleet's average return is 6% a year with 15% volatility. Do it yourself: each household's result has its own additional fluctuation, is 1% lower each year because of trading and errors of judgement, and takes 3 hours a week. Active managers: ten managers; those with real skill earn 2% more a year, the rest do not, and each has its own fluctuation; the chosen fee is deducted. Hold everything in proportion: earns the fleet's average return, with a fee of 0.1%. When switching, principals move each year to last year's best-performing manager and pay an extra 0.5% for switching.

9. What this step leaves open

Delegation lets ordinary people take part in complex investment too, but new questions follow:

  1. The manager may misappropriate the principals' assets. He holds everyone's ship shares; how can the principals confirm they are still there?
  2. Sellers know more. A manager knows far more about a product's risks than the principal. He may talk only about returns and not about risks, or recommend unsuitable products to people they do not suit.
  3. Principals make their own mistakes. Switching managers to chase last year's performance and redeeming during falls often leave principals with lower returns than the funds themselves earned.
  4. Delegation itself is expensive. Research, monitoring and fees all cost money; if these costs fell sharply, how would the boundary of delegation shift?

What this step leaves open

Four questions still unresolved once delegation exists. Select a question to see the assumption it rests on.

Whom to hand it toPrincipals and agents

10. Implications for products

Funds, investment advisers and all kinds of products that manage money on clients' behalf are built on the mechanisms in this chapter. Three implications follow. First, the value of delegation comes from the time saved and the research cost shared, and its price is the agency cost; a delegation product should make clear what principals pay and what they get. Second, past performance is mixed with luck, and recommending managers by short-term rankings is unreliable; the more of the process the principal can see, the more credible the delegation. Third, the cheapest delegation is often also the hardest to beat; the higher a delegation product's fees, the more it needs to explain what the extra payment buys.

Chapter summary: delegation

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

Value of delegationSaves time, shares research

Research once and use it on every principal's money; the price is agency costs.

Ability is hard to seeA few years of results are mostly luck

Reliably telling true skill apart often takes more years than a career.

IncentivesResults-linked pay and a visible process

Linking pay makes the manager try, and also makes him bear luck; the more can be seen, the cheaper the constraint; a share of gains without losses encourages risk.

The cheapest delegationHold everything in proportion

The benefit of skill mostly goes to the manager; fees compound year after year into a large sum over decades.

References