A ship may come home safely while another is lost. A harvest may fail in one valley while the next has rain. The owner who divides a fortune between ventures whose fortunes differ can make the whole less precarious without asking either venture to become less precarious itself. This is the modest miracle of diversification: a change in ownership can remove a danger that no change in production has removed. The crops still fail, the ships still sink, and the separate accounts still record their losses. What changes is the chance that one person must meet all those losses together. Here the justification of the premium encounters an awkward economy. If an owner can shed a risk merely by spreading a holding, why should anyone pay that owner to keep it?
There is a precise argument beneath the proverb about baskets. The expected return on a portfolio is the weighted average of the expected returns on its parts. Its variance also depends on the relations between them. A share that is volatile by itself may steady a collection if its movements offset those of the other holdings; a second apparently different business may add little protection if both businesses prosper and suffer for the same reasons. Harry Markowitz made these relations the center of portfolio choice. The question became which combinations offered the least variance for a given expected return, or the greatest expected return for a given variance. Counting names on a statement could not answer it. A hundred names might conceal one exposure.
Take an invented pair of ventures, each equally likely to return nothing or twenty percent in a year. Each offers an expected ten percent, with a standard deviation of ten percentage points. If their outcomes are independent, an equal holding in both returns nothing one quarter of the time, ten percent half the time, and twenty percent one quarter of the time. The expected return remains ten percent; the standard deviation falls to about 7.07 percentage points. No dividend has been sacrificed to obtain the reduction. But let the ventures always succeed and fail together, and the equal holding fluctuates just as much as either one alone. The second certificate has bought no second fate. The gain arose from the relationship between the outcomes, and it disappears when that relationship changes.
The distinction between a venture’s own hazard and a shared hazard can be made equally clear. Suppose, again by invention, that every return consists of an expected ten percent, a common disturbance with a standard deviation of eight percentage points, and a separate disturbance with a standard deviation of twelve. Let all the separate disturbances be independent of one another and of the common one. With equal holdings, four ventures give a portfolio standard deviation of ten percentage points; a hundred bring it down to about 8.09. Adding ventures keeps reducing the separate part, while the common part remains. The limiting eight is the risk of the condition to which every venture is exposed. Diversification has done exactly what was asked of it. The condition was never among the things that this particular spreading could cancel.
The phrase “for free” therefore deserves its full meaning. In the first example, diversification lowers variance without lowering the weighted average expected return. It does not promise that every safer collection has the expected return of its most lucrative member, that trading has no cost, or that every desired combination can be purchased. Changing weights may change both mean and risk. Fees, taxes, indivisible investments and limits on borrowing can alter the feasible set. More fundamentally, variance need not describe everything an owner fears: a distribution’s asymmetry, the size of an extreme loss and the date at which money will be needed can matter. The mathematical gain remains. Its practical value depends on the opportunity to assemble and hold the collection through the period for which the calculation was made.
Nor does this arithmetic by itself establish what the market will pay. That requires a further argument about the people who set prices. If investors can obtain diversified portfolios, compete over the same assets, and evaluate risk in the manner the model specifies, the price of a holding responds to the risk it contributes to a portfolio. An avoidable fluctuation peculiar to one company supplies no independent reason for a higher expected return in that equilibrium. William Sharpe’s capital-asset-pricing argument develops the step from selection to price under strong common conditions, including shared assessments of returns and access to borrowing and lending at a common risk-free rate. The conditions do real work. They connect the owner’s opportunity to diversify with the market’s refusal to reward an exposure that diversification can eliminate.
The familiar measure is beta: a holding’s covariance with the market portfolio divided by the market portfolio’s variance. Within the model, the expected excess return on the holding is its beta times the expected market excess return. Invent a risk-free rate of two percent and an expected market return of eight. A beta of one and a half then calls for an expected return of eleven percent. A beta of zero calls for two, even if the holding fluctuates violently for reasons unrelated to the market. The second holding has not become safe in isolation. The model says that its separate fluctuations do not require compensation from a diversified holder. And the eleven percent is an expectation embodied in a price, not a promise that the account will show eleven at the end of the year.
A loss is costly in relation to the circumstances in which it arrives. A claim that pays when other resources are abundant supplies something different from a claim that pays when they are scarce. Consumption-based pricing expresses that relation through the value of an additional unit of consumption in each possible state. Market covariance is one particular way of organizing the relevant exposure; it is not a definition of every danger that could command a price in every model. “Systematic” also does not mean that every asset must fall on every bad day. It concerns a relationship across possible outcomes. The amount of compensation required for the shared exposure still needs explaining. That is the question taken up by The Equity.
The owner in this argument has a freedom that some owners lack. A worker’s future earnings may already depend on the employer whose shares appear in a retirement account. A home, a local business and the demand for the owner’s labor may depend on the same town. None is made independent by being entered on a different line of a balance sheet. The person can understand diversification perfectly and still lack a market in which to sell the labor income, move the home without cost, or divide the business while retaining the work it provides. A market price set through the opportunities of investors who can spread their holdings need not compensate this person for every additional burden of concentration. The price and the burden answer different questions, and can coexist without contradiction.
Concentration may also be part of producing the return. An entrepreneur can bring judgment, control and sustained attention to a venture in which much of her wealth is tied. Spreading the wealth may change those incentives or require relinquishing control; it is then more than the exchange of one passive financial claim for another. The risk that accompanies this commitment cannot establish by itself how much of the eventual proceeds represents effort, information, scarcity, luck or bargaining power. Neither can the success of a concentrated holding establish that concentration earned its reward. The earlier distinction between peril and fortune survives the portfolio: an exposure can be deliberately taken, valuable work can accompany it, and the realized windfall can still contain a large gift of circumstances.
A further difficulty appears when the owners’ financing connects ventures that seemed separate in their operating accounts. Losses can exhaust an investor’s capital; a demand for more collateral can force sales; the sales can depress prices and weaken other balance sheets. Markus Brunnermeier’s account of the 2007–2008 crisis distinguishes the liquidity of a market from the funding needed to keep a position open, and shows how the two can reinforce each other. The mechanism requires the relevant frictions and constrained resources. It does not make every correlation equal to one. It does mean that common creditors, common funding terms and common needs for immediate cash can become part of the dependence a portfolio must bear. Geographic variety on the asset side will not necessarily diversify the demand made by one balance sheet on all its assets at once.
The hedge thus economizes on risk-bearing and exposes the conditions under which risk-bearing can be sold. Where cancellation is possible, assembling the collection can be a real service: fewer resources need stand ready against losses that will not all arrive together. Where a common exposure remains, someone must still be willing and able to absorb it. The premium gives a price to that willingness under a particular distribution of wealth and opportunities. It cannot, merely by existing, vindicate the distribution that makes one person able to wait through a loss and another unable to meet next month’s bills. The capacity to spread is itself an economic advantage, and the price formed by those who possess it can be intelligible without describing the experience of those who do not.
Spreading a fortune can remove a danger; it cannot tell us who was free to spread.
In the ideal diversified market, the premium attaches to the exposure a holding contributes to the relevant whole. The venture’s avoidable, separate hazard supplies no additional claim merely because one owner chooses to carry it alone. Outside that model, the task is to identify the actual opportunity set, the actual dependence and the actual people whose resources stand behind the return. The Policy asks how a pool can bear the claims of many; The Tail asks what happens when the losses arrive together or exceed the pool. The hedge has narrowed the justification of the premium and made its remaining burden more exact. It has not abolished the burden. The argument remains open.