1. Real diversification versus apparent diversification

Risk 5: Building the portfolio

Almost everybody believes they have a diversified portfolio, and almost everybody means the same thing by it: how many different names appear on the statement. It is the wrong measure. Diversifying is not spreading money across many labels but across things that do not fail for the same reason. The distance between those two ideas is far greater than it looks, and this module is about measuring it.

The risk of a share is not one thing, it is two

What moves the price of any share breaks down into two parts that behave in radically different ways:

• Specific risk. What happens to that company and to that one alone: an accounting fraud, a patent thrown out, a chief executive who crashes, a plant that burns down, a failed clinical trial. It is idiosyncratic and, precisely because it bears no relation to what happens to the others, it cancels out between positions.
• Systematic risk. What happens to all of them at once: the discount rate, the economic cycle, the equity risk premium, the tax regime, the currency they trade in. It does not go away by adding names, because it is inside every one of them.

Harry Markowitz formalized this in 1952: a portfolio's risk is not the average of the risk of its parts, because it depends on how they move relative to one another. A new position only takes risk away from you if it does not go along with the ones you already hold.

The arithmetic of adding names

Put plausible figures on a developed stock market: an individual share has an annual volatility of the order of 35%, and the average correlation between any two stocks in the same index is around 0.3. With equally weighted positions, portfolio volatility follows this staircase:

• 1 position: 35%.
• 5 positions: around 23.2%.
• 10 positions: 21.3%.
• 20 positions: 20.3%.
• 30 positions: 19.9%.
• 100 positions: 19.4%.
• Infinitely many positions: 19.2%. That is the floor, and there is no getting below it.

Read it twice. Going from one position to twenty takes almost fifteen points of volatility off you. Going from thirty to a hundred takes off half a point. And from a hundred to infinity, two tenths. With thirty stocks you have already removed around 95% of all the risk that was removable; whatever you do after that buys nothing worth mentioning.

The empirical evidence says the same thing with qualifications. The classic work of the late sixties put the bulk of the benefit at ten or fifteen stocks; later studies, done when idiosyncratic volatility was higher, raised it to several dozen. The sensible range is between twenty and forty well-spread positions. Above that you are not diversifying: you are replicating the index by hand, with more commissions, more tax and more surface area for mistakes.

What survives the staircase

The interesting number is not the 19.9% of the thirty positions but the 19.2% at the end: that is the risk they all share. Thirty stocks from the same index and the same country trade in the same currency, depend on the same central bank, discount at the same rate and collect the same equity risk premium. When that common factor moves, all thirty move.

And there is an aggravating factor. Those thirty names rarely come out of a lottery: they come out of a filter, and a filter selects for similarity. Thirty companies chosen for sales growth and high margins are not thirty bets, they are a single bet written out thirty times. Their effective correlation is far above the 0.3 in the example, and the floor rises.

Apparent diversification: the overlap that shows up on no screen

The commonest case is not the thirty-share one but the investor with five or six funds who believes he holds six portfolios. A global fund weighted by market capitalization today devotes something like two thirds of its weight to a single country and a good part of the rest to a handful of companies in the same sector. With five products like that you have bought the same twenty companies five times over, paying five sets of fees.

The useful test is not how many lines you hold. It is this one: how many different things would have to go wrong for the portfolio to sink. If the answer is one, you hold one position, however many rows it takes up.

Diversify between sources of risk, not between names

The sources of risk are few and can almost be counted on your fingers: equities, duration, credit, inflation, currency, commodities, liquidity. Each has its own engine and answers different questions. Antti Ilmanen has spent years insisting that what you buy when you invest is not companies, it is risk premiums, and that the useful allocation is made between those premiums.

The arithmetic confirms it beyond argument. A portfolio of forty shares from the same market comes in at around 19% volatility. Take half of that money, put it into government bonds with a volatility of 6% and a correlation close to zero with equities, and total volatility falls to around 10%. Two decisions have achieved what five hundred shares never manage.

2008: the year holding thirty names was no use at all

In 2008 the S&P 500 lost around 37% with dividends included, and the ten sectors into which the index was then divided all closed the year in the red, without exception. The most defensive of them, consumer staples, gave up around 15%; financials lost more than half. Spreading thirty stocks across ten sectors prevented nothing, because all of them were the same source of risk with a different label.

That same year, long-dated American government debt closed with double-digit gains, not because it was a better asset but because it answered to a different engine: the collapse in rates and the flight to safety. Whoever held both things cushioned the blow; whoever held thirty names took it in full.