3. Sizing by volatility: equalizing risk instead of equalizing money

Risk 2: Position sizing

The most widespread way of dividing up a portfolio is to split the money equally between the ideas. Ten positions, 10% in each. It looks even-handed and neutral. It is not: it is a risk decision taken without meaning to, and it almost always concentrates the risk in two or three names.

Equalizing money equalizes nothing

Put 100,000 euros into an asset that swings 8% a year and another 100,000 into one that swings 40%. The money is split at 50% each. The risk is not: the first contributes some 8,000 euros of typical annual movement and the second some 40,000. Five out of every six euros of uncertainty in that portfolio come from a single position.

If what you want is for both ideas to weigh the same in the result, you have to invest more money in the one that moves less. With those 200,000 euros split as 166,667 and 33,333, each position contributes about 13,333 euros of annual movement. Now they really are equalized, even though the money is split five to one.

That is the whole mechanism: the size in euros is adjusted inversely to the asset's volatility, so that what gets equalized is the contribution to risk, not the capital committed. It is the practical translation of the idea in the first module, where we saw that what decides the compounded result is not how much you put in but how much what you put in swings.

What happens in a real 60/40 portfolio

The canonical example is the classic portfolio of 60% in equities and 40% in bonds. With equities swinging around 15% a year and bonds swinging around 5%, the contributions are 0.60 times 15, that is 9 points, against 0.40 times 5, that is 2 points.

Doing the full portfolio calculation, the equity leg explains something like 90% or 95% of the total variability, depending on the correlation you assume. In other words: an investor who believes he holds a 60/40 portfolio holds, in risk terms, something very close to an equity portfolio with a small cushion. His experience of 2008 or of 2020 looked far more like that of pure equities than the split of the money suggested.

To genuinely equalize the contribution of the two legs with those volatilities you would need weights of the order of 25% in equities and 75% in bonds. The money ends up deeply unbalanced precisely so that the risk is not.

Risk parity: the idea taken to its limit

That reasoning, generalized to many asset classes and formalized in the nineties, is what is known as risk parity: building the portfolio so that each component contributes the same amount of risk instead of the same amount of money.

Its defenders point to three reasonable things:

• An asset's volatility is far easier to estimate than its future return, so building on volatilities means leaning on the more reliable of the two figures.
• A portfolio with equalized contributions depends less on any single market behaving well.
• The resulting portfolio is more stable across the cycle, because it does not end up dominated by whichever asset moves the most.

The criticisms, which are serious

Antti Ilmanen and others have insisted that risk parity is not neutral, and the objections deserve to be taken seriously.

The first is that it deliberately ignores expected return. Equalizing the risk of an asset with a high expected premium and one with a low premium is not balancing: it is throwing information away. The usual reply is that premiums per unit of risk are similar across asset classes, but that is a hypothesis, not a fact.

The second is that, with typical historical volatilities, the result loads an enormous amount of weight into bonds, and the period in which the idea became popular coincided with four decades of falling rates. A good part of its excellent record may be the record of those bonds rather than of the technique. In 2022, with equities and bonds falling at the same time, risk parity strategies suffered double-digit losses, worse than those of a conventional 60/40 portfolio.

The third is that sizing by recent volatility is procyclical: when volatility spikes, the mechanism forces positions to be cut, and if a lot of people do it at once the selling happens at the worst moment and amplifies the fall.

Real case: the Turtles and the risk unit, 1983

In 1983 Richard Dennis bet William Eckhardt that he could teach a group of people with no experience to trade. Those selected, known as the Turtles, were handed a complete trend-following system. The part that has aged best is not the entry signal but the sizing rule.

The Turtles did not buy a fixed number of contracts or a fixed amount of money. They calculated a measure of each market's typical daily range, which they called N, and adjusted the number of contracts so that a move of one N moved the account by around 1% of capital. The direct consequence: in a quiet market they bought many contracts and in a turbulent one very few, without changing their mind about the signal.

That turned positions as different as the US Treasury bond, sugar and sterling into comparable bets, each one able to move the account by roughly the same amount. It is exactly the same principle that underlies risk parity, applied fifteen years earlier at a futures desk and without a single line of portfolio theory behind it. The complete system was a great deal more than that, and several of those traders ended up abandoning it; but the rule of sizing by volatility has stayed in the trade.