4. Risk budgeting: allocating risk instead of allocating money

Risk 5: Building the portfolio

The three previous modules all point to the same place. Diversifying is not about names, concentrating does not change the mean but the dispersion, and rebalancing serves above all to preserve the level of risk you chose. All of that presupposes that you know how much risk each part of your portfolio carries. Almost nobody does, because almost everybody measures their portfolio in euros.

Allocating the money does not allocate the risk

The canonical example is the 60/40. Take a volatility of 16% for equities, 5% for bonds and a correlation close to zero. The portfolio's volatility comes out at around 9.8%, and when you break down where it comes from the interesting part appears: around 96% comes from the equity leg and less than 5% from the bond one. With moderate positive correlations, like those observed in some periods, the equity share is still above 90%.

A 60/40 portfolio is not a balanced portfolio. It is an equity portfolio with a cushion. And that is not necessarily a flaw, but it is worth knowing before calling it prudent.

How the contribution to risk is measured

The idea is simple to state: a position contributes risk in proportion to its weight multiplied by how much it moves and by how much it goes along with the rest of the portfolio. A large, quiet asset can contribute next to nothing; a small, violent one can contribute most of it. The sum of all the contributions gives exactly the portfolio's volatility, which is what makes it possible to allocate it like a budget.

A complete example. Four positions, with movements independent of one another:

• 40% in government bonds, volatility of 5%.
• 30% in developed equities, volatility of 16%.
• 20% in emerging equities, volatility of 24%.
• 10% in a single small-capitalization share, volatility of 55%.

The portfolio's volatility turns out to be 8.96%, and the risk is allocated like this:

• Government bonds: close to 5% of the total risk, with 40% of the money.
• Developed equities: around 29%.
• Emerging equities: around 29%, with two thirds of the money of the previous one.
• The individual share: almost 38%, with 10% of the money.

Look at the two middle positions: they weigh 30% and 20%, and they contribute the same. It is no coincidence, it is that the product of weight and volatility is identical. And now stop at the two extreme rows. The smallest position in the portfolio contributes more risk than any other, and eight times more than the one holding four times its money. An investor looking at his statement will see a conservative portfolio with a small bet on the side. The reality is that almost four tenths of what is going to happen to him depend on that small bet.

Budgeting risk the way you budget money

The framework consists of reversing the order of the questions. Instead of deciding how much money goes where and then discovering what risk you are carrying, you first set the total risk you are prepared to bear and allocate it between sources: equities, duration, credit, currency, commodities. Only at the end do you translate that allocation into euros.

The exercise is uncomfortable for one specific reason: it forces you to put in writing that an idea with plenty of conviction and little money is, in risk terms, a large position. And it forces you to accept that if you want government bonds to cushion anything for real, 40% of the money does not get you remotely close.

Risk parity: the extreme version of the framework

Risk parity takes the idea to its logical conclusion: allocating the budget in equal parts between the sources. When assets move independently, that amounts to weighting each one in inverse proportion to its volatility. In the portfolio in the example, equalizing the four contributions would give around 62% in government bonds, 19% in developed equities, 13% in emerging and 6% in the individual share. Total volatility would fall from 8.96% to 6.2%.

Its logic is sound: if you do not know which asset is going to return most, at least do not let one of them alone decide everything that happens to you. The criticisms are sound as well, and there are four of them:

• It ignores expected returns. Equalizing risk is only optimal if every asset offers a similar reward per unit of risk, which is neither known nor necessarily true.
• It depends on unstable estimates. Volatilities and correlations are calculated by looking backwards and they change exactly when they matter.
• It usually requires leverage. Bringing volatility down to 6.2% leaves a low expected return; to recover it you have to leverage up, which brings in different risks dealt with in another level of this course.
• Its record is contaminated. A good part of the strong results of the past decade and more came from a bond leg that lived through an exceptionally long bull market.

2022: the year that put the framework to the test

In 2022 rates rose at the fastest pace in forty years, and equities and bonds fell at the same time. The 60/40 portfolio lost around 17%. Risk parity funds, which carried far more weight in bonds and often leverage as well, had their worst year since the category has existed, and a significant proportion of them fell more than the 60/40 itself.

The right reading is not that risk budgeting does not work. It is that a budget is built on a hypothesis, namely that the sources of risk really are different, and in 2022 they stopped being different, because the blow arrived through the common denominator of all of them. A risk budget is an excellent tool for knowing where you stand. It is not a guarantee that what you have separated on the spreadsheet will still be separate on the day of the scare.