1. What leverage multiplies exactly, and what it does not

Risk 4: Leverage

Almost everybody believes they understand leverage in a single sentence: it multiplies the gains and it multiplies the losses. The sentence is true and it is seriously insufficient. If that were all, leveraging up would be a neutral decision about the size of the bet, a simple volume knob. It is not. Leverage multiplies one thing, subtracts a different one and adds a third that simply did not exist before. And it is the third that ruins people.

Exposure, capital and multiple

Three precise words are needed. Your capital is the money that is yours. Your exposure is the market value of whatever moves in your favor or against you. The multiple is the ratio of the two.

With no debt, exposure and capital coincide: the multiple is 1. If you have 10,000 euros, borrow 20,000 and buy 30,000 euros of an asset, your exposure is 30,000, your capital is still 10,000 and your multiple is 3. None of this depends on the product you use: it depends solely on that ratio. We will come back to it in module 3, because it is the key to spotting the leverage that carries no label.

What it multiplies: the asset's movement, not how right you were

With a multiple of 3, a 10% rise in the asset turns the 30,000 into 33,000. You pay back the 20,000 and are left with 13,000: you have made 30% on your 10,000. A 10% fall leaves the position at 27,000, you pay back 20,000 and are left with 7,000: you have lost 30%. The symmetry is clean and it is the part everybody understands.

It is worth noticing exactly what has been multiplied: the percentage the asset moves, not the quality of your decision. It multiplies the result of an edge you either had or did not have. On a mediocre decision, it produces a mediocre disaster on a larger scale.

What it subtracts: the rent on somebody else's money

Here begins the part the famous sentence skips over. Borrowed money has a price, and that price is paid out of your capital, nobody else's.

Carry on with the example. If the loan costs 6% a year, you will pay 1,200 euros for the 20,000 borrowed. On your 10,000 of capital, that is 12%. Put another way: the asset has to rise 4% just for you to end the year where you started, because 4% of 30,000 is exactly those 1,200 euros.

The general arithmetic is straightforward. With a multiple of *k*, an asset return of *r* and a borrowing cost of *c*, your result is *k* times *r* minus (*k* minus 1) times *c*. With three scenarios and the figures above:

• The asset returns 8%. Result: 24% minus 12%, that is, 12% against the 8% you would have had with no debt.
• The asset returns 6%, exactly what the loan costs. Result: 18% minus 12%, 6%. Identical to not having leveraged up at all, with three times the risk.
• The asset returns 2%. Result: 6% minus 12%, a loss of 6% with the asset in positive territory.

That third case is the one worth internalizing: leverage can make you lose money in a year in which you got the direction right. The threshold is not that the asset rises, it is that it returns more than the interest you are paying on it.

Which fall wipes you out: the inverse of the multiple

The useful question is not how much you make if you are right, but what adverse move exhausts your capital. The answer is a division: the fall that wipes it out is one divided by the multiple.

• Multiple 2: a 50% fall leaves your capital at zero.
• Multiple 3: 33.3% is enough.
• Multiple 5: 20% is enough.
• Multiple 10: 10% is enough.
• Multiple 50: 2% is enough, a move many assets make in a quiet morning.

Two qualifications that change the picture. The first is that the interest keeps running while you fall, so the real threshold arrives sooner. The second matters more: nobody lets you get all the way to zero. They close you out long before, and that is what module 4 is about.

What it adds: a risk that did not exist without debt

Without leverage, the only person who decides when your position is closed is you: you can be wrong about the price and about the timing, and your mistake only materializes when you materialize it. That ability to hold on is worth a great deal and it is free as long as you owe nothing.

With leverage a third party appears: whoever lent to you. That third party has a contractual right to demand more collateral from you or to sell your position if its value falls below a threshold. It is no longer your mistake that takes you out of the market, it is somebody else's calendar. This is not a larger loss. It is a risk of a different nature, and that is why it has a module of its own.

Case study: the Swiss franc, January 15, 2015

For three years the Swiss National Bank held a floor in the euro's exchange rate against the franc, committing itself to defend 1.20. On January 15, 2015 it removed it without warning. The franc appreciated violently and the pair moved by something like 30% in a matter of minutes, in a market that had been regarded as low-volatility for years.

A good part of the retail currency business at the time operated with multiples of 50 or 100. With 50, a 2% fall exhausts the capital; the move was more than ten times that size, and on top of that it happened without intermediate prices at which to execute. The result was not that many clients lost their money, but that they ended up owing the broker money beyond what they had deposited. Several firms were badly damaged: Alpari UK went into insolvency and FXCM needed an emergency injection of hundreds of millions of dollars to keep trading.

The lesson is not that currencies are dangerous. It is that with high multiples the margin between trading and disappearing is measured in single-digit percentages, and markets produce double-digit moves more often than any calm historical series suggests.