The multiplier applies to the losses

Here is the sentence that sells leverage, and it is arithmetically correct:

Put in 40,000, control 100,000, and a 10% rise in the asset makes you 10,000 instead of 4,000. Two and a half times the gain, for the same money down.

Every word of that is true. The lesson is what the same sentence says when you turn it around, so that is the half we will compute first.

The downside, computed before anything else

A position: 100,000 of assets, 60,000 of it borrowed at 6%, so 40,000 is yours. No repayments this year and nothing saved into it — this is the position, held for twelve months, and nothing else.

Find out what a bad year does to the 40,000.

Net worth projection

≈ Hypothetical model, not a forecast

Projects assets growing and debts being repaid side by side, and the difference between them.

It assumes

• The position is held for exactly one year with no payments made against the debt.
• The interest on the borrowing accrues whatever the asset happens to do.
• The asset can be valued and sold at the price the model shows.
• Nobody demands repayment early, which is the subject of the next lesson.

It ignores

• Income, tax and the fact that both flows compete for the same money
• Illiquid assets that cannot be sold at the value shown
• Any new borrowing during the period
• Inflation — the whole projection is nominal

Move the return on assets down until one year has taken roughly a quarter off net worth — a final net worth between 27,000 and 30,000. Write down the asset return that did it.

Return on assets0%

Net worth today

40,000

Net worth at the end

36,400

Assets at the end

100,000

Debts at the end

63,600

Year the debt clears

1

Debt clears inside the period

0

◷ Not there yet — keep moving the controls.

The answer is a fall of about 6.4%.

Not 10%. A quarter of your money is removed by an asset falling six and a bit percent — a move so ordinary that most assets do it in a quiet quarter without anybody calling it a bad year.

The bill that arrives before the asset does anything

Before you look at the upside, look at the number the model shows when the asset return is exactly zero: net worth 36,400, down from 40,000.

The asset did nothing at all and roughly 9% of your equity has gone. That is the interest on 60,000, charged to a 40,000 stake. Borrowing at 6% against a position where you own 40% of the capital is a 9% annual headwind on your own money, payable before the first unit of return arrives.

Which gives the hurdle. For net worth to stand still, the asset has to return 3.6% — the borrowing rate multiplied by the share of the position that is borrowed. Below that line, a positive year on the asset is still a losing year for you.

Now the upside

Same position, same year. Find what it takes to add a quarter.

Net worth projection

≈ Hypothetical model, not a forecast

Projects assets growing and debts being repaid side by side, and the difference between them.

It assumes

• Identical to the position above, held for the same single year.
• The borrowing rate does not change when the asset has a good year.
• Gains are on paper until sold, and selling has costs this model ignores.
• No lender intervenes at any point during the twelve months.

It ignores

• Income, tax and the fact that both flows compete for the same money
• Illiquid assets that cannot be sold at the value shown
• Any new borrowing during the period
• Inflation — the whole projection is nominal

Now move the return upward until one year has added roughly a quarter to net worth — a final net worth between 50,000 and 53,000. Compare that asset return with the one you found a moment ago.

Return on assets0%

Net worth today

40,000

Net worth at the end

36,400

Assets at the end

100,000

Debts at the end

63,600

Year the debt clears

1

Debt clears inside the period

0

◷ Not there yet — keep moving the controls.

It takes a rise of about 13.6% to gain what a fall of 6.4% takes away.

Predict

Why is the move needed to gain a quarter more than twice the move that loses a quarter?

Choose one answer

Because losses always hurt more than gains in percentage termsBecause the interest bill shifts every outcome down by the same amountBecause the model compounds the debt and not the assetBecause 40,000 is a small stake relative to the position

Lock in answer

The same effect, at three levels of gearing

Hold the borrowing rate at 6% and vary how much of the position is yours. The pattern is worth memorising because it does not depend on any of the specific numbers here.

At 40,000 of equity in a 100,000 position, a fall of about 6.4% costs you a quarter of your money. At 20,000 of equity in the same position, borrowing 80,000, the interest bill alone is 24% of your stake — it has already taken almost the whole quarter, and an asset fall of two tenths of one percent finishes the job. At 80,000 of equity, borrowing only 20,000, it takes a fall of nearly 19%.

Three positions in the same asset, three completely different assets from where you are standing. The thing you own is not the asset. It is the asset minus the debt, and that object behaves nothing like the one on the label.

Check

Two people buy the same asset on the same day. One pays cash; the other borrows 60% at 6%. The asset returns exactly 3.6% over the year. What happened?

Choose one answer

Both made money, the borrower moreThe cash buyer made 3.6%; the borrower broke evenBoth broke even, since it was the same assetThe borrower lost money and the cash buyer made some

Check answer

Worth remembering

• Gearing is the ratio of the position you control to the equity you own, and it multiplies moves in both directions.
• The interest bill shifts every outcome down by the same amount, so the up and down cases are not mirror images.
• A geared position has a hurdle rate: roughly the borrowing rate times the borrowed share of the position.
• In the worked example, a fall of about 6.4% removed a quarter of the equity while a rise of about 13.6% was needed to add one.
• What you own is the asset minus the debt, and that object behaves very differently from the asset itself.