Week 8: Short Selling, Margin and Leverage

Short selling and margin are where leverage enters the course, on the simplest instrument it will ever apply to — an ordinary stock — before Weeks 9 and 10 apply the same idea to futures and options. The lecture treats a margin call as the mechanical consequence of leverage that it is, not an edge case, and short selling as a position with a loss that isn’t capped at 100%.

The question this week answers#

What does it mean, mechanically, to trade with borrowed money — and at what exact price does that borrowing force you out of a position?

By the end of this lecture#

• explain how a margin loan works on an ordinary stock position
• explain why a short position’s risk profile differs from a long position’s
• describe leverage as a multiplier applied to both gains and losses
• calculate the price at which a simulated margin account triggers a margin call

Key ideas#

Margin means borrowing part of a position’s cost from a broker, using the position (and other account equity) as collateral. Leverage is the resulting ratio between the total position size and the trader’s own money in it — a $10,000 position bought with $5,000 of own money and $5,000 borrowed is 2x leveraged. Leverage does not change the underlying instrument; it changes how much a given price move affects the trader’s own capital — and, more to the point, it shortens the distance between an account and a forced exit it doesn’t get to choose the timing of.

Short selling means borrowing shares, selling them, and later buying them back to return them — profiting if the price falls. Its risk profile is shaped differently from a long position: a long position’s maximum loss is capped at 100% (the price can’t go below zero), but a short position’s loss is theoretically unbounded, because there’s no ceiling on how high a price can rise before the shares must be bought back.

A margin call happens when a leveraged position’s value falls far enough that the account no longer meets the broker’s minimum equity requirement (the maintenance margin), forcing the trader to add funds or have the position closed.

A worked example#

A simulated trader buys $10,000 of stock using $5,000 of their own money and a $5,000 margin loan (2x leverage), against a broker’s maintenance margin requirement of 25% of position value.

The numbers#

Margin call trigger price. Equity equals position value minus the loan, which stays fixed at $5,000. The call triggers when equity falls to 25% of position value:

position − 5,000 = 0.25 × position

0.75 × position = 5,000

position = 6,666.67

That’s 6,666.67 ÷ 10,000 = 66.7% of the original position value — a 33.3% drop in the stock’s price is enough to trigger a margin call on this 2x-leveraged position, well before the position would be worth zero.

Short-sale loss comparison. A trader shorts 100 shares at $20 (proceeds: $2,000). If the price doubles to $40, buying the shares back costs $4,000 — a $2,000 loss, 100% of the original proceeds. If the price instead triples to $60, the loss is $4,000, or 200% of the original proceeds — there is no price at which the loss stops growing, unlike a long position bought outright.

What a diagram would show#

A comparison table: rows for “long position” and “short position”, columns for “maximum possible gain” and “maximum possible loss”, making the capped-versus-uncapped asymmetry visible in one glance rather than in prose.

Try it yourself#

The takeaway#

Leverage doesn’t just make gains and losses bigger — it changes the price at which a trader can be forced out of a position entirely. Weeks 9 and 10 apply this same margin-and-leverage logic to futures and options, where it arrives built into the instrument rather than as an optional account setting.