CFA Level I Exam · Equity Issuance and Trading

Margin Transactions and Leverage for CFA Level I

Updated 7 October 2026 · Fact-checked

Buying on margin means borrowing part of the purchase price, so you control a bigger position with less equity. This magnifies gains and losses. To solve questions, find the loan, compute equity, then find the price where equity ÷ position value falls to the maintenance margin. That price triggers a margin call.

Understand Margin Transactions and Leverage

Buying on margin means you pay for part of a stock purchase with your own money and borrow the rest from a broker. Your own money is your equity. The borrowed money is the loan. The broker holds the shares as collateral and charges interest on the loan.

The initial margin requirement is the minimum equity, as a percentage of the purchase value, you must put up when you open the position. If it is 40%, you pay 40% and borrow 60%. The maintenance margin requirement is the minimum equity percentage you must keep after that. If the price falls and your equity percentage drops below it, the broker issues a margin call. You must add cash or securities, or the position is reduced.

Leverage is the size of the position divided by your equity. It equals 1 ÷ initial margin. At 40% initial margin, leverage is 2.5. A 10% move in the stock becomes a 25% move in your equity, before interest and costs. Losses can exceed your starting equity if the price falls far enough.

In a short sale, you borrow shares and sell them, hoping to buy them back cheaper. The sale proceeds stay with the broker as collateral, and you also deposit initial margin. If the price rises, your equity falls, so a margin call comes when the price goes up, not down. You must also pay the lender any dividends paid on the shares.

Exams test three things: the loan and equity at the start, the price that triggers a margin call, and the percentage return on equity after the price moves.

Key formulas to remember

Leverage ratio: Leverage = Position value ÷ Equity = 1 ÷ Initial margin %; A 50% initial margin gives leverage of 2.
Equity and loan at purchase (long): Equity = Initial margin % × P0 × N; Loan = P0 × N − Equity; P0 is the purchase price and N is the number of shares.
Margin percentage (long): Margin % = (Market value of shares − Loan) ÷ Market value of shares; A margin call occurs when this falls below the maintenance margin.
Margin call price (long): Margin call price = P0 × (1 − Initial margin) ÷ (1 − Maintenance margin); Assumes no interest or costs added to the loan. Price must fall to this level.
Margin call price (short): Margin call price = P0 × (1 + Initial margin) ÷ (1 + Maintenance margin); Short sellers get the call when price rises. Equity as a percentage is measured against the market value of the shares owed.
Return on equity (long): Return = [(P1 − P0) × N + Dividends − Interest − Commissions] ÷ Equity; Divide by your own equity, not by the position value.
Return on equity (short): Return = [(P0 − P1) × N − Dividends paid − Costs] ÷ Equity; Add interest earned on proceeds only if the question says so.
Leveraged return: R equity = R asset + (Loan ÷ Equity) × (R asset − borrowing rate); Useful when the question gives percentage returns instead of prices.

How to solve Margin Transactions and Leverage questions

Use the same sequence for any margin question, long or short.

1Identify the position: long (bought on margin) or short (sold borrowed shares).
2Write down the price, number of shares, initial margin and maintenance margin.
3Compute the position value, then equity = initial margin × value, and loan = value − equity. For a short sale, the proceeds are the price × shares.
4If asked for the margin call price, use the formula for long or short. Check the direction: long falls, short rises.
5If asked for a return, compute the gain or loss on the shares, adjust for dividends, interest and commissions, and divide by your initial equity.
6Check the sign and size. Leveraged returns should be larger in magnitude than the unleveraged return, except for borrowing costs.
7Pick the option that matches. Remove options that use the wrong direction or that divide by the wrong base.

Quickest way: Margin call price in one line

When to use it: Use when the question gives initial and maintenance margins and asks for the price that triggers a call, with no interest or dividends.

Long: price × (1 − IM) ÷ (1 − MM). Short: price × (1 + IM) ÷ (1 + MM).
On the BA II Plus, key: 40 × 0.5 ÷ 0.7 = to get 28.57 for a $40 purchase with IM 50% and MM 30%.
Sanity check: a long call price must be below the purchase price. A short call price must be above the sale price.
Of the three options, remove any on the wrong side of the starting price first.

Common mistakes in Margin Transactions and Leverage

Using maintenance margin as the loan percentage, for example price × (1 − MM) as the call price.
The loan stays fixed in rupee or dollar terms, but students treat it as a percentage of the new price.
Fix: Keep the loan fixed in currency. Solve (P × N − Loan) ÷ (P × N) = MM for P.
Calculating return on the position value instead of on equity.
The price move looks like the return, so students stop there.
Fix: Divide the total gain or loss, after interest and dividends, by your initial equity.
Applying the long formula to a short sale and getting a price below the sale price.
Students forget the short seller loses when price rises.
Fix: For shorts, margin call price is above the sale price. Use (1 + IM) ÷ (1 + MM).
Forgetting dividends in a short sale.
Long positions receive dividends, so students add them without thinking.
Fix: The short seller pays dividends to the lender. Subtract them from the profit.
Mixing up initial and maintenance margin, using the lower figure at purchase.
Both are percentages given in the stem, and the order is easy to swap.
Fix: Initial margin is the higher figure and applies at opening. Maintenance is lower and applies afterward.
Ignoring interest on the loan when the question gives a borrowing rate.
Students focus on the price move.
Fix: Interest = loan × rate × time. Subtract it from the gain before dividing by equity.

Worked examples

Example 1

You buy 1,000 shares at $40 with a 50% initial margin requirement. The maintenance margin is 30%. Ignore interest and dividends. At what share price will you receive a margin call? A) $20.00 B) $28.57 C) $34.00

Show the solution

Position value = 1,000 × $40 = $40,000.
Equity = 50% × $40,000 = $20,000. Loan = $20,000.
A margin call occurs when (1,000 × P − 20,000) ÷ (1,000 × P) = 0.30.
So 1,000 P − 20,000 = 300 P, which gives 700 P = 20,000.
P = 20,000 ÷ 700 = $28.57. Check with the formula: 40 × 0.5 ÷ 0.7 = 28.57.
Option A ($20) wrongly treats the loan per share as the trigger. Option C ($34) is above the correct level, but a call happens only at the lower price.

Answer: B) $28.57

Example 2

You short 2,000 shares at $30. Initial margin is 40% and maintenance margin is 25%. Ignore interest and dividends. At what price will you receive a margin call? A) $32.00 B) $33.60 C) $37.50

Show the solution

Short proceeds = 2,000 × $30 = $60,000.
Initial equity = 40% × $60,000 = $24,000.
Total collateral = $60,000 + $24,000 = $84,000.
Equity at price P = 84,000 − 2,000 P. Set (84,000 − 2,000 P) ÷ (2,000 P) = 0.25.
So 84,000 = 2,500 P, which gives P = $33.60. Check: 30 × 1.4 ÷ 1.25 = 33.60.
Check direction: a short seller is called when price rises, and 33.60 is above 30. Option C comes from 30 × 1.25, which ignores initial margin.

Answer: B) $33.60

Exam tips

Write the loan in currency first. It stays fixed while the price moves, and every margin question builds on it.
Before calculating, decide which direction triggers the call. This often eliminates one or two options straight away.
Read the denominator in return questions. The answer is a percentage of your equity, not of the position.
Look for hidden costs: interest on the loan, dividends, commissions. If the stem lists them, subtract them before dividing by equity.
Options are listed from smallest to largest. Estimate whether the answer should be above or below the starting price, then compute only if two options remain.

Practice questions from Equity Issuance and Trading

Margin Transactions and Leverage: frequently asked questions

How do I calculate the margin call price for a long position?

Multiply the purchase price by (1 − initial margin) and divide by (1 − maintenance margin). This assumes the loan is fixed and there is no interest added. For a $40 purchase with 50% initial and 30% maintenance margin, the price is $28.57.

What is the difference between initial margin and maintenance margin?

Initial margin is the minimum equity percentage you must deposit when opening the position. Maintenance margin is the lower minimum you must keep afterward. If equity falls below maintenance margin, you get a margin call.

What is a margin call?

A margin call is a demand from your broker to add cash or securities because your equity has fallen below the maintenance requirement. If you do not respond, the broker can close part or all of your position.

Why does leverage increase risk?

Leverage makes your equity move by a multiple of the price change. At 2.5 times leverage, a 10% price fall causes about a 25% fall in equity before costs. Loan interest must also be paid whatever the outcome.

Who pays dividends in a short sale?

The short seller pays the dividend to the lender of the shares. Treat it as a cost that reduces your profit.