Charta is on Google Play: practise on the go. Get the app
Charta

Outline how stock is bought on margin when no CCP is involved and compute the margin requirements.

FRM® Part I · Financial Markets and Products · Exchanges and OTC Markets · FRM1.FM.5.e

The idea

When stock is bought on margin without a CCP, the broker lends part of the price and holds the shares as collateral. Under the initial margin requirement, commonly 50% in the United States, the investor funds that share of the purchase and borrows the rest at interest. Equity is market value − loan, and the margin ratio is equity ÷ market value. When the ratio falls below the maintenance margin, often 25% to 30%, a margin call follows. For a long purchase at price P0, the price that triggers a call is given by: Call price = P0 × (1 − initial margin) ÷ (1 − maintenance margin). For a short sale the account holds the sale proceeds plus the deposit, so the call comes on a rise in price: Call price = P0 × (1 + initial margin) ÷ (1 + maintenance margin). Leverage magnifies returns in both directions, and interest on the loan is a cost that must be included.

Formulas

Price at which a margin call comes

margin call price = P₀ × (1 − initial margin) ÷ (1 − maintenance margin)

P₀
the price paid per share
initial margin
the share of the purchase the buyer put up in equity
maintenance margin
the minimum equity share the broker requires

A long purchase on margin with no CCP. The call comes on a fall in price; ignoring loan interest overstates how far the price can fall.

Price at which a margin call comes on a short sale

short margin call price = P₀ × (1 + initial margin) ÷ (1 + maintenance margin)

P₀
the price at which the shares were sold short
initial margin
the deposit as a share of the sale proceeds
maintenance margin
the minimum equity as a share of the current value of the shares

The account holds the proceeds plus the deposit, so the call comes on a rise in price. Using the long-position formula, with minus signs, is the usual slip.

Margin ratio on a margin account

margin ratio = (market value − loan) ÷ market value

market value
the current value of the shares held
loan
the amount borrowed from the broker

The numerator is the investor's equity. A call follows when the ratio falls below maintenance margin, and restoring the initial margin means paying in enough to lift equity back to that share of market value.

A practice question

From the question bank, with the reason each wrong option is wrong.

An investor buys 1,000 shares at USD 40 on margin with a 50 percent initial margin requirement. How much does the investor borrow from the broker?

  1. USD 20,000 - correct
  2. USD 40,000, the full priceWhy not: Borrows the full price, as if no equity were required.
  3. USD 10,000Why not: Applies a 25 percent borrowing share, confusing the maintenance level with the loan portion.
  4. USD 30,000Why not: Applies a 25 percent equity share, confusing maintenance margin with initial margin.

Purchase price = 1,000 x 40 = 40,000. At 50 percent initial margin the investor funds 20,000 and borrows the other 20,000.

A harder one

An investor buys 500 shares at USD 60 with a 50 percent initial margin and a 30 percent maintenance margin. At what share price, closest to, does a margin call occur?

  1. USD 42.00Why not: Applies a 30 percent price fall (60 x 0.70), ignoring the loan taken at purchase.
  2. USD 30.00Why not: Applies a 50 percent price fall, which is the point where equity is wiped out for no loan reduction.
  3. USD 42.86 - correct
  4. USD 36.00Why not: Scales the price by maintenance over initial margin (0.30 / 0.50), which has no basis.

Loan = 60 x 0.5 = 30 per share. Call when (P - 30)/P = 0.30, so P = 30 / 0.70 = 42.86.

The hardest tier

An investor buys 1,000 shares at USD 80 with a 50 percent initial margin and a 25 percent maintenance margin. The price falls to USD 50 and the investor wants to restore the account to the 50 percent initial margin by paying down the loan. How much cash is needed?

  1. USD 15,000 - correct
  2. USD 2,500Why not: Restores only to the 25 percent maintenance margin rather than the initial margin.
  3. USD 25,000 in totalWhy not: Reports the equity needed after the call, not the extra cash to be added.
  4. USD 30,000Why not: Restores equity to its original 40,000 instead of to 50 percent of the new value.

Loan = 40,000; market value = 50,000; equity = 10,000 (20 percent), below maintenance. At 50 percent, equity must be 25,000, so the investor pays in 15,000.

In the app: 6 practice questions on this outcome, spaced review that brings it back before you forget it.

Start free →

More in Exchanges and OTC Markets