9.4 Margin Calculations

Long Margin Account Math

A long margin account has three values: Long Market Value (LMV), the Debit Balance (DR) owed to the broker, and Equity (EQ), the customer's stake.

EQ = LMV − DR, which rearranges to LMV = DR + EQ.

The single most important behavior: the debit balance does not change as prices move — it changes only when the customer pays it down or borrows more. So when LMV rises or falls, equity absorbs the entire change.

Worked Long Example

A customer deposits $10,000 to buy $20,000 of stock:

• Stock rises to $24,000: EQ = 24,000 − 10,000 = $14,000.
• Stock falls to $16,000: EQ = 16,000 − 10,000 = $6,000.

The debit stayed $10,000 both times.

Long Maintenance Call Trigger

A maintenance call hits when long equity drops below 25% of LMV. Find the market value at which equity equals exactly 25% with:

Trigger price = DR ÷ (1 − maintenance %) = DR ÷ 0.75

Example: DR = $10,000 → trigger = 10,000 ÷ 0.75 = $13,333. At that LMV, equity is $3,333, exactly 25%. Below it, a maintenance call goes out.

Call amount (cash needed to restore to maintenance): (maintenance % × LMV) − current equity. If LMV = $12,000, DR = $10,000, EQ = $2,000, then (0.25 × 12,000) − 2,000 = $1,000.

Special Memorandum Account (SMA)

SMA is a line of credit that builds when equity exceeds the 50% Reg T requirement. Use either equivalent formula:

SMA = EQ − (0.50 × LMV) or SMA = (0.50 × LMV) − DR

Example: LMV = $30,000, DR = $10,000 → EQ = $20,000; Reg T requirement = 0.50 × 30,000 = $15,000; SMA = 20,000 − 15,000 = $5,000.

SMA increases from appreciation above Reg T, cash dividends, cash deposits, and sale proceeds. Crucially, SMA does not fall when the market falls — it is a memorandum balance, not real cash.

Buying Power

Each $1 of SMA supports $2 of new marginable stock because Reg T requires only 50% down:

Buying power = SMA × 2.

So $5,000 SMA = $10,000 buying power. A customer may also withdraw cash up to the SMA amount if maintenance still holds afterward.

Short Margin Account Math

Short positions flip the signs: the customer owes shares, not dollars. The values are Short Market Value (SMV), the Credit Balance (CR), and Equity (EQ).

EQ = CR − SMV, so CR = SMV + EQ.

The credit balance is the constant here: it equals sale proceeds plus the margin deposit and does not change as the stock moves.

Worked Short Example

Short 100 shares at $60 (SMV = $6,000), deposit 50% ($3,000):

• Stock falls to $40 (a gain for the short): EQ = 9,000 − 4,000 = $5,000.
• Stock rises to $80 (a loss): EQ = 9,000 − 8,000 = $1,000 — a call.

Short Maintenance Call Trigger

Short maintenance is 30%, so equity must be at least 30% of SMV. The trigger price (where equity equals exactly 30%) is:

Trigger price = CR ÷ (1 + maintenance %) = CR ÷ 1.30

Example: CR = $9,000 → trigger = 9,000 ÷ 1.30 = $6,923. If SMV rises above $6,923, a maintenance call is issued (rising prices hurt the short seller).

Combined (Mixed) Accounts

With both long and short positions:

Combined equity = (LMV + CR) − (DR + SMV).

Maintenance is evaluated for the account as a whole.

Formula Cheat Sheet

Restricted Accounts

An account is restricted when equity falls below the 50% Reg T requirement but is still above the maintenance minimum — for example, equity at 40% of LMV. The account is not in a maintenance call, but special rules apply. The customer is not forced to deposit money, yet certain actions are limited: under the retention requirement, if the customer sells securities in a restricted account, 50% of the sale proceeds must be retained to reduce the debit balance, and only the other 50% (which becomes SMA) is released.

This is a favorite distractor, so distinguish a restricted account (below 50%, above maintenance) from an account in a maintenance call (below 25% long).

How SMA Behaves Over Time

SMA is a one-way ratchet. It rises when the market appreciates, when cash dividends post, when cash is deposited, and when securities are sold (50% of proceeds). It does not shrink when the market declines — the broker keeps the memorandum balance on the books. However, using SMA reduces it dollar-for-dollar and increases the debit balance, which can push a thin account toward a maintenance call. A customer near maintenance who draws SMA may immediately trigger a call, so SMA is real borrowing power, not free money.

Step-by-Step: Solving a Maintenance Call Problem

1. Identify whether the account is long or short.
2. Find the constant balance — debit for long, credit for short.
3. For a long account, divide the debit by 0.75 to get the trigger price; for a short account, divide the credit by 1.30.
4. Compare current market value to the trigger to see if a call exists.
5. If a call exists, compute the deposit as (maintenance % × market value) − current equity.

Quick Numerical Drill

• Long: DR = $30,000 → trigger = 30,000 ÷ 0.75 = $40,000.
• Short: CR = $26,000 → trigger = 26,000 ÷ 1.30 = $20,000.
• SMA: LMV = $40,000, DR = $12,000 → equity $28,000, Reg T need $20,000, SMA = $8,000, buying power $16,000.

On the Exam

Watch which balance is constant: the debit in long accounts and the credit in short accounts. Memorize the two trigger prices (debit ÷ 0.75 for longs, credit ÷ 1.30 for shorts), remember that SMA never decreases on a market drop, and recall that SMA buys twice its dollar amount of marginable securities.