What is a debit balance (in plain terms)
– A debit balance in a margin account is the dollar amount you have borrowed from your broker to buy securities. It is a liability on your account and must be repaid, typically with interest.
Key definitions (first-use jargon explained)
– Margin account: a brokerage account that lets you borrow cash (or borrow shares to short-sell) using the account’s cash and securities as collateral.
– Debit balance: the outstanding loan amount you owe the broker in the margin account.
– Initial margin: the minimum equity you must put up when you open a leveraged position (U.S. rule: up to 50% of purchase price under Federal Reserve Regulation T).
– Maintenance margin: the minimum percentage of the current market value of
the account’s securities that must be maintained as equity to keep the position open. If equity (account value minus the debit balance) falls below the maintenance requirement, the broker can issue a margin call or liquidate positions to bring the account back into compliance. Broker-specific maintenance requirements vary (commonly 25% for many U.S. brokerages but often higher for concentrated or volatile positions).
Key formulas (first-use jargon explained)
– Market value (MV): current market price × number of shares.
– Equity: MV − Debit balance. (Equity is the portion of your holdings that you own outright.)
– Maintenance requirement (d): minimum fraction of MV that must be equity (e.g., d = 0.25).
– Margin call condition: Equity P_critical + buffer): monitor; no immediate action.
– Warning zone (P ≈ P_critical ± buffer): prepare to act — have funds available, plan partial sell sizes, or ready orders.
– Danger zone (P < P_critical): execute the plan (add cash, trim the position, or accept forced liquidation risk).
6. Recompute after each trade or cash movement. Every buy/sell or repayment/borrow changes MV, Debit, and therefore P_critical. Re-run the formulas before placing large trades.
7. Document and test the workflow. Keep a short written checklist you follow when a position moves toward the warning or danger zones. Practice the math on a paper trade or spreadsheet so the steps become fast and accurate.
Worked numeric example (long stock bought on margin)
– Setup: You buy 100 shares at $50 = $5,000 total market value (MV). You put up 50% initial margin, so equity initial = $2,500 and Debit (loan) = $2,500. Your broker’s maintenance margin m = 25% (0.25).
– Formulas:
– Equity = MV − Debit = N*P − Debit, where N = shares, P = current price.
– Maintenance requirement = m * MV = m * N * P.
– Margin condition: Equity ≥ Maintenance requirement → N*P − Debit ≥ m*N*P.
– Solve for the critical price P_critical (price triggering a margin call if crossed):
P_critical = Debit / (N * (1 − m)).
– For this example: P_critical = 2,500 / (100 * (1 − 0.25)) = 2,500 / 75 = $33.33 per share.
– Check scenarios:
– If P = $40: MV = 4,000; Equity = 4,000 − 2,500 = $1,500; Required = 0.25*4,000 = $1,000 → OK.
– If P = $30: MV = 3,000; Equity = 3,000 − 2,500 = $500; Required = 0.25*3,000 = $750 → Equity < Required → margin call likely.
Notes, assumptions, and caveats
– The P_critical formula assumes a single long position financed by a single debit balance and that the broker applies the maintenance percentage m to the entire position’s market value. With multiple positions, options, shorts, or special house rules, calculations differ.
– Debit balance accrues interest. If interest
charges are added to the debit balance, equity falls and the critical price rises, increasing the chance of a margin call. Interest is usually charged at an annual percentage rate (APR) but accrues daily; many brokers compound monthly or daily, so small balances over time can meaningfully change margin metrics.
Worked example — interest effect
– Starting values (from earlier): N = 100 shares, D0 = $2,500 (debit balance), m = 25% maintenance.
– APR on debit = 8%. Interest for 30 days ≈ D0 * 0.08 * (30/365) = 2,500 * 0.08 * 0.08219 ≈ $16.44.
– New debit D1 = 2,500 + 16.44 = $2,516.44.
– New critical price P_crit = D1 / (N*(1 − m)) = 2,516.44 / (100 * 0.75) = 2,516.44 / 75 ≈ $33.55.
Takeaway: modest interest increased the critical price from $33.33 to ~$33.55. Over longer holding periods or with higher APR, the effect is larger.
Formula summary and derivation
– Equity E = N*P − D, where N = number of shares, P = market price, D = debit balance.
– Maintenance requirement R = m * N * P, where m is maintenance margin (decimal).
– A margin call occurs when E < R.
– Solve E = R for the critical price P_crit:
N*P − D = m*N*P → N*P*(1−m) = D → P_crit = D / (N*(1−m)).
Assumptions: single long position, broker applies m to full MV, no dividends, no other positions or special house rules.
How margin calls can be satisfied — numeric example and logic
Using the earlier scenario where P = $30 triggered a call:
– At P = $30: MV = 100*30 = $3,000; E = 3,000 − 2,500 = $500; Required = 0.25*3,000 = $750; shortfall = $250.
Two common ways to meet a call:
1) Deposit cash: Deposit $250 → D stays $2,500,
→ E becomes $500 + $250 = $750, which equals the required $750, so the margin call is satisfied immediately. (No change to N or D.)
2) Sell shares (use proceeds to reduce the margin loan). Typical broker practice when you sell stock in a margin account is to use sale proceeds either to reduce the debit balance (D) or to leave cash in the account; here we show the common case where proceeds pay down the loan. Let s be shares sold at the current market price P.
– New shares: N' = N − s.
– New market value: MV' = (N − s) * P.
– New debit balance: D' = D − s * P (sale proceeds used to pay loan).
– New equity: E' = MV' − D' = (N − s)P − (D − sP) = NP − D = E (remarkably, equity stays the same if sale proceeds pay down the loan).
– Required equity: R' = m * MV' =
R' = m * MV' = m * (N − s) * P.
The post‑sale equity remains E' = E (see previous line). To avoid a margin shortfall after the sale we need E' ≥ R', so:
E ≥ m (N − s) P
Rearrange to solve for the minimum number of shares s to sell:
m s P ≥ m N P − E
s ≥ (m N P − E) / (m P)
A simpler and equivalent form is:
s ≥ N − E / (m P)
Interpretation and implementation checklist
– Compute current values:
– N = shares held
– P = current price per share
– MV = N * P (market value)
– D = debit balance (amount borrowed)
– E = MV − D (equity)
– m = maintenance margin requirement (decimal, e.g., 0.25 for 25%)
– If E ≥ m * MV, no sale required.
– If E < m * MV, compute s_min = N − E/(m P). This is the minimum number of shares to sell (before rounding).
– Because brokers typically require whole shares, round s_min up to the next whole share.
– After selling s shares, check:
– N' = N − s
– MV' = N' * P
– D' = D − s * P (assumes proceeds are used to pay down the loan)
– E' = MV' − D' (should equal original E)
– Confirm E' ≥ m * MV'
– Practical caveats: assume price P stays constant during the sale, ignore commissions, taxes, and bid/ask spreads; many brokers charge fees or will liquidate different positions; some accounts allow fractional shares—confirm with your broker.
Worked numeric example
– Given: N = 100 shares, P = $40, D = $3,200, so MV = 100 * 40 = $4,000 and E = MV − D = $800. Let m = 0.30 (30%).
– Required equity initially: R = m * MV = 0.30 * 4,000 = $1,200 → E < R