/margin-operations

Margin Operations — Worked Examples

Contents

1. Example 1: Calculating margin requirements and buying power for a diversified brokerage account
2. Example 2: Managing a margin call sequence from generation through resolution
3. Example 3: Evaluating portfolio margin benefits for an active options trader

Example 1: Calculating margin requirements and buying power for a diversified brokerage account

Given: A client opens a new margin account and deposits $150,000 in cash. The client wants to build a diversified portfolio.

Step 1 — Determine Reg T buying power:

• Cash deposit: $150,000
• SMA: $150,000 (initial cash deposit establishes the SMA)
• Reg T buying power: $150,000 x 2 = $300,000

Step 2 — Client purchases a diversified portfolio:

• $120,000 in large-cap equity ETF (VTI)
• $60,000 in international equity ETF (VXUS)
• $40,000 in investment-grade bond ETF (BND)
• $30,000 in REIT ETF (VNQ)
• Total purchases: $250,000

Step 3 — Post-purchase account status:

• Market value: $250,000
• Debit balance: $250,000 - $150,000 = $100,000
• Account equity: $250,000 - $100,000 = $150,000
• Equity percentage: $150,000 / $250,000 = 60% (above 50% Reg T requirement)
• Remaining SMA: $150,000 - ($250,000 x 50%) = $150,000 - $125,000 = $25,000
• Remaining buying power: $25,000 x 2 = $50,000

Step 4 — Determine maintenance call trigger (assuming 30% house requirement):

• House maintenance: 30%
• Call triggered when: equity / market value < 30%
• Equivalently: market value falls to debit balance / (1 - 0.30) = $100,000 / 0.70 = $142,857
• This represents a decline of ($250,000 - $142,857) / $250,000 = 42.9% from current value

Step 5 — Margin interest cost estimate:

• Debit balance: $100,000
• Assume margin rate: broker call rate (6.50%, illustrative — actual rates vary with the rate environment) + 0.75% = 7.25%
• Annual interest: $100,000 x 7.25% = $7,250
• Monthly interest: approximately $604
• This cost must be offset by portfolio returns exceeding 7.25% (on the borrowed portion) to add value through leverage

Step 6 — Impact of a 15% market decline:

• New market value: $250,000 x 0.85 = $212,500
• Debit balance unchanged: $100,000
• New equity: $212,500 - $100,000 = $112,500
• Equity percentage: $112,500 / $212,500 = 52.9% (still above 30% house requirement; no margin call)
• New SMA: remains at $25,000 (SMA is a high-water mark; does not decrease with market decline)

Example 2: Managing a margin call sequence from generation through resolution

Given: An existing margin account with the following position prior to market decline:

• Market value: $400,000 (80% equities, 20% bonds)
• Debit balance: $160,000
• Equity: $240,000 (60%)
• House maintenance requirement: 35%

Days 1-12 — progressive decline, no call: Equities fall in stages (down 18%, 28%, 35%, then 45% cumulatively from the original $320,000; bonds drift down 5%), taking the equity percentage from 60% to 53.3%, 48.5%, 44.0%, and finally 36.5% on Day 12 — approaching but never breaching the 35% house requirement.

Day 14 — Call triggered:

• Equities down 48% total; bonds down 5%
• New equity market value: $320,000 x 0.52 = $166,400
• New bond market value: $76,000
• New total market value: $166,400 + $76,000 = $242,400
• Debit balance: $160,000
• New equity: $242,400 - $160,000 = $82,400
• Equity percentage: $82,400 / $242,400 = 34.0% — below 35% house requirement
• House margin call generated at end of day

Margin call amount calculation:

• Required equity: 35% x $242,400 = $84,840
• Current equity: $82,400
• Call amount: $84,840 - $82,400 = $2,440

Day 14 — Notification and communication:

• Automated margin call alert sent via system notification and email
• Margin department places phone call to client
• Notification states: $2,440 due by Day 19 (T+5 business days)
• Options presented: deposit cash, deposit marginable securities (at loan value), or liquidate positions

Day 16 — Client responds:

• Client deposits $5,000 cash (exceeds call amount to provide buffer)
• New debit balance: $160,000 - $5,000 = $155,000
• Assuming market unchanged: equity = $242,400 - $155,000 = $87,400
• Equity percentage: $87,400 / $242,400 = 36.1% (above 35%)
• Margin call satisfied

Alternative resolution — Partial liquidation:

• If client cannot deposit, sell $7,000 of bond ETF
• Proceeds reduce debit balance: $160,000 - $7,000 = $153,000
• New market value: $242,400 - $7,000 = $235,400
• New equity: $235,400 - $153,000 = $82,400
• Equity percentage: $82,400 / $235,400 = 35.0% (at the requirement; call met but no buffer)
• Better approach: sell more to create a buffer above the requirement

Example 3: Evaluating portfolio margin benefits for an active options trader

Given: An experienced options trader maintains the following portfolio:

• Account equity: $500,000
• Long 2,000 shares SPY at $450 = $900,000
• Long 20 SPY 420 puts (protective puts, 3-month expiry), premium paid $8 per contract = $16,000
• Short 20 SPY 480 calls (covered calls, 3-month expiry), premium received $5 per contract = $10,000
• Net portfolio delta: reduced from 2,000 to approximately 1,400 (hedged)

Step 1 — Calculate Reg T margin requirement: Under Reg T, margin is calculated position-by-position:

• Long 2,000 shares SPY at $450: 50% initial margin = $450,000
• Long 20 SPY 420 puts: fully paid (no margin required; cost $16,000 already paid)
• Short 20 SPY 480 calls: covered by long shares (no additional margin required)
• Total Reg T margin requirement: $450,000
• Account equity: $500,000
• Excess equity: $500,000 - $450,000 = $50,000
• The protective puts and covered calls provide risk reduction, but Reg T does not recognize the hedge

Step 2 — Calculate portfolio margin requirement: Under portfolio margin (OCC TIMS), the entire position is evaluated as a unit under stress scenarios:

• The key stress scenario is SPY -15% (worst case for this long-biased portfolio):
  • SPY drops from $450 to $382.50
  • Long stock loss: 2,000 x ($450 - $382.50) = -$135,000
  • Long 420 puts gain: puts move deep in-the-money; approximate gain: 20 x 100 x ($420 - $382.50 - $8) = +$59,000
  • Short 480 calls gain: calls expire worthless; gain: 20 x 100 x $5 = +$10,000
  • Net portfolio loss under -15% stress: -$135,000 + $59,000 + $10,000 = -$66,000
• Additional stress scenarios (+15%, +/-5%, +/-10%) produce smaller losses for this position
• Portfolio margin requirement: approximately $66,000 (the largest loss across all scenarios)

Step 3 — Compare Reg T vs portfolio margin:

Step 4 — Assess the implications:

• Portfolio margin reduces the requirement by 85% because it recognizes the protective puts and covered calls as risk-reducing hedges
• The trader can deploy excess capital to additional strategies or maintain a larger cash buffer
• Risk consideration: The 13.6x available leverage is dangerous if fully utilized. The trader should maintain a self-imposed margin buffer well above the minimum — targeting no more than 50-60% utilization of portfolio margin capacity
• Stress test beyond the model: If SPY gaps down 25% overnight (beyond the 15% stress scenario), the portfolio loss would be approximately $100,000 — still within the $500,000 equity but illustrating that the OCC TIMS scenarios do not capture tail risk. The trader should run their own stress tests at more extreme levels
• Qualification check: The account meets the $100,000 minimum equity requirement. The trader must have appropriate options approval and complete the firm's portfolio margin agreement