Every calculation you need for the Series 7 exam in one place — formulas, worked examples, and memory aids. Print this page and review before the exam.
Options Formulas
The T-Chart Method (Use This on Every Options Question)
Draw a T-chart for every options problem. Left side = money OUT (debits). Right side = money IN (credits). The side that's bigger determines whether you have a gain or a loss.
Money OUT (Debits)
Money IN (Credits)
Buy (premiums paid)
Exercise to buy stock
Exercise to buy stock
Sell (premiums received)
Exercise to sell stock
Exercise to sell stock
Max Gain = Maximum the right side can exceed the left Max Loss = Maximum the left side can
exceed the right Breakeven = The point where both sides are equal
Long Call
| Metric | Formula |
|---|---|
| Max Gain | Unlimited (stock can rise indefinitely) |
| Max Loss | Premium paid |
| Breakeven | Strike + Premium |
Example: Buy 1 ABC Jul 50 Call @ $4
Max Loss = $4 per share = $400
Breakeven = $50 + $4 = $54
Max Gain = Unlimited (if ABC rises to $100, profit = $100 - $54 = $46 x 100 = $4,600)
Max Loss = $4 per share = $400
Breakeven = $50 + $4 = $54
Max Gain = Unlimited (if ABC rises to $100, profit = $100 - $54 = $46 x 100 = $4,600)
Short Call (Naked)
| Metric | Formula |
|---|---|
| Max Gain | Premium received |
| Max Loss | Unlimited (stock can rise indefinitely) |
| Breakeven | Strike + Premium |
Example: Sell 1 ABC Jul 50 Call @ $4
Max Gain = $4 per share = $400
Breakeven = $50 + $4 = $54 (same as the buyer — opposite sides of same contract)
Max Loss = Unlimited
Max Gain = $4 per share = $400
Breakeven = $50 + $4 = $54 (same as the buyer — opposite sides of same contract)
Max Loss = Unlimited
Long Put
| Metric | Formula |
|---|---|
| Max Gain | Strike - Premium (stock goes to $0) |
| Max Loss | Premium paid |
| Breakeven | Strike - Premium |
Example: Buy 1 XYZ Oct 60 Put @ $3
Max Loss = $3 per share = $300
Breakeven = $60 - $3 = $57
Max Gain = $57 per share = $5,700 (if XYZ goes to $0, you sell at $60, minus $3 premium)
Max Loss = $3 per share = $300
Breakeven = $60 - $3 = $57
Max Gain = $57 per share = $5,700 (if XYZ goes to $0, you sell at $60, minus $3 premium)
Short Put
| Metric | Formula |
|---|---|
| Max Gain | Premium received |
| Max Loss | Strike - Premium (stock goes to $0) |
| Breakeven | Strike - Premium |
Example: Sell 1 XYZ Oct 60 Put @ $3
Max Gain = $3 per share = $300
Breakeven = $60 - $3 = $57
Max Loss = $57 per share = $5,700 (if XYZ goes to $0, you must buy at $60, minus $3 received)
Max Gain = $3 per share = $300
Breakeven = $60 - $3 = $57
Max Loss = $57 per share = $5,700 (if XYZ goes to $0, you must buy at $60, minus $3 received)
Breakeven Memory Aid — CAL / PSB:
Calls: Add premium to strike | Puts: Subtract premium from strike
Quick Patterns:
Buyers pay premium → max loss = premium paid
Sellers receive premium → max gain = premium received
Unlimited loss = short a naked call or short a straddle
Unlimited gain = long a call or long a straddle
Calls: Add premium to strike | Puts: Subtract premium from strike
Quick Patterns:
Buyers pay premium → max loss = premium paid
Sellers receive premium → max gain = premium received
Unlimited loss = short a naked call or short a straddle
Unlimited gain = long a call or long a straddle
Covered Call (Long Stock + Short Call)
| Metric | Formula |
|---|---|
| Max Gain | (Strike - Stock Cost) + Premium |
| Max Loss | Stock Cost - Premium (stock goes to $0) |
| Breakeven | Stock Cost - Premium |
Example: Buy 100 ABC at $48, sell 1 ABC Jul 50 Call @ $3
Max Gain = ($50 - $48) + $3 = $5 x 100 = $500
Max Loss = $48 - $3 = $45 x 100 = $4,500 (if ABC goes to $0)
Breakeven = $48 - $3 = $45
Max Gain = ($50 - $48) + $3 = $5 x 100 = $500
Max Loss = $48 - $3 = $45 x 100 = $4,500 (if ABC goes to $0)
Breakeven = $48 - $3 = $45
Protective Put (Long Stock + Long Put)
| Metric | Formula |
|---|---|
| Max Gain | Unlimited (stock can rise indefinitely) |
| Max Loss | (Stock Cost - Strike) + Premium |
| Breakeven | Stock Cost + Premium |
Example: Buy 100 ABC at $48, buy 1 ABC Jul 45 Put @ $2
Max Loss = ($48 - $45) + $2 = $5 x 100 = $500
Breakeven = $48 + $2 = $50
Max Gain = Unlimited
Max Loss = ($48 - $45) + $2 = $5 x 100 = $500
Breakeven = $48 + $2 = $50
Max Gain = Unlimited
Spreads — Master Table
| Type | Max Gain | Max Loss |
|---|---|---|
| Debit Spread | Width of strikes - Net debit | Net debit (premium paid) |
| Credit Spread | Net credit (premium received) | Width of strikes - Net credit |
Spread Breakevens: Call Spread BE = Lower strike + Net premium Put Spread BE = Higher strike -
Net premium Width of strikes = difference between the two strike prices
Bull Call Spread (Debit) — Worked Example
Position: Buy 1 ABC Jan 50 Call @ $5, Sell 1 ABC Jan 60 Call @ $2
Net Debit = $5 - $2 = $3 (you paid more than you received)
Width = $60 - $50 = $10
Max Loss = Net Debit = $3 x 100 = $300 (ABC at or below $50 at expiration)
Max Gain = Width - Net Debit = $10 - $3 = $7 x 100 = $700 (ABC at or above $60)
Breakeven = Lower Strike + Net Premium = $50 + $3 = $53
Net Debit = $5 - $2 = $3 (you paid more than you received)
Width = $60 - $50 = $10
Max Loss = Net Debit = $3 x 100 = $300 (ABC at or below $50 at expiration)
Max Gain = Width - Net Debit = $10 - $3 = $7 x 100 = $700 (ABC at or above $60)
Breakeven = Lower Strike + Net Premium = $50 + $3 = $53
Bear Put Spread (Debit) — Worked Example
Position: Buy 1 ABC Jan 60 Put @ $6, Sell 1 ABC Jan 50 Put @ $2
Net Debit = $6 - $2 = $4
Width = $60 - $50 = $10
Max Loss = Net Debit = $4 x 100 = $400 (ABC at or above $60 at expiration)
Max Gain = Width - Net Debit = $10 - $4 = $6 x 100 = $600 (ABC at or below $50)
Breakeven = Higher Strike - Net Premium = $60 - $4 = $56
Net Debit = $6 - $2 = $4
Width = $60 - $50 = $10
Max Loss = Net Debit = $4 x 100 = $400 (ABC at or above $60 at expiration)
Max Gain = Width - Net Debit = $10 - $4 = $6 x 100 = $600 (ABC at or below $50)
Breakeven = Higher Strike - Net Premium = $60 - $4 = $56
Bear Call Spread (Credit) — Worked Example
Position: Sell 1 ABC Jan 50 Call @ $5, Buy 1 ABC Jan 60 Call @ $2
Net Credit = $5 - $2 = $3 (you received more than you paid)
Width = $60 - $50 = $10
Max Gain = Net Credit = $3 x 100 = $300 (ABC at or below $50 at expiration)
Max Loss = Width - Net Credit = $10 - $3 = $7 x 100 = $700 (ABC at or above $60)
Breakeven = Lower Strike + Net Premium = $50 + $3 = $53
Net Credit = $5 - $2 = $3 (you received more than you paid)
Width = $60 - $50 = $10
Max Gain = Net Credit = $3 x 100 = $300 (ABC at or below $50 at expiration)
Max Loss = Width - Net Credit = $10 - $3 = $7 x 100 = $700 (ABC at or above $60)
Breakeven = Lower Strike + Net Premium = $50 + $3 = $53
Bull Put Spread (Credit) — Worked Example
Position: Sell 1 ABC Jan 60 Put @ $6, Buy 1 ABC Jan 50 Put @ $2
Net Credit = $6 - $2 = $4
Width = $60 - $50 = $10
Max Gain = Net Credit = $4 x 100 = $400 (ABC at or above $60 at expiration)
Max Loss = Width - Net Credit = $10 - $4 = $6 x 100 = $600 (ABC at or below $50)
Breakeven = Higher Strike - Net Premium = $60 - $4 = $56
Net Credit = $6 - $2 = $4
Width = $60 - $50 = $10
Max Gain = Net Credit = $4 x 100 = $400 (ABC at or above $60 at expiration)
Max Loss = Width - Net Credit = $10 - $4 = $6 x 100 = $600 (ABC at or below $50)
Breakeven = Higher Strike - Net Premium = $60 - $4 = $56
Spread Memory Aids:
Debit = you paid → max loss is what you paid (the net debit)
Credit = you received → max gain is what you received (the net credit)
All spreads: max gain + max loss = width of strikes
Which is bull? Which is bear?
Bull = buy the lower strike (calls) or sell the higher strike (puts) — you profit if stock rises
Bear = sell the lower strike (calls) or buy the higher strike (puts) — you profit if stock falls
Debit = you paid → max loss is what you paid (the net debit)
Credit = you received → max gain is what you received (the net credit)
All spreads: max gain + max loss = width of strikes
Which is bull? Which is bear?
Bull = buy the lower strike (calls) or sell the higher strike (puts) — you profit if stock rises
Bear = sell the lower strike (calls) or buy the higher strike (puts) — you profit if stock falls
Long Straddle (Buy Call + Buy Put, Same Strike & Expiration)
| Metric | Formula |
|---|---|
| Max Gain | Unlimited (to upside); Strike - Combined Premiums (to downside) |
| Max Loss | Combined premiums paid |
| Upside BE | Strike + Combined premiums |
| Downside BE | Strike - Combined premiums |
Example: Buy 1 ABC Jan 50 Call @ $3, Buy 1 ABC Jan 50 Put @ $4
Combined Premiums = $3 + $4 = $7
Max Loss = $7 x 100 = $700 (ABC at exactly $50 at expiration — both expire worthless)
Upside BE = $50 + $7 = $57
Downside BE = $50 - $7 = $43
Max Gain = Unlimited (upside); or $43 x 100 = $4,300 (downside, if stock goes to $0)
Combined Premiums = $3 + $4 = $7
Max Loss = $7 x 100 = $700 (ABC at exactly $50 at expiration — both expire worthless)
Upside BE = $50 + $7 = $57
Downside BE = $50 - $7 = $43
Max Gain = Unlimited (upside); or $43 x 100 = $4,300 (downside, if stock goes to $0)
Short Straddle (Sell Call + Sell Put, Same Strike & Expiration)
| Metric | Formula |
|---|---|
| Max Gain | Combined premiums received |
| Max Loss | Unlimited (to upside); Strike - Combined Premiums (to downside) |
| Upside BE | Strike + Combined premiums |
| Downside BE | Strike - Combined premiums |
Example: Sell 1 ABC Jan 50 Call @ $3, Sell 1 ABC Jan 50 Put @ $4
Combined Premiums = $3 + $4 = $7
Max Gain = $7 x 100 = $700 (ABC at exactly $50 at expiration — both expire worthless)
Upside BE = $50 + $7 = $57
Downside BE = $50 - $7 = $43
Max Loss = Unlimited (upside); or $43 x 100 = $4,300 (downside)
Combined Premiums = $3 + $4 = $7
Max Gain = $7 x 100 = $700 (ABC at exactly $50 at expiration — both expire worthless)
Upside BE = $50 + $7 = $57
Downside BE = $50 - $7 = $43
Max Loss = Unlimited (upside); or $43 x 100 = $4,300 (downside)
Combinations (Different Strikes or Expirations)
A combination is like a straddle but the call and put have different strike prices and/or expirations. The formulas work the same way:
Long Combination: Max Loss = Combined premiums paid Upside BE = Call strike + Combined premiums
Downside BE = Put strike - Combined premiums Short Combination: Max Gain = Combined premiums
received Upside BE = Call strike + Combined premiums Downside BE = Put strike - Combined
premiums
Example: Buy 1 ABC Jan 55 Call @ $2, Buy 1 ABC Jan 45 Put @ $3
Combined Premiums = $2 + $3 = $5
Upside BE = $55 + $5 = $60
Downside BE = $45 - $5 = $40
Max Loss = $5 x 100 = $500 (stock between $45 and $55 at expiration)
Combined Premiums = $2 + $3 = $5
Upside BE = $55 + $5 = $60
Downside BE = $45 - $5 = $40
Max Loss = $5 x 100 = $500 (stock between $45 and $55 at expiration)
Straddle Memory Aids:
A straddle has TWO breakevens: Strike +/- Combined premiums
Long straddle = you WANT movement (either direction). You paid, so max loss = what you paid.
Short straddle = you WANT the stock to sit still. You received, so max gain = what you received.
The long straddle buyer and short straddle seller are on opposite sides — same breakevens, flipped gain/loss.
A straddle has TWO breakevens: Strike +/- Combined premiums
Long straddle = you WANT movement (either direction). You paid, so max loss = what you paid.
Short straddle = you WANT the stock to sit still. You received, so max gain = what you received.
The long straddle buyer and short straddle seller are on opposite sides — same breakevens, flipped gain/loss.
Margin Formulas
Initial Margin (Reg T = 50%)
Long Margin: Margin Required = Market Value x 50% Loan Amount = Market Value x 50% Short Margin:
Margin Required = Short Market Value x 50% Credit Balance = Short Proceeds + Margin Deposit
Equity Calculations
Long Margin Equity = Market Value - Debit Balance Short Margin Equity = Credit Balance - Short
Market Value
SMA (Special Memorandum Account)
SMA = Equity - (Market Value x 50%) (Only when equity > 50%) SMA increases when: - Stock price
rises (50% of increase) - Dividends received - Cash deposits - Sale proceeds above loan value
Buying Power
Buying Power = SMA / Reg T Buying Power = SMA / 0.50 Buying Power = SMA x 2
Example: Customer has $5,000 SMA
Buying Power = $5,000 x 2 = $10,000 in additional securities they can buy
Buying Power = $5,000 x 2 = $10,000 in additional securities they can buy
Maintenance Margin & Trigger Prices
LONG Positions (25% maintenance): Margin Call when: Equity < 25% of Market Value Trigger Price:
Debit Balance / 0.75 SHORT Positions (30% maintenance): Margin Call when: Equity < 30% of Market
Value Trigger Price: Credit Balance / 1.30
Long Example: Debit balance = $40,000
Trigger = $40,000 / 0.75 = $53,333 — margin call if market value falls below this
Short Example: Credit balance = $130,000
Trigger = $130,000 / 1.30 = $100,000 — margin call if short market value rises above this
Trigger = $40,000 / 0.75 = $53,333 — margin call if market value falls below this
Short Example: Credit balance = $130,000
Trigger = $130,000 / 1.30 = $100,000 — margin call if short market value rises above this
Pattern Day Trader
Minimum Equity: $25,000 Buying Power: 4 x Maintenance Excess Buying Power (with outstanding
margin call): 2 x Maintenance Excess
Margin Memory Aids:
SMA x 2 = Buying Power
Long trigger: Debit / 0.75 | Short trigger: Credit / 1.30
Shorts are riskier = higher maintenance (30% > 25%)
PDT: 4 day trades in 5 days → $25K minimum → 4x buying power
SMA x 2 = Buying Power
Long trigger: Debit / 0.75 | Short trigger: Credit / 1.30
Shorts are riskier = higher maintenance (30% > 25%)
PDT: 4 day trades in 5 days → $25K minimum → 4x buying power
Bond Formulas
The Yield Seesaw (Triangle / Ladybug)
Price and yield move in opposite directions. The coupon rate (Nominal Yield) is the fixed fulcrum — it never changes. The four yields stack in a predictable order depending on whether the bond is at a premium or discount.
| Yield | What It Measures | Formula |
|---|---|---|
| Nominal Yield (NY) | Coupon rate. Fixed at issuance. Never changes. | Stated on the bond (e.g., 6%) |
| Current Yield (CY) | Annual income relative to current price | Annual Interest / Market Price |
| Yield to Maturity (YTM) | Total return if held to maturity (includes price gain/loss) | Approximation formula below |
| Yield to Call (YTC) | Total return if called early (shorter time amplifies effect) | Same as YTM but uses call date & call price |
Yield Ordering Rules
DISCOUNT BOND (Price < Par)
Lowest ←——————————→ Highest
NY < CY < YTM < YTC
Price is low → all yields are pushed UP above the coupon
YTC is highest because you get back par SOONER on less money
Lowest ←——————————→ Highest
NY < CY < YTM < YTC
Price is low → all yields are pushed UP above the coupon
YTC is highest because you get back par SOONER on less money
PREMIUM BOND (Price > Par)
Lowest ←——————————→ Highest
YTC < YTM < CY < NY
Price is high → all yields are pushed DOWN below the coupon
YTC is lowest because you lose the premium FASTER when called early
Lowest ←——————————→ Highest
YTC < YTM < CY < NY
Price is high → all yields are pushed DOWN below the coupon
YTC is lowest because you lose the premium FASTER when called early
PAR BOND (Price = Par)
NY = CY = YTM = YTC
All four yields are equal at par
NY = CY = YTM = YTC
All four yields are equal at par
Current Yield
Current Yield = Annual Interest / Market Price
Discount Example: 7% coupon bond trading at $800
Annual Interest = $1,000 x 0.07 = $70
CY = $70 / $800 = 8.75%
(CY > NY because bond is at a discount — confirms the seesaw)
Annual Interest = $1,000 x 0.07 = $70
CY = $70 / $800 = 8.75%
(CY > NY because bond is at a discount — confirms the seesaw)
Premium Example: 5% coupon bond trading at $1,100
Annual Interest = $1,000 x 0.05 = $50
CY = $50 / $1,100 = 4.55%
(CY < NY because bond is at a premium — confirms the seesaw)
Annual Interest = $1,000 x 0.05 = $50
CY = $50 / $1,100 = 4.55%
(CY < NY because bond is at a premium — confirms the seesaw)
Yield to Maturity (YTM) — Approximation Formula
Annual Interest + (Par - Price) / Years to Maturity YTM =
------------------------------------------------------- (Par + Price) / 2
Discount Example: 6% bond, 10 years to maturity, trading at $900
Numerator = $60 + ($1,000 - $900) / 10 = $60 + $10 = $70
Denominator = ($1,000 + $900) / 2 = $950
YTM = $70 / $950 = 7.37%
(YTM > CY > NY — 7.37% > 6.67% > 6.00% — confirms discount ordering)
Numerator = $60 + ($1,000 - $900) / 10 = $60 + $10 = $70
Denominator = ($1,000 + $900) / 2 = $950
YTM = $70 / $950 = 7.37%
(YTM > CY > NY — 7.37% > 6.67% > 6.00% — confirms discount ordering)
Premium Example: 8% bond, 10 years to maturity, trading at $1,100
Numerator = $80 + ($1,000 - $1,100) / 10 = $80 + (-$10) = $70
Denominator = ($1,000 + $1,100) / 2 = $1,050
YTM = $70 / $1,050 = 6.67%
(YTM < CY < NY — 6.67% < 7.27% < 8.00% — confirms premium ordering)
Numerator = $80 + ($1,000 - $1,100) / 10 = $80 + (-$10) = $70
Denominator = ($1,000 + $1,100) / 2 = $1,050
YTM = $70 / $1,050 = 6.67%
(YTM < CY < NY — 6.67% < 7.27% < 8.00% — confirms premium ordering)
Tax-Equivalent Yield
TEY = Municipal Yield / (1 - Tax Bracket)
Example: 4% muni bond, investor in 32% tax bracket
TEY = 0.04 / (1 - 0.32) = 0.04 / 0.68 = 5.88%
A taxable bond must yield at least 5.88% to match this muni after taxes.
TEY = 0.04 / (1 - 0.32) = 0.04 / 0.68 = 5.88%
A taxable bond must yield at least 5.88% to match this muni after taxes.
Accrued Interest
Accrued Interest = (Annual Interest / Days in Year) x Days Since Last Payment Corporate &
Municipal: 30/360 (30-day months, 360-day year) Government: Actual/Actual (real calendar days)
Example: 6% corporate bond ($1,000 par), last payment Jan 1, sold April 15
Days = 3 months x 30 + 15 days = 105 days (using 30/360)
Accrued Interest = ($60 / 360) x 105 = $0.1667 x 105 = $17.50
Buyer pays seller this amount on top of the bond price.
Days = 3 months x 30 + 15 days = 105 days (using 30/360)
Accrued Interest = ($60 / 360) x 105 = $0.1667 x 105 = $17.50
Buyer pays seller this amount on top of the bond price.
Bond Yield Memory Aids:
PDY / DIY: Premium Decreases Yield; Discount Increases Yield
Discount ordering: NY < CY < YTM < YTC (smallest to largest, alphabetical-ish)
Premium ordering: YTC < YTM < CY < NY (reverse of discount)
CY quick check: If CY > NY, it's a discount. If CY < NY, it's a premium. If CY = NY, it's at par.
Why YTC is the extreme: Calling a bond early amplifies the effect. Discount → you get par back sooner (boost). Premium → you lose premium sooner (drag).
PDY / DIY: Premium Decreases Yield; Discount Increases Yield
Discount ordering: NY < CY < YTM < YTC (smallest to largest, alphabetical-ish)
Premium ordering: YTC < YTM < CY < NY (reverse of discount)
CY quick check: If CY > NY, it's a discount. If CY < NY, it's a premium. If CY = NY, it's at par.
Why YTC is the extreme: Calling a bond early amplifies the effect. Discount → you get par back sooner (boost). Premium → you lose premium sooner (drag).
Investment Company Formulas
NAV and Sales Charges
NAV = (Total Assets - Liabilities) / Shares Outstanding POP = NAV + Sales Charge POP = NAV / (1
- Sales Charge %) Sales Charge % = (POP - NAV) / POP Maximum Sales Charge = 8.5% of POP
Example: Fund has $100M in assets, $5M in liabilities, 5M shares
NAV = ($100M - $5M) / 5M = $19.00
With 5% sales charge: POP = $19.00 / (1 - 0.05) = $19.00 / 0.95 = $20.00
NAV = ($100M - $5M) / 5M = $19.00
With 5% sales charge: POP = $19.00 / (1 - 0.05) = $19.00 / 0.95 = $20.00
Critical Numbers
| Item | Number |
|---|---|
| Options contract size | 100 shares |
| Reg T initial margin | 50% |
| Long maintenance margin | 25% |
| Short maintenance margin | 30% |
| Pattern day trader minimum equity | $25,000 |
| PDT buying power multiplier | 4x (2x with outstanding call) |
| Max mutual fund sales charge | 8.5% |
| Settlement (stocks/bonds) | T+1 |
| Reg T payment deadline | S+2 (= T+3) |
| Options agreement return | 15 days |
| Frozen account period | 90 days |
| Regular IRA contribution limit | $7,000 (2024) |
| 401(k) contribution limit | $23,000 (2024) |
Print this page. Review before the exam. Formulas should be automatic.