Series 7

1. A profile constrains the recommendation

Learning goal: Compare needs and risks before a product feature.

Practice focus: editorial, not a measured error-frequency claim. This lesson uses original examples.

The Series 7 outline includes customer profiles, investment recommendations and applicable conduct standards [F 4]. Regulation Best Interest should not be reduced to a generic suitability slogan. These educational scenarios isolate how a stated short-term liquidity need conflicts with committing those funds to an illiquid choice; they do not decide a real customer recommendation or claim a complete legal checklist.

Name the goal, timeline, cash needs and risk tolerance before comparing products. A high advertised return is only one feature. Missing customer information is a reason to obtain the needed facts, not to invent them. Keep hypothetical product assumptions explicit so no label is treated as an automatic recommendation.

Worked example

A toy customer needs $8,000 in six months. Product A locks all funds for five years; B is accessible under the stated model. What is the first relevant conflict?

1. Identify six months as the required liquidity horizon.
2. A five-year lock conflicts with access to those funds at six months.
3. A higher stated return for A does not remove the conflict.
4. More profile facts and applicable standards are still needed before any real recommendation.

Mental model: Match the product tradeoff to a verified profile.

Common trap: A numerical remainder is not permission or a recommendation.

2. Spreads require both legs

Learning goal: Compute a bull call debit spread with signed cash flows.

Practice focus: editorial, not a measured error-frequency claim. This lesson uses original examples.

Options positions and spreads are within Series 7 product coverage [F 4]. A toy bull call debit spread buys a lower-strike call and sells a higher-strike call with the same expiration and 100-share multiplier supplied for both. The collected premium reduces the initial debit. At expiration the short call offsets part of the long-call upside, capping the net gain.

Assume premiums as given, ignore fees and taxes, and model intrinsic values at expiration. This does not cover early assignment, margin handling or live option pricing. Compute the two legs separately, subtract the net debit, then scale once. It is the combined position, not the long call alone, that determines the cap.

Worked example

Buy strike-50 call for $7/share, sell strike-60 call for $2/share; same expiration, 100 shares each. Find debit, breakeven, max loss and gain.

1. Net debit=(7-2)×100=$500.
2. Width=60-50=$10/share.
3. Breakeven=50+5=$55; max loss is debit $500.
4. Max gain=(10-5)×100=$500. At stock 40, 55, 70, profits are -500, 0, +500.

Mental model: Track both legs and signed premiums.

Common trap: The spread is not the standalone long call.

3. Evaluate a spread at a new stock price

Learning goal: Use piecewise intrinsic values rather than a memorized label.

Practice focus: editorial, not a measured error-frequency claim. This lesson uses original examples.

A spread formula must match the specific position and stock-price region. For a lower-strike long call and higher-strike short call, below both strikes intrinsic values are zero; between strikes only the long call is active; above both, their difference is the strike width. This is original arithmetic practice within options coverage [F 4].

Write max(S-K,0) for each call at expiration. Long profit includes positive intrinsic value; short profit includes negative intrinsic value. Use the initially paid net debit only once. All examples supply identical expiration and quantity so no calendar-spread or ratio-spread assumption is hidden.

Worked example

Toy spread: long strike 40 at $6, short strike 50 at $2, multiplier 100 each. Profit at S=$46?

1. Net debit=6-2=$4/share.
2. Long intrinsic=max(46-40,0)=$6/share.
3. Short intrinsic=max(46-50,0)=0.
4. Profit=(6-0-4)×100=$200.

Mental model: A payoff region determines which legs are active.

Common trap: Positive long-call intrinsic value need not mean profitable spread.

4. Covered call: premium offsets, upside is capped

Learning goal: Calculate the combined stock and short-call result.

Practice focus: editorial, not a measured error-frequency claim. This lesson uses original examples.

Covered-call questions require the stock leg as well as the written call [F 4]. Our toy investor buys 100 shares and sells one call covering those same 100 shares. The premium provides a limited offset to stock loss. Above strike, the short call's intrinsic obligation offsets further stock gains in the expiration model.

Ignore dividends, fees, taxes, early exercise and financing. "Covered" refers to the stock position supporting the option obligation; it does not mean no downside risk. Compute the stock change and short-option result explicitly so the option receipt is not mistaken for the whole position's profit.

Worked example

Buy 100 shares at $40 and write strike-45 call for $2/share. Stock $50 at expiration. Combined profit?

1. Stock change=(50-40)×100=$1,000.
2. Short-call intrinsic obligation=(50-45)×100=$500.
3. Premium received=2×100=$200.
4. Combined=1,000-500+200=$700; equivalently strike minus basis plus premium, scaled.

Mental model: Coverage does not eliminate downside.

Common trap: Do not add full stock upside to premium above the strike.

5. Yield names encode different cash flows

Learning goal: Distinguish current yield, maturity and call questions.

Practice focus: editorial, not a measured error-frequency claim. This lesson uses original examples.

Bond pricing and yield distinctions are in Series 7 product coverage [F 4]. Current yield divides annual coupon by market price. Maturity and call yields depend on the timing and amount of redemption as well as coupons. A stated current yield cannot by itself decide the total return if a bond is bought above or below redemption value.

Use the question's specified payoff schedule before comparing yields. In a toy one-year bond, buying for $950 and receiving $1,050 next year gives a one-period return of (1,050-950)/950. That differs from a $50 coupon/950 current-yield ratio because principal gain contributes. This does not supply a general YTM solver for multi-year bonds.

Worked example

Toy one-year bond costs $950, pays a $50 coupon and redeems for $1,000 next year. Find current yield and one-year total return.

1. Current yield=50/950=1/19≈5.2632%.
2. Total payoff=50+1,000=$1,050.
3. Gain=1,050-950=$100.
4. One-year return=100/950=2/19≈10.5263%; it includes principal gain.

Mental model: Match yield to the cash-flow question.

Common trap: Do not call every coupon/price ratio YTM.

6. Tax-equivalent yield is a conditional equation

Learning goal: Solve for the taxable yield under stated assumptions.

Practice focus: editorial, not a measured error-frequency claim. This lesson uses original examples.

Municipal structures and tax-related product knowledge are in the Series 7 outline [F 4]. This lesson assumes a specified yield is wholly exempt from the investor's stated tax rate, with no state-tax, AMT or other effects. Those are toy assumptions, not a claim that every municipal instrument or investor has that treatment.

If taxable yield y loses fraction t to tax, after-tax yield is y(1-t). Set that equal to the exempt yield and solve y=exempt/(1-t). This equalizes only the stated tax-adjusted yield, not credit quality, duration or liquidity. The arithmetic alone is not a recommendation between unlike bonds.

Worked example

Toy exempt yield 3.6%, tax rate 25%, all other tax effects ignored. Taxable equivalent?

1. Retention rate=1-0.25=0.75.
2. Set y×0.75=3.6%.
3. y=3.6%/0.75=4.8%.
4. Check 4.8%×0.75=3.6%; do not claim the two bonds are otherwise equivalent.

Mental model: Tax-equivalent yield solves a conditional equation.

Common trap: Do not assume actual tax eligibility from the municipal label.

7. Long margin equity is value minus debit

Learning goal: Keep account equity distinct from market value.

Practice focus: editorial, not a measured error-frequency claim. This lesson uses original examples.

The Series 7 outline includes margin and transaction processing [F 4]. In a simplified long margin account, equity is securities market value minus the debit owed. If the debit is fixed and market value falls, equity dollars and the equity fraction both fall. A market-value total is not the customer's net equity.

We intentionally supply any maintenance percentage as a hypothetical rule for an arithmetic exercise, not a current regulatory minimum. Actual account requirements, interest and product-specific rules need current source checks. Solve the toy threshold from (value-debit)/value = stated fraction rather than assuming a memorized rate.

Worked example

Toy long account: value $20,000, debit $8,000. Equity and equity percentage?

1. Equity=20,000-8,000=$12,000.
2. Equity fraction=12,000/20,000=0.60=60%.
3. If value falls to 16,000 with debit fixed, equity becomes 8,000.
4. The fraction then is 50%; these are not initial/maintenance rule claims.

Mental model: Long equity = market value - debit.

Common trap: Do not substitute a market-value number for equity.

8. Short margin has a different balance sign

Learning goal: Compute equity from credit minus current short value.

Practice focus: editorial, not a measured error-frequency claim. This lesson uses original examples.

In a simplified short margin account, an explicitly supplied credit balance is compared with the current value of securities owed. Equity=credit balance-current short market value. If the shorted security rises, the liability grows and equity falls, assuming the credit balance stays fixed. This is margin arithmetic within the Series 7 outline [F 4].

Our credit balance is given rather than inferred from an unstated initial-margin rule. Ignore interest, dividends owed, borrowing fees and additional transactions. If a threshold rate is supplied, it is a toy assumption. The educational calculation is not a statement of current maintenance requirements or permission to short.

Worked example

Toy short account credit $18,000, current short market value $12,000. Equity? Then short value rises to $15,000.

1. Initial equity=18,000-12,000=$6,000.
2. New liability=$15,000 while credit stays $18,000.
3. New equity=18,000-15,000=$3,000.
4. The price rise reduced equity by $3,000.

Mental model: Short equity = credit - short market value.

Common trap: Do not borrow a long-account formula with the wrong sign.

9. Costs and net proceeds need a complete scope

Learning goal: Separate charges from product features and sales claims.

Practice focus: editorial, not a measured error-frequency claim. This lesson uses original examples.

Funds, variable products, costs, risks and disclosure obligations are in the Series 7 outline [F 4]. This lesson isolates the arithmetic of an explicitly specified charge. A cost comparison must say which charges are included and over what period. A lower one-time charge alone does not prove lower lifetime cost or a better customer outcome.

Actual fee schedules may use different bases, timing or contingent terms. Do not apply the toy formula to a real product without checking its documents. A projected return is not a guarantee, and a fee label does not establish that every other cost is zero. Here zero other costs is an explicit exercise assumption only.

Worked example

Toy purchase $10,000 with a 2% charge on purchase amount and no other costs. Net invested?

1. Charge=10,000×0.02=$200.
2. Net invested=10,000-200=$9,800.
3. The charge base is explicitly the gross purchase.
4. This does not compare recurring costs or recommend a product.

Mental model: Name the cost base, period and included charges.

Common trap: One fee comparison is not a full recommendation.

10. Records: reconcile instructions with confirmed amounts

Learning goal: Check authority, quantity and cash flow without assuming a settlement cycle.

Practice focus: editorial, not a measured error-frequency claim. This lesson uses original examples.

Account authority, records and transaction confirmations are in Series 7 functions 2-4 [F 4]. In a scenario, distinguish a customer's instruction from verified authorization and from confirmed execution facts. Do not invent missing account permission or infer a fill from a quoted price. Exact settlement cycles and rule deadlines are deliberately outside this module unless separately checked.

The current exam has 125 scored items plus five unidentified pretest items, 225 minutes, and scaled passing score 72; sponsorship and the SIE corequisite apply [F 3, F 4]. The job functions are unevenly weighted, with 91 scored questions in function 3, not equal quarters. These facts frame preparation, but final transfer here is a fresh reconciliation problem, not exam trivia.

Worked example

Toy confirmed purchase: 80 shares filled at $25.50, stated transaction fee $4. Requested quantity had been 100. What cash debit is supported?

1. Use confirmed 80 shares, not requested 100.
2. Securities cost=80×25.50=$2,040.
3. Add the supplied purchase fee $4.
4. Cash debit=$2,044; the remaining 20 shares are not assumed filled.

Mental model: Reconcile verified authority and execution facts with the cash direction.

Common trap: A quote or request is not a confirmed fill.

11. A straddle adds two premiums

Learning goal: Calculate combined option payoff and subtract the complete cost.

A long straddle combines a call and a put with the same strike in this simplified expiration model. It benefits from sufficiently large price movement in either direction, but the buyer pays both premiums. The payoff is not the profit. FINRA includes options characteristics and strategies in the Series 7 outline; the numerical model here excludes fees and contract multipliers unless stated.

Original per-share example: buy a call and put at strike fifty, paying three and two. Total premium is five. At expiration with stock at sixty, call payoff is ten and put payoff zero, so combined profit is five. At stock forty, put payoff ten and call zero, again profit five. At fifty, both payoffs are zero and loss is the five-unit premium.

The break-even prices are strike minus total premium and strike plus total premium, forty-five and fifty-five in this case. A move inside that interval can still produce a positive payoff but a negative profit. This is why a directionally correct prediction may fail to earn a profit. The model also assumes expiration exercise values and does not describe pre-expiration option valuation.

Practice set: strike forty, call premium four, put premium three. At price fifty, payoff ten minus cost seven gives profit three. At price forty-two, payoff two gives loss five. These are invented values, not quotes or trading recommendations. State per-share versus per-contract units before applying any multiplier. Keeping both premiums visible is the main reasoning step.

Source alignment: [F 4]. All numerical data and practice questions here are original teaching examples, not official exam questions or observed results.

Worked example

Strike 50,call premium 3,put premium 2,expiration price 60. Find per-share profit.

1. Add both premiums:5.
2. Call payoff 10,put 0.
3. Combined payoff 10.
4. Profit 10-5=5.

Mental model: Calculate combined option payoff and subtract the complete cost.

Common trap: Subtract only one premium from a combined strategy.

12. Protective puts create a modeled floor with a cost

Learning goal: Combine stock and put payoffs before describing the downside.

A protective put pairs a stock position with a put that can offset declines below its strike in a simplified expiration model. The put costs money, and the floor depends on strike, purchase price and premium. Saying downside is protected does not mean the investment cannot lose. FINRA options content provides the scope; these values are original teaching assumptions.

Buy stock at fifty and a put at strike forty-five for two per share. At expiration with stock thirty, the stock loses twenty and the put pays fifteen. Net profit is minus seven after the premium. At stock sixty, the stock gains ten while the put expires with zero intrinsic payoff; net profit is eight. The put changes the downside, but the premium reduces results in every modeled price outcome.

The minimum modeled profit is strike minus stock purchase price minus premium, or forty-five minus fifty minus two equals minus seven. This expression assumes the positions are held through the common modeled expiration and ignores fees, dividends and financing. A floor for that horizon is not a statement about every earlier mark-to-market price.

Practice set: stock purchased at forty, put strike thirty-eight, premium one. At expiration stock twenty-five, put pays thirteen and stock loses fifteen, so net loss three. At stock fifty, net profit nine. Explain the sign and include both components. The exercise does not determine suitability, guarantee a market fill or recommend purchasing options.

Source alignment: [F 4]. All numerical data and practice questions here are original teaching examples, not official exam questions or observed results.

Worked example

Stock 50,put strike 45,premium 2,expiration stock 30. Find combined per-share profit.

1. Stock change 30-50=-20.
2. Put payoff 45-30=15.
3. Combine=-5 before premium.
4. Subtract premium 2:profit=-7.

Mental model: Combine stock and put payoffs before describing the downside.

Common trap: Call a downside floor a zero-loss guarantee.

13. Conversion compares stock value with the bond price

Learning goal: Use the conversion ratio without confusing it with current yield.

A convertible bond includes a conversion feature described in its terms. In a simplified comparison, conversion value equals the number of shares obtained times their market price. That is different from coupon income, current yield and the bond market price. FINRA includes convertible features in debt-products scope. The exercise grants immediate conversion without extra costs; real terms may impose conditions.

Original bond converts into twenty shares. If stock price is forty, conversion value is eight hundred. A quoted bond price of one thousand is higher than that conversion value. This arithmetic alone does not establish whether the bond is attractive: coupons, credit risk, optionality, timing and terms matter. It simply compares two specified values.

If the stock rises to sixty, conversion value becomes twelve hundred under the same ratio. The ratio remains twenty unless the terms say otherwise. A bond premium to conversion value is not a coupon rate. Keep the definitions in separate rows and do not infer a guaranteed arbitrage from a static simplified comparison.

Practice set: a bond converts into twenty-five shares and stock trades at thirty-two. Conversion value is eight hundred. If the bond price is one thousand, the stock price that makes conversion value equal that price is forty. This parity price comes from 1000/25, not the coupon. Label the given conversion ratio, stock price and bond price before calculating.

Source alignment: [F 4]. All numerical data and practice questions here are original teaching examples, not official exam questions or observed results.

Worked example

Conversion ratio 20 shares,stock 40. Find conversion value.

1. Use shares obtained per bond.
2. Multiply 20 by 40.
3. Conversion value 800.
4. Coupon does not enter this comparison.

Mental model: Use the conversion ratio without confusing it with current yield.

Common trap: Use coupon rate instead of conversion terms.

14. A sales charge denominator can be the offering price

Learning goal: Follow the supplied charge convention rather than assume it is a markup on NAV.

A sales-charge problem must state its denominator. A charge expressed as a fraction of offering price is not the same as adding that percentage to net asset value. In a simplified mutual-fund model, offering price equals net asset value divided by one minus the charge rate when the charge is defined as a percentage of offering price. FINRA includes offering price and sales-charge calculations in the Series 7 outline.

Original example: net asset value is nineteen and the charge is five percent of offering price. If offering price is P, the amount left after charge is 0.95 P=19. Thus P=20 and the charge is one. Adding five percent of nineteen would give 19.95, which fails the stated denominator convention. The difference is small but the reasoning matters.

The problem is mathematical, not a claim that every product uses a five-percent charge. Real terms may include breakpoints, different share classes, discounts or no sales charge. Do not infer an actual fee from this example. Read the question convention and keep the charge in both dollar and percentage form as a cross-check.

Practice set: NAV is forty-five and the stipulated charge is ten percent of offering price. Offering price is fifty and charge five. Next, offering price fifty with charge four percent leaves forty-eight as NAV in this simple model. The reverse calculation multiplies by 0.96, while the forward calculation divides by it. State which direction the question asks before using the formula.

Source alignment: [F 4]. All numerical data and practice questions here are original teaching examples, not official exam questions or observed results.

Worked example

NAV 19,charge 5% of offering price. Find offering price.

1. Let offering price=P.
2. After charge 0.95 P=19.
3. Divide 19 by 0.95.
4. P=20.

Mental model: Follow the supplied charge convention rather than assume it is a markup on NAV.

Common trap: Apply a charge percentage to the wrong base.

15. Dollar-cost averaging totals shares, not prices

Learning goal: Calculate average cost from total dollars and total shares in an original schedule.

Equal-dollar purchases buy more units at a lower price and fewer at a higher price. Average cost per share is total spending divided by total shares acquired, not the simple mean of the quoted prices. FINRA includes dollar-cost averaging in investment-company sales-practice scope. This arithmetic does not guarantee profits or protect against a declining investment.

Original schedule: invest one hundred at price ten to buy ten shares, then one hundred at price five to buy twenty. Total spending is two hundred and total shares thirty, so average cost per share is about 6.67. The simple price average 7.50 gives equal weight to periods rather than weighting by acquired shares. It describes a different statistic.

If the final price is four, thirty shares are worth 120 and the position has lost 80 before fees, despite the lower average cost than the simple mean. The method does not make every end price profitable. A plan also requires continued funding; no calculation establishes suitability for a particular person.

Practice set: spend 120 at price twelve, then 120 at price six. Acquire ten plus twenty shares for 240 total, average cost eight. At final price ten, value is 300 and modeled profit 60 before fees. At final price five, value 150 and modeled loss 90. Track each purchase and the final valuation separately. Every amount is invented for the exercise, not a historical backtest.

Source alignment: [F 4]. All numerical data and practice questions here are original teaching examples, not official exam questions or observed results.

Worked example

Spend 100 at 10 and 100 at 5. Find total shares.

1. First purchase 100/10=10.
2. Second 100/5=20.
3. Total 30 shares.
4. Average cost 200/30≈6.67.

Mental model: Calculate average cost from total dollars and total shares in an original schedule.

Common trap: Average price observations instead of acquired shares.

16. Mixed product practice names every cost

Learning goal: Combine option and fund calculations without dropping premiums or changing bases.

This original set links a straddle, a protective put and a stated sales charge. Each calculation has its own cost definition. A payoff ignores the option premium; a combined position includes both stock and option components; an offering-price percentage has a different base from a NAV markup. State the requested quantity before doing arithmetic.

First, a straddle has strike fifty and total premium five. At expiration stock price sixty, calculate profit per share. Second, stock was bought at fifty with a put strike forty-five and premium two; stock ends at thirty. Third, NAV nineteen is subject to a charge five percent of offering price. Try the three problems without viewing the earlier solutions.

The answers are five, minus seven and twenty. The straddle payoff ten is reduced by premium five. The protective put combines stock loss twenty, put payoff fifteen and premium two. The fund problem solves 0.95 P=19. These are simplified expiration and pricing models, not executable quotes or product recommendations.

For follow-up, change the straddle strike to forty and total premium seven with stock fifty; profit becomes three. Change the protected stock to purchase forty, put strike thirty-eight and premium one with stock twenty-five; profit is minus three. Change NAV to forty-five and charge to ten percent of offering price; price becomes fifty. An answer key is useful only if you can explain the cost or denominator in each model. FINRA official materials govern full exam scope and current rules.

Source alignment: [F 4]. All numerical data and practice questions here are original teaching examples, not official exam questions or observed results.

Worked example

NAV 19,charge 5% of offering price. Find price.

1. State charge base as offering price.
2. 0.95 P=19.
3. P=20.
4. Charge 1 is 5% of 20.

Mental model: Combine option and fund calculations without dropping premiums or changing bases.

Common trap: Omit one component when combining positions.