- Which of the following statements regarding portfolio rebalancing is true?
Answer: In a sustained one-directional market, rebalancing back to the target allocation generally trails a buy-and-hold strategy, while in a volatile, range-bound market it generally outperforms by selling positions that have risen and buying positions that have fallen.
Portfolio rebalancing: returning the portfolio to its target allocation means selling asset classes that have appreciated and buying those that have declined. In a sustained trend, that discipline trims the winning asset and adds to the losing one, so it generally trails buy-and-hold; in a range-bound market, the same discipline systematically buys low and sells high, so it generally outperforms. The correct statement captures both results. The statement that rebalancing keeps the risk level at the intended level at all times overstates the effect: the allocation drifts between rebalancing dates, and the risk of the underlying asset classes themselves changes over time. The statement that the investor sells declined securities and buys risen ones reverses the discipline, and rebalancing restores market-value percentages, not cost bases. The statement calling calendar rebalancing market timing is wrong because the schedule is fixed in advance and requires no forecast of which asset class will lead.
- Which of the following correctly states the maximum loss and the breakeven at expiration for a protective put with a $75 strike price and a $3 premium on stock purchased at $80 per share?
Answer: The position's maximum loss is $8 per share, and its breakeven at expiration is $83 per share.
Protective put: the investor owns the stock and buys a put, so the maximum loss per share is the purchase price minus the strike price plus the premium — $80 - $75 + $3 = $8 — and the breakeven at expiration is the purchase price plus the premium, $83. The option with an $8 maximum loss and an $83 breakeven is correct. The option with a $3 maximum loss and an $83 breakeven states the premium alone as the maximum loss; that is the maximum loss of a long put held by itself, and it ignores the $5-per-share gap between the $80 cost and the $75 strike that the put does not cover. The option with an $8 maximum loss and a $78 breakeven misstates the breakeven as the strike price plus the premium, which is a long call breakeven, instead of the stock's actual cost plus the premium. The option with a $3 maximum loss and a $72 breakeven gives both the maximum loss and the breakeven of a long put held by itself — strike minus premium — and therefore treats the position as if the stock were not owned.
An investor expects Verity stock, currently $50, to remain nearly unchanged over the next month. The investor sells one Verity 50 call for $3.00 and one Verity 50 put for $2.00, both expiring in one month. Each contract covers 100 shares. At expiration, Verity is $58.
What is the investor's gain or loss on the short straddle? Answer: $300 loss, because the short call is $8 in the money and the premiums total $5 per share
Short straddle payoff: the premiums collected are $3 + $2 = $5 per share. At $58, the short call is $8 in the money, so its intrinsic liability is $8 per share; the short put expires worthless. Net result is $5 − $8 = −$3 per share, or −$300 per contract. The $500 gain ignores the $8 call liability; the $800 loss ignores the $5 premium collected; the $300 gain reverses the sign of the correct $3-per-share net loss.
With a court ruling pending, an investor expects a very large price move in a stock but is uncertain of the direction. The stock is $50. The investor buys a call option and a put option, each with a strike price of $50, paying premiums of $3.20 and $2.80 per share, respectively. Both options expire in one month.
Which statement correctly describes the profit pattern at expiration? Answer: The strategy is profitable only if the stock closes below $44 or above $56.
Long straddle analysis (per-share terms): total premium paid is $3.20 + $2.80 = $6.00 per share. At $50, both options expire worthless and the loss is $6.00 per share. The lower break-even is $50 − $6 = $44 and the upper break-even is $50 + $6 = $56, so profits occur only outside that range. The $47/$53 range would be the break-evens for a $3.00 total premium, and the between-$44-and-$56 description reverses the profit and loss regions. The maximum loss occurs at $50, not below $44 or above $56.
An investor owns 100 shares of Halden stock purchased at $80 per share. The stock is now $95. The investor buys one Halden 90 put for $2.50 and sells one Halden 105 call for $2.50, both expiring in six months. At expiration, Halden is $108 and the call is assigned.
What is the investor's realized gain per share on the combined position? Answer: $25, because the shares are sold at $105 and the premiums net to zero
Collar payoff analysis: the net option premium is zero because the $2.50 put premium paid is offset by the $2.50 call premium received. If the call is assigned, the shares are sold at $105, not at the $108 market price, so the gain per share is $105 − $80 = $25. The $28 figure values the assigned shares at the market price; the $22.50 figure ignores the call premium received; the $27.50 figure ignores the put premium paid.
- Which of the following correctly states the maximum gain and the breakeven at expiration for a covered call with a $55 strike price and a $4 premium on stock purchased at $50 per share?
Answer: The position's maximum gain is $9 per share, and its breakeven at expiration is $46 per share.
Covered call: the investor owns the stock and writes a call, so the maximum gain per share is the premium received plus the stock's appreciation up to the strike price — $4 + ($55 - $50) = $9 — and the breakeven at expiration is the purchase price minus the premium, $50 - $4 = $46. The option with a $9 maximum gain and a $46 breakeven is correct. The option with a $9 maximum gain and a $50 breakeven computes the gain correctly but ignores the premium in the breakeven, leaving it at the purchase price. The option with a $5 maximum gain and a $54 breakeven ignores the premium in the gain and uses the purchase price plus the premium, which is the protective put's breakeven. The option with a $5 maximum gain and a $51 breakeven also ignores the premium in the gain and uses the strike price minus the premium, which is a long put's breakeven.
An adviser manages a $2,400,000 portfolio of large-cap stocks with a beta of 1.20. The S&P 500 index is 4,800, and standard S&P 500 index options have a $100 multiplier. The adviser wants to hedge a projected market decline over the next three months by buying S&P 500 put options. For this calculation, assume the puts have an absolute delta of 1.00.
Using the standard beta-hedging formula, how many put contracts should the adviser buy? Answer: 6 contracts, applying the portfolio beta to the value being hedged
Index put hedge formula: number of contracts = (portfolio value × beta) ÷ (index value × multiplier × absolute delta) = ($2,400,000 × 1.20) ÷ (4,800 × $100 × 1.00) = 6. The 5-contract figure ignores beta and would under-hedge a portfolio with beta above 1. The 60- and 600-contract figures use incorrect contract multipliers.
- Which of the following statements regarding dollar-cost averaging is true?
Answer: Because the same dollar amount is invested each period, the strategy buys more shares at low prices than at high prices, so its average cost per share is below the average of the purchase-date market prices whenever those prices differ.
Dollar-cost averaging: investing a fixed dollar amount at regular intervals acquires more shares when the price is low and fewer when the price is high, so the average cost per share is the harmonic mean of the purchase prices, which is below the arithmetic average of those prices whenever they are not identical. The statement describing the strategy as buying fewer shares at low prices and more at high prices reverses the mechanism; that pattern would raise, not lower, the average cost. The statement promising a profit whenever the ending price exceeds the starting price is an over-guarantee: if equal dollar amounts are invested at prices of $10, $190, and $20, the average cost is about $19.32, so an ending price of $15 exceeds the starting price of $10 but still produces a loss. The statement describing increasing amounts after declines describes value averaging, not dollar-cost averaging, and dollar-cost averaging requires no price forecast.
An investor owns 300 shares of Mercer stock purchased at $48 per share. The stock is now $52. The investor sells three Mercer 55 call options at $2.50 per share, all expiring in three months. At expiration, Mercer is $58 and the calls are exercised.
What is the investor's total gain on the combined stock-and-option position at expiration? Answer: $2,850, equal to the stock gain to $55 plus the call premium
Covered call payoff analysis: the investor receives 300 × $2.50 = $750 in premium. At assignment, the shares are sold at the $55 strike, not at the $58 market price, so the stock gain is ($55 − $48) × 300 = $2,100. Total gain is $2,850. The $750 figure counts only the premium; the $2,100 figure omits the premium; the $3,750 figure incorrectly values assigned shares at $58 instead of $55.
An investor has $35,000 in a money market account and wants to acquire 500 shares of Vantage stock if it falls to $65 or below. The stock is now $72. Three-month Vantage 65 puts are quoted at $3.20. The investor is willing to accept assignment and would otherwise leave the cash in a low-yielding account.
Which options strategy best meets the investor's objective? Answer: Sell five cash-secured 65 puts; if assigned, net cost is $61.80 per share, and if not assigned, keep the $1,600 premium.
A cash-secured put writer receives $3.20 × 500 = $1,600 in premium. If assigned, the investor buys at $65 but keeps the premium, making the effective cost $61.80 per share. This matches the goal of buying only after a decline and earning premium otherwise. A long put gives the right to sell, not buy; buying shares now and writing covered calls buys at $72 rather than waiting for $65; long calls do not create the desired purchase obligation if the stock declines.
An investor establishes a bull call spread on Radex stock, now trading at $58. The investor buys one Radex 55 call for $6.00 and sells one Radex 65 call for $2.50. Each contract covers 100 shares. Both options expire in four months. At expiration, Radex is $71.
What is the investor's gain or loss on the spread? Answer: $650 gain, equal to the maximum gain on the spread
Bull call spread payoff: net debit = $6.00 - $2.50 = $3.50 per share. At expiration, Radex is above both strike prices, so the spread is worth its maximum value: the long 55 call is worth $16 and the short 65 call is worth $6, for a spread value of $10. Profit per share = $10 - $3.50 = $6.50, or $650 per contract. The net debit is the maximum loss, not the result at this expiration price; the $1,000 figure ignores the net debit; the $250 figure ignores the long call's gain.
- Which of the following statements regarding a short straddle is true?
Answer: The maximum gain is the combined premium received, and the position is profitable at expiration only if the stock price is between the two breakeven points.
Options payoff concept: a short straddle is created by writing a call and a put with the same strike price and expiration. The maximum gain is the combined premium received, realized only if the stock settles exactly at the shared strike at expiration; the position is profitable at expiration only for stock prices between the two breakeven points (strike price plus or minus the combined premium). The statement that the maximum loss is the combined premium received reverses the payoff: the short straddle's gain is capped at the premium, while its loss is not. The statement that profits occur beyond either breakeven describes a long straddle's profit zone, not a short straddle's, and a long straddle's gain is not capped at the combined premium. The statement that the maximum loss is only the premium on whichever option expires in the money also understates the risk: the loss depends on how far the stock moves beyond the breakeven, is unlimited on the upside, and on the downside is limited only by the stock falling to zero.
An investor buys 200 shares of a stock at $74 per share and also buys two put options on that stock with a $70 strike price, each covering 100 shares, at $2.40 per share, expiring in six months. At expiration, the stock is $63 and the investor exercises the puts, selling the shares.
What is the investor's net loss per share on the combined position? Answer: $6.40, the loss from $74 to the $70 strike plus the put premium
Protective put analysis: the put fixes the sale price at $70, not at the $63 market price. The protection costs $2.40 per share, so the net loss per share is ($74 - $70) + $2.40 = $6.40. The $4.00 figure ignores the premium; the $11.00 figure ignores the option and uses the market price; the $13.40 figure assumes both the full decline to $63 and the premium are borne even though the put is exercised.
An investor is bearish on Marlin stock, now $64. The investor buys one Marlin 65 put for $5.20 and sells one Marlin 55 put for $2.20. Each contract covers 100 shares. Both options expire in three months. At expiration, Marlin is $50.
What is the investor's gain or loss on the bear put spread? Answer: $700 gain, equal to the $10 spread value less the $3 net debit
Bear put spread payoff: net debit = $5.20 − $2.20 = $3.00 per share. At $50, the long 65 put pays $15 and the short 55 put costs $5, so the net spread payoff is $10 per share; profit is $10 − $3 = $7 per share, or $700 per contract. The net debit is the maximum loss, not a loss when the spread is at maximum value; the strike-width figure ignores the debit; the short-premium figure ignores the long put's payoff.
- All of the following statements regarding a collar on stock that the investor already owns are true EXCEPT:
Answer: The potential gain is unlimited because the call's strike price is above the put's strike price, so the stock's upside remains fully available.
Collar: the position combines ownership of the stock with a long put and a short call at a higher strike. The statements on the collar's structure, its zero-cost case and its maximum loss are true: the long put combined with the higher-strike written call is the collar's structure; equal put and call premiums produce a net cost of zero before commissions; and the maximum loss is the stock's cost minus the put's strike, increased by any net debit or reduced by any net credit. The false statement is the one claiming unlimited upside: the written call obligates the investor to sell the stock at the call strike if the stock rises above it, so the gain is capped at that strike. The collar gives up upside above the call strike in exchange for the downside floor at the put strike.
