Practice: Options
Twenty-one scored problems on calls and puts, premiums and break-evens, intrinsic and time value, exercise and assignment, the Greeks, implied volatility, covered calls and protective puts, and the arithmetic of option risk.
What you'll do
This set works through the Options module. You'll work out results at expiration for buyers and sellers, split premiums into intrinsic value and time value, decide between exercising and selling, use delta, theta, and vega to estimate price changes, turn an implied volatility into an expected move, and price out a covered call, a protective put, and a collar. Each answer comes with the working, and your score appears as you go. Nothing is recorded outside this browser.
This draws on
Work through the problems in order and check each answer once you've committed to it. The score counts your first try. Every option here is a standard contract on 100 shares, and all the companies and prices are hypothetical.
Calls and puts
1. You buy one call with a strike of $60 for a premium of $2.50. At expiration the shares are at $66. What's your profit on the contract?
The call is worth $66 − $60 = $6 a share, and it cost $2.50. ($6 − $2.50) × 100 = $350. Review: Calls and Puts.
2. You buy a put with a strike of $40 for $1.80. What share price at expiration is your break-even?
A put buyer breaks even at the strike minus the premium: $40 − $1.80 = $38.20. Below that, each dollar the shares fall adds $100 to the contract's profit.
3. You sell one put with a strike of $30 and collect $1.20 a share. At expiration the shares are at $25 and you're assigned. What's your result? Enter a loss as a negative number.
You must buy 100 shares at $30 that are worth $25, a loss of $500, less the $120 premium you kept: −$380. You also now own the shares.
4. What's the most each position can lose?
- Buying a call
- Selling a call without owning the shares
- Buying a put
- Selling a put
Buyers can lose only what they paid. An uncovered call seller must deliver shares at the strike however high the price goes. A put seller's worst case is buying worthless shares at the strike, offset by the premium kept.
Premiums, moneyness, and time value
5. Shares trade at $50. Is each option in or out of the money?
- A call with a $45 strike
- A put with a $45 strike
- A call with a $55 strike
- A put with a $55 strike
A call is in the money when the share price is above its strike, and a put when the share price is below it. The same strike is in the money for one and out of the money for the other. Review: Intrinsic Value, Extrinsic Value, and Moneyness.
6. Shares trade at $47. A put with a $50 strike costs $4.10. How much of the premium is time value?
Intrinsic value is $50 − $47 = $3. Time value is the rest: $4.10 − $3.00 = $1.10.
7. Three calls on the same shares expire on the same date. Which has the most time value?
Time value is largest at the money. A deep in-the-money option is mostly intrinsic value, and a far out-of-the-money option, though entirely time value, has little of it because its chance of paying is slim.
8. Shares are at $50. A one-month $60 call costs $0.10 and a one-year $60 call costs $4.65. Why is the difference so large?
Neither call has intrinsic value. The one-year call is worth more because there's much more time for the shares to rise above $60. Time matters most for options that need a big move. Review: Strike, Expiration, and Premium.
Exercise and assignment
9. You hold one call with a $30 strike. The shares are at $37 and the call can be sold for $7.60. No dividend is due. How much more do you get by selling the call than by exercising and selling the shares?
Exercising yields the intrinsic value, $7 a share or $700. Selling the call yields $760, which includes $0.60 of time value. Selling is $60 better. Review: Exercise and Assignment.
10. You've sold a call that's deep in the money, with little time value left. The shares go ex-dividend tomorrow, with a dividend larger than that time value. What's likely?
Options aren't adjusted for ordinary dividends, so a call holder gets the dividend only by exercising before the ex-dividend date. When the dividend is worth more than the time value given up, exercising pays, and the writer's chance of assignment rises.
The Greeks and implied volatility
11. You hold three call contracts, each with a delta of 0.40. For small moves, how many shares does the position behave like?
3 contracts × 100 shares × 0.40 = 120 shares. Review: The Greeks.
12. A call costs $2.50 and has a delta of 0.45. The shares rise $2. Using delta alone, roughly what's the call's new price?
$2.50 + 0.45 × $2 = $3.40. Gamma would add a little more, since delta rises as the shares do.
13. An option has a theta of −0.05. Ten days pass and nothing else changes. How much has one contract lost? Enter a loss as a negative number.
−$0.05 a share a day × 10 days × 100 shares = −$50. In practice theta grows as expiration approaches, so the loss would speed up near the end.
14. An option has a vega of 0.12. Implied volatility falls 10 points after an earnings report, with the share price unchanged. Roughly how much does the premium change per share? Enter a fall as a negative number.
0.12 × −10 = −$1.20 a share, or $120 a contract, with no move in the shares at all. Review: Implied Volatility.
15. Shares trade at $80 and their options carry an implied volatility of 30%. What one-standard-deviation move does that imply over one month? Give the answer in dollars.
30% × √(1 ÷ 12) = 30% × 0.2887 = 8.66%, and 8.66% of $80 is $6.93. Volatility scales with the square root of time, not with time itself.
Strategies
16. You own 100 shares bought at $40 and sell a $45 call for $1.50. At expiration the shares are at $52. What's your total gain?
The shares are called away at $45, a gain of $500, plus the $150 premium: $650. Holding the shares alone would have gained $1,200. Review: Covered Calls and Protective Puts.
17. You own 100 shares bought at $40 and buy a $36 put for $1.20. What's the most you can lose before the put expires?
The shares can fall $4 to the strike before the put takes over, and the put cost $1.20: ($4 + $1.20) × 100 = $520, however far the shares fall.
18. With the same shares, you buy the $36 put for $1.20 and sell a $45 call for $1.50, forming a collar. What's the most you can gain?
The call caps the sale price at $45, a $500 gain on the shares, and the two premiums leave a net credit of $0.30, or $30. Most gain: $530. The most you can lose is $400 − $30 = $370.
19. Which simpler position has the same shape of result as a covered call?
A covered call gains up to the strike and then stops, and loses as the shares fall. A sold put has the same shape: the premium at best, and a growing loss below the strike. The two differ only by about the interest on the money tied up in the shares.
Risk
20. You put $3,000 into ten call contracts with a $50 strike at $3 a share. At expiration the shares are at $52. What's your return? Give one decimal place, and enter a loss as a negative number.
Each call is worth $2 a share, so the ten are worth $2,000, against $3,000 paid. That's −33.3%, though the shares rose. Break-even needed $53. Review: The Major Risks of Options.
21. A buyer puts equal amounts into a series of option trades. Three in four expire worthless. What average gain do the winners need, just to break even overall?
For every four trades, three lose 100% of their stake, so the one winner has to make three stakes of profit: a gain of 300% on average, before any trading costs.
In your own words
A friend says they've found a way to earn 16% a year: buy shares and sell calls on them every three months for about 4% each time. Explain what they're giving up and what risk they're keeping.
Compare with a model answer
The premiums are payment for every dollar of gain above the strike, so in any quarter when the shares rise strongly the friend hands over more than the premium was worth. They keep nearly all of the risk of a fall, cushioned only by the premium, so in a crash they lose almost as much as a plain shareholder. The 16% assumes the shares never fall and never get called away at a price they regret. It's the same shape as selling puts: many small gains and occasional large losses, and the record of a few calm years says little about it.