19 May 6pm study - options practices
Last updated
Last updated
Stanley Kumar Singh, CFA, is the risk manager at SKS Asset Management. He works with individual clients to manage their investment portfolios. One client, Sherman Hopewell, is worried about how short-term market fluctuations over the next three months might impact his equity position in Walnut Corporation. Although Hopewell is concerned about short-term downside price movements, he wants to remain invested in Walnut shares because he remains positive about its long-term performance. Hopewell has asked Singh to recommend an option strategy that will keep him invested in Walnut shares while protecting against a short-term price decline. Singh gathers the information in Exhibit 1 to explore various strategies to address Hopewell’s concerns.
Exhibit 1:
Walnut Corporation Current Stock Price: $67.79 Walnut Corporation European Options
Exercise Price
Market Call Price
Call Delta
Market Put Price
Put Delta
$55.00
$12.83
1.00
$0.24
–0.05
$65.00
$3.65
0.91
$1.34
–0.29
$67.50
$1.99
0.63
$2.26
–0.42
$70.00
$0.91
0.37
$3.70
–0.55
$80.00
$0.03
0.02
$12.95
–0.76
Q.
The option strategy Singh is most likely to recommend to Hopewell is a:
Solution
C is correct. A protective put accomplishes Hopewell’s goal of short-term price protection. A protective put provides downside protection while retaining the upside potential. Although Hopewell is concerned about the downside in the short term, he wants to remain invested in Walnut shares because he is positive on the stock in the long term.
Another client, Nigel French, is a trader who does not currently own shares of Walnut Corporation. French has told Singh that he believes that Walnut shares will experience a large move in price after the upcoming quarterly earnings release in two weeks. French also tells Singh, however, that he is unsure which direction the stock will move. French asks Singh to recommend an option strategy that would allow him to profit should the share price move in either direction.
Q.
The option strategy that Singh is most likely to recommend to French is a:
Solution
A is correct. The long straddle strategy is based on expectations of volatility in the underlying stock being higher than the market consensus. The straddle strategy consists of simultaneously buying a call option and a put option at the same strike price. Singh could recommend that French buy a straddle using near at-the-money options ($67.50 strike). This allows French to profit should the Walnut stock price experience a large move in either direction after the earnings release.
A third client, Wanda Tills, does not currently own Walnut shares and has asked Singh to explain the profit potential of three strategies using options in Walnut: a long straddle, a bull call spread, and a bear put spread. In addition, Tills asks Singh to explain the gamma of a call option. In response, Singh prepares a memo to be shared with Tills that provides a discussion of gamma and presents his analysis on three option strategies:
Strategy 1: A long straddle position at the $67.50 strike option
Strategy 2: A bull call spread using the $65 and $70 strike options
Strategy 3: A bear put spread using the $65 and $70 strike options
Q.
Based on Exhibit 1, Strategy 1 is profitable when the share price at expiration is closest to:
Solution
A is correct. The straddle strategy consists of simultaneously buying a call option and buying a put option at the same strike price. The market price for the $67.50 call option is $1.99, and the market price for the $67.50 put option is $2.26, for an initial net cost of $4.25 per share. Thus, this straddle position requires a move greater than $4.25 in either direction from the strike price of $67.50 to become profitable. So, the straddle becomes profitable at $67.50 – $4.26 = $63.24 or lower, or $67.50 + $4.26 = $71.76 or higher. At $63.00, the profit on the straddle is positive.
Q.
Based on Exhibit 1, the maximum profit, on a per share basis, from investing in Strategy 2, is closest to:
Solution
A is correct. The bull call strategy consists of buying the lower-strike option and selling the higher-strike option. The purchase of the $65 strike call option costs $3.65 per share, and selling the $70 strike call option generates an inflow of $0.91 per share, for an initial net cost of $2.74 per share. At expiration, the maximum profit occurs when the stock price is $70 or higher, which yields a $5.00 per share payoff ($70 – $65) on the long call position. After deduction of the $2.74 per share cost required to initiate the bull call spread, the profit is $2.26 ($5.00 – $2.74).
Solution
B is correct. The bear put spread consists of buying a put option with a high strike price ($70) and selling another put option with a lower strike price ($65). The market price for the $70 strike put option is $3.70, and the market price for the $65 strike put option is $1.34 per share. Thus, the initial net cost of the bear spread position is $3.70 – $1.34 = $2.36 per share. If Walnut shares are $66 at expiration, the $70 strike put option is in the money by $4.00, and the short position in the $65 strike put expires worthless. After deducting the cost of $2.36 to initiate the bear spread position, the net profit is $1.64 per contract.
Q.
Based on the data in Exhibit 1, Singh would advise Tills that the call option with the largest gamma would have a strike price closest to:
A.$ 55.00.
B.$ 67.50.
C.$ 80.00.
Solution
B is correct. The $67.50 call option is approximately at the money because the Walnut share price is currently $67.79. Gamma measures the sensitivity of an option’s delta to a change in the underlying. The largest gamma occurs when options are trading at the money or near expiration, when the deltas of such options move quickly toward 1.0 or 0.0. Under these conditions, the gammas tend to be largest and delta hedges are hardest to maintain.
Nuñes considers the following option strategies relating to IZD:
Strategy 1: Constructing a synthetic long put position in IZD
Strategy 2: Buying 100 shares of IZD and writing the April €95.00 strike call option on IZD
Strategy 3: Implementing a covered call position in IZD using the April €97.50 strike option
Q.
Strategy 1 would require Nuñes to buy:
Solution
C is correct. To construct a synthetic long put position, Nuñes would buy a call option on IZD. Of course, she would also need to sell (short) IZD shares to complete the synthetic long put position.
Exhibit 1:
Share Price and Option Premiums as of 1 February (share prices and option premiums in €)
Company
Share Price
Call Premium
Option Date/Strike
Put Premium
9.45
April/87.50
1.67
IZD
93.93
2.67
April/95.00
4.49
1.68
April/97.50
5.78
4.77
April/24.00
0.35
QWY
28.49
3.96
April/25.00
0.50
0.32
April/31.00
3.00
0.23
February/80.00
5.52
XDF
74.98
2.54
April/75.00
3.22
2.47
December/80.00
9.73
Q.
Based on Exhibit 1, Nuñes should expect Strategy 2 to be least profitable if the share price of IZD at option expiration is:
Solution
A is correct. Strategy 2 is a covered call, which is a combination of a long position in shares and a short call option. The breakeven point of Strategy 2 is €91.26, which representsthe price per share of €93.93 minus the call premium received of €2.67 per share (S0 – c0). So, at any share price less than €91.26 at option expiration, Strategy 2 incurs a loss. If the share price of IZD at option expiration is greater than €91.26, Strategy 2 generates a gain.
Q.
Based on Exhibit 1, the breakeven share price of Strategy 3 is closest to:
Solution
A is correct. Strategy 3 is a covered call strategy, which is a combination of a long position in shares and a short call option. The breakeven share price for a covered call is the share price minus the call premium received, or S0 – c0. The current share price of IZD is €93.93, and the IZD April €97.50 call premium is €1.68. Thus, the breakeven underlying share price for Strategy 3 is S0 – c0 = €93.93 – €1.68 = €92.25.
Nuñes next reviews the following option strategies relating to QWY:
Strategy 4: Implementing a protective put position in QWY using the April €25.00 strike option
Strategy 5: Buying 100 shares of QWY, buying the April €24.00 strike put option, and writing the April €31.00 strike call option
Strategy 6: Implementing a bear spread in QWY using the April €25.00 and April €31.00 strike options
Q.
Based on Exhibit 1, the maximum loss per share that would be incurred by implementing Strategy 4 is:
Solution
B is correct. Strategy 4 is a protective put position, which is a combination of a long position in shares and a long put option. By purchasing the €25.00 strike put option, Nuñes would be protected from losses at QWY share prices of €25.00 or lower. Thus, the maximum loss per share from Strategy 4 would be the loss of share value from €28.49 to €25.00 (or €3.49) plus the put premium paid for the put option of €0.50: S0 – X + p0 = €28.49 – €25.00 + €0.50 = €3.99.
Q.
Strategy 5 is best described as a:
A.collar.
B.straddle.
C.bear spread.
Solution
A is correct. Strategy 5 describes a collar, which is a combination of a long position in shares, a long put option with an exercise price below the current stock price, and a short call option with an exercise price above the current stock price.
Q.
Based on Exhibit 1, Strategy 5 offers:
A.unlimited upside.
B.a maximum profit of €2.48 per share.
C.protection against losses if QWY’s share price falls below €28.14.
Solution
B is correct. Strategy 5 describes a collar, which is a combination of a long position in shares, a long put option, and a short call option. Strategy 5 would require Nuñes to buy 100 QWY shares at the current market price of €28.49 per share. In addition, she would purchase a QWY April €24.00 strike put option contract for €0.35 per share and collect €0.32 per share from writing a QWY April €31.00 strike call option. The collar offers protection against losses on the shares below the put strike price of €24.00 per share, but it also limits upside to the call strike price of €31.00 per share. Thus, the maximum gain on the trade, which occurs at prices of €31.00 per share or higher, is calculated as (X2 – S0) – p0 + c0, or (€31.00 – €28.49) – €0.35 + €0.32 = €2.48 per share.
Q.
Based on Exhibit 1, the breakeven share price for Strategy 6 is closest to:
A.€22.50.
B.€28.50.
C.€33.50.
Solution
B is correct. Strategy 6 is a bear spread, which is a combination of a long put option and a short put option on the same underlying, where the long put has a higher strike price than the short put. In the case of Strategy 6, the April €31.00 put option would be purchased and the April €25.00 put option would be sold. The long put premium is €3.00 and the short put premium is €0.50, for a net cost of €2.50. The breakeven share price is €28.50, calculated as XH – (pH – pL) = €31.00 – (€3.00 – €0.50) = €28.50.
Finally, Nuñes considers two option strategies relating to XDF:
Strategy 7: Writing both the April €75.00 strike call option and the April €75.00 strike put option on XDF
Strategy 8: Writing the February €80.00 strike call option and buying the December €80.00 strike call option on XDF
Q.
Based on Exhibit 1, the maximum gain per share that could be earned if Strategy 7 is implemented is:
A.€5.74.
B.€5.76.
C.unlimited.
Solution
B is correct. Strategy 7 describes a short straddle, which is a combination of a short put option and a short call option, both with the same strike price. The maximum gain is €5.76 per share, which represents the sum of the two option premiums, or c0 + p0 = €2.54 + €3.22 = €5.76. The maximum gain per share is realized if both options expire worthless, which would happen if the share price of XDF at expiration is €75.00.
Q.
Based on Exhibit 1, the best explanation for Nuñes to implement Strategy 8 would be that, between the February and December expiration dates, she expects the share price of XDF to:
A.decrease.
B.remain unchanged.
C.increase.
Solution
C is correct. Nuñes would implement Strategy 8, which is a long calendar spread, if she expects the XDF share price to increase between the February and December expiration dates. This strategy provides a benefit from the February short call premium to partially offset the cost of the December long call option. Nuñes likely expects the XDF share price to remain relatively flat between the current price €74.98 and €80 until the February call option expires, after which time she expects the share price to increase above €80. If such expectations come to fruition, the February call would expire worthless and Nuñes would realize gains on the December call option.
Q.
Over the past few months, Nuñes and Pereira have followed news reports on a proposed merger between XDF and one of its competitors. A government antitrust committee is currently reviewing the potential merger.
Pereira expects the share price to move sharply upward or downward depending on whether the committee decides to approve or reject the merger next week.
Pereira asks Nuñes to recommend an option trade that might allow the firm to benefit from a significant move in the XDF share price regardless of the direction of the move.
The option trade that Nuñes should recommend relating to the government committee’s decision is a:
Solution
C is correct. Nuñes should recommend a long straddle, which is a combination of a long call option and a long put option, both with the same strike price. The committee’s announcement is expected to cause a significant move in XDF’s share price. A long straddle is appropriate because the share price is expected to move sharply up or down depending on the committee’s decision. If the merger is approved, the share price will likely increase, leading to a gain in the long call option. If the merger is rejected, then the share price will likely decrease, leading to a gain in the long put option.
Anneke Ngoc is an analyst who works for an international bank, where she advises high-net-worth clients on option strategies. Ngoc prepares for a meeting with a US-based client, Mani Ahlim.
Ngoc notes that Ahlim recently inherited an account containing a large Brazilian real (BRL) cash balance. Ahlim intends to use the inherited funds to purchase a vacation home in the United States with an expected purchase price of US$750,000 in six months. Ahlim is concerned that the Brazilian real will weaken against the US dollar over the next six months. Ngoc considers potential hedge strategies to reduce the risk of a possible adverse currency movement over this time period.
Q.
Which of the following positions would best mitigate Ahlim’s concern regarding the purchase of his vacation home in six months?
Solution
B is correct. Ahlim could mitigate the risk of the Brazilian real weakening against the US dollar over the next six months by (1) purchasing an at-the-money six-month BRL/USD call option (to buy US dollars), (2) purchasing an at-the-money six-month USD/BRL put option (to sell Brazilian reals), or (3) taking a long position in a six-month BRL/USD futures contract (to buy US dollars).
Purchasing an at-the-money six-month USD/BRL put option (to sell Brazilian reals) would mitigate the risk of a weakening Brazilian real. If the Brazilian real should weaken against the US dollar over the next six months, Ahlim could exercise the put option and sell his Brazilian reals at the contract’s strike rate (which would have been the prevailing market exchange rate at the time of purchase, since the option is at the money).
A is incorrect because purchasing (not selling) an at-the-money six-month BRL/USD call option (to buy US dollars) would mitigate the risk of the Brazilian real weakening against the US dollar over the next six months. The long call position would give Ahlim the right to buy US dollars (and sell Brazilian reals). A call on US dollars is similar to a put on Brazilian reals. So, a put to sell Brazilian reals at a given strike rate can be viewed as a call to buy US dollars.
C is incorrect because going long (not short) a six-month BRL/USD futures contract (to buy US dollars) would mitigate the risk of the Brazilian real weakening against the US dollar over the next six months. A long futures position would obligate Ahlim to buy US dollars (and sell Brazilian reals) at the futures contract rate.
Ahlim holds shares of Pselftarô Ltd. (PSÔL), which has a current share price of $37.41. Ahlim is bullish on PSÔL in the long term. He would like to add to his long position but is concerned about a moderate price decline after the quarterly earnings announcement next month, in April. Ngoc recommends a protective put position with a strike price of $35 using May options and a $40/$50 bull call spread using December options. Ngoc gathers selected PSÔL option prices for May and December, which are presented in Exhibit 1.
Exhibit 1:
Selected PSÔL Option Prices (all prices in US dollars)
Exercise Price
Expiration Month
Call Price
Put Price
35
May
3.00
1.81
40
December
6.50
10.25
50
December
4.25
20.50
Q.
Based on Exhibit 1, the maximum loss per share of Ngoc’s recommended PSÔL protective put position is:
Solution
C is correct. Ngoc recommends a protective put position with a strike price of $35 using May options. The maximum loss per share on the protective put is calculated as
Maximum loss per share of protective put = S0 − X + p0.
Maximum loss per share of protective put = $37.41 − $35.00 + $1.81 = $4.22.
In summary, with the protective put in place, Ahlim is protected against losses below $35.00. Thus, taking into account the put option purchase price of $1.81, Ahlim’s maximum loss occurs at the share price of $33.19, resulting in a maximum loss of $4.22 per share (= $37.41 – $33.19).
A is incorrect because $0.60 reflects incorrectly subtracting (rather than adding) the put premium in the calculation of the maximum loss of protective put (i.e., $37.41 − $35.00 − $1.81 = $0.60).
B is incorrect because $2.41 does not include the put premium in the calculation but only reflects the difference between the current share price ($37.41) and the put exercise price ($35.00).
Q.
Based on Exhibit 1, the breakeven price per share of Ngoc’s recommended PSÔL protective put position is:
Solution
C is correct. Ngoc recommends a protective put position with a strike price of $35 using May options. The breakeven price per share on the protective put is calculated as
Breakeven price per share of protective put = S0 + p0.
Breakeven price per share of protective put = $37.41 + $1.81 = $39.22.
In summary, Ahlim would need PSÔL’s share price to rise by the price of the put option ($1.81) from the current price of $37.41 to reach the breakeven share price—the price at which the gain from the increase in the value of the stock offsets the purchase price of the put option.
A is incorrect because $35.60 represents incorrectly subtracting (rather than adding) the put premium in the calculation of the protective put breakeven price: $37.41 − $1.81 = $35.60.
B is incorrect because $36.81 represents incorrectly adding the put premium to the strike price (not the current share price): $35.00 + $1.81 = $36.81.
Q.
Based on Exhibit 1, the maximum profit per share of Ngoc’s recommended PSÔL bull call spread is:
Solution
B is correct. Ngoc recommends a $40/$50 bull call spread using December options. To construct this spread, Ahlim would buy the $40 call, paying the $6.50 premium, and simultaneously sell the $50 call, receiving a premium of $4.25. The maximum gain or profit of a bull call spread occurs when the stock price reaches the high exercise price ($50) or higher at expiration. Thus, the maximum profit per share of a bull call spread is the spread difference between the strike prices less the net premium paid, calculated as
Maximum profit per share of bull call spread = (XH – XL) – (cL – cH).
Maximum profit per share of bull call spread = ($50 – $40) – ($6.50 – $4.25).
Maximum profit per share of bull call spread = $7.75.
A is incorrect because $2.25 represents only the net premium and does not include the spread difference.
C is incorrect because $12.25 represents the net premium being incorrectly added (rather than subtracted) from the spread difference.
Q.
Based on Exhibit 1, the breakeven price per share of Ngoc’s recommended PSÔL bull call spread is:
Solution
A is correct. Ngoc recommends a $40/$50 bull call spread using December options. To construct this spread, Ahlim would buy the $40 call, paying a $6.50 premium, and simultaneously sell the $50 call, receiving a $4.25 premium. The breakeven price per share of a bull call spread is calculated as
Breakeven price per share of bull call spread = XL + (cL – cH).
Breakeven price per share of bull call spread = $40 + ($6.50 – $4.25).
Breakeven price per share of bull call spread = $42.25.
In summary, in order to break even, the PSÔL stock price must rise above $40 by the amount of the net premium paid of $2.25 to enter into the bull call spread. At the price of $42.25, the lower $40 call option would have an exercise value of $2.25, exactly offsetting the $2.25 cost of entering the trade.
B is incorrect because $47.75 represents the net premium being incorrectly subtracted from the high exercise price (rather than being added to the low exercise price): $50 – ($6.50 – $4.25) = $47.75.
C is incorrect because $52.25 represents the net premium being added to the high exercise price (rather than the low exercise price): $50 + ($6.50 – $4.25) = $52.25.
Ahlim also expresses interest in trading options on India’s NIFTY 50 (National Stock Exchange Fifty) Index. Ngoc gathers selected one-month option prices and implied volatility data, which are presented in Exhibit 2. India’s NIFTY 50 Index is currently trading at a level of 11,610.
Exhibit 2:
Selected One-Month Option Prices and Implied Volatility Data: NIFTY 50 Index (all prices in Indian rupees)
Exercise Price
Market Call Price
Market Put Price
Implied Call Volatility
Implied Put Volatility
11,200
526.00
61.90
5.87
17.72
11,400
365.45
102.60
10.80
17.01
11,600
240.00
165.80
12.26
16.44
11,800
135.00
213.00
12.14
16.39
12,000
65.80
370.00
11.98
16.56
Q.
Based on Exhibit 2, the NIFTY 50 Index implied volatility data most likely indicate a:
Solution
B is correct.
When the implied volatility decreases for OTM (out-of-the-money) calls relative to ATM (at-the-money) calls - [11.98 <- 12.26] and
increases for OTM puts relative to ATM puts [17.72 -> 16.44]
a volatility skew exists.
Put volatility is higher, rising from 16.44 ATM to 17.72 OTM, likely because of the higher demand for puts to hedge positions in the index against downside risk.
Call volatility decreases from 12.26 for ATM calls to 11.98 for OTM calls since calls do not offer this valuable portfolio insurance.
A is incorrect because a risk reversal is a delta-hedged trading strategy seeking to profit from a change in the relative volatility of calls and puts.
C is incorrect because a volatility smile exists when both call and put volatilities, not just put volatilities, are higher OTM than ATM. (!! Important)
Ngoc reviews a research report that includes a one-month forecast of the NIFTY 50 Index. The report’s conclusions are presented in Exhibit 3.
Exhibit 3: Research Report Conclusions: NIFTY 50 Index
One-month forecast:
We have a neutral view on the direction of the index’s move over the next month.
The rate of the change in underlying prices (vega) is expected to increase.
The implied volatility of index options is expected to be above the consensus forecast.
Based on these conclusions, Ngoc considers various NIFTY 50 Index option strategies for Ahlim.
QuestionQ.
Based on Exhibit 3, which of the following NIFTY 50 Index option strategies should Ngoc recommend to Ahlim?
Solution
A is correct. The research report concludes that the consensus forecast of the implied volatility of index options is too low and anticipates greater-than-expected volatility over the next month. Given the neutral market direction forecast, Ngoc should recommend a long straddle, which entails buying a one-month 11,600 call and buying a one-month put with the same exercise price. If the future NIFTY 50 Index level rises above its current level plus the combined cost of the call and put premiums, Ahlim would exercise the call option and realize a profit. Similarly, if the index level falls below the current index level minus the combined cost of the call and put premiums, Ahlim would exercise the put option and realize a profit. Thus, Ahlim profits if the index moves either up or down enough to pay for the call and put premiums.
B is incorrect because the strategy to buy a call option would be reasonable given an increase in expected implied volatility with a bullish NIFTY 50 Index forecast, not a neutral trading range.
C is incorrect because a long calendar spread is based on the expectation that implied volatility will remain unchanged, not increase, until the expiry of the shorter-term option.
Prior to discussing client portfolios, Navarro, Cho, and Lyons discuss ways to create synthetic long and short positions in a stock using call and put options.
Cho states, “It is possible to create a synthetic short position by buying a put and selling a call on the stock with the same strike price and expiration.” Navarro states, “No, to create a synthetic short position you would sell a put and buy a call with the same strike and expiration date. Lyons disagrees with both Navarro and Cho, stating that the correct combination is to sell a call and a put on the stock with the same strike price and expiration.
Who is most likely correct regarding the creation of the synthetic short stock position?
Solution
A is correct. Cho is correct. A synthetic short position in a stock can be created by buying puts and selling calls on the stock with the same strike and expiration price.
B is incorrect. Lyons is incorrect. A short put and a short call create a short straddle.
C is incorrect. Navarro is incorrect. By purchasing calls and selling puts, you create a synthetic long position in the stock.
Options Strategies Learning Outcome
Demonstrate how an asset’s returns may be replicated by using options
Patel is bearish on shares of Company A and has shorted 500 shares at $117.43. Patel has approached Navarro about advice on using options to hedge this short position. Option information for Company A is presented in Exhibit 1.
Exhibit 1
Option Data for Company A, 25 March 2019
Option
Expiration
Strike
Price
Delta
Vega
Theta
Call
June 2019
120
3.65
0.439
0.221
–0.027
Put
June 2019
115
3.70
–0.399
0.216
–0.028
Navarro suggests that Patel buy five contracts of June 120 calls. Alternatively, she notes that Patel write five June 115 put contracts. Navarro then makes the following statements:
Statement 1
“While the position deltas of the stock + call portfolio and the stock + put portfolio are bearish, the position delta of the call position would be more bearish than that of the put position.”
Statement 2
“The stock + call portfolio is long vega and thus will benefit from increased volatility. However, the stock + put portfolio is short vega and thus will benefit from reduced volatility.”
Statement 3
“The stock + call portfolio benefits from time decay, and the stock + put portfolio is exposed to time decay.”
With respect to Company A, which of Navarro’s statements to Patel is most likely correct?
Solution
B is correct. Statement 2 is correct. The short stock/long call position is long vega and will benefit from increased volatility, whereas the short stock/short put position is short vega and will benefit from reduced volatility. Statement 1 is incorrect. The delta of her short position is –500. The call delta is 500 × 0.439 = 219.5. The delta of the combined position is –280.5. The short put delta is 0.199.5 = 500 × –(–0.399). The delta of the combined position is –300.5. Thus, both positions are bearish, but the put delta position is more bearish. Statement 3 is incorrect. The theta of the short stock/long call position is negative and is exposed to time decay. The theta for the short stock/short put position is positive [= –(–0.028)] and benefits from time decay.
A is incorrect. Statement 1 is incorrect. The delta of her short position is –500. The call delta is 500 × 0.439 = 219.5. So, the stock + call position delta is –280.5. The short put delta is 500 × –(–0.399) = 199. So, the stock + short put position delta is –300.5. Thus, while both positions are bearish, the stock + short put delta position is more bearish.
C is incorrect. Statement 3 is incorrect. The theta of the short stock/long call position is negative and is exposed to time decay. The theta for the short stock/short put position is positive [= –(–0.028) and benefits from time decay.
Options Strategies Learning Outcome
Compare the effect of buying a call on a short underlying position with the effect of selling a put on a short underlying position
Patel is also bearish on shares of Company B. Information for Company B is presented in Exhibit 2.
Exhibit 2
Option Data for Company A, 25 March 2019, Current Share Price = $139.81
Option
Expiration
Strike
Price
Delta
Theta
Call
June 2019
140
5.40
0.510
–0.035
Call
November 2019
140
8.64
0.517
–0.021
Put
June 2019
140
6.15
–0.508
–0.034
Put
November 2019
140
10.55
–0.507
–0.019
Lyons confirms Patel’s bearish outlook and states, “We expect the stock to remain stable in the near term, but in the long term, the outlook is bearish.” Patel asks Lyons to provide recommendations on an appropriate option strategy.
Based on Patel’s outlook for Company B and using the information in Exhibit 2, the most appropriate strategy that Lyons could recommend to Patel is:
Solution
C is correct. A long calendar spread can be constructed by buying the distant November 2019 put and selling the near-term June 2019 put. A long calendar spread using puts is appropriate if the expectation is for a stable market in the near term with a long-term bearish outlook. The purchase of the June 2019 call and put is a straddle. A straddle is directionally neutral—that is, neither bullish nor bearish—and is, therefore, inappropriate. The sale of the distant November 2019 put and purchase of the near-term June 2019 put is a short calendar spread. The short calendar spread is appropriate if the expectation is for a big move in the underlying stock, not if the outlook for shares is stable.
A is incorrect. The purchase of the June 2019 call and put is a straddle. A straddle is directionally neutral—that is, neither bullish or bearish—and is, therefore, inappropriate.
B is incorrect. The sale of the distant November 2019 put and purchase of the near-term June 2019 put is a short calendar spread. The short calendar spread is appropriate if the expectation is for a big move in the underlying stock, not if the outlook for shares is stable.
Options Strategies Learning Outcome
Describe uses of calendar spreads
Patel has also asked for recommendations on other option strategies for her to consider. Cho notes that the implied volatility of an underlying stock is an important factor in the determination of the price of the option and states that it is possible to devise strategies based on volatility skew. She states,
Generally speaking, implied volatility increases for put options at strike prices that are lower than the current stock price, whereas implied volatilities decrease for call options for strike prices that are higher than the current stock price; this is called the volatility skew.
However, sometimes implied volatility decreases for put options at strike prices that are lower than the current stock price, whereas implied volatilities increase for call options at strike prices that are higher than the current stock price; this is called the volatility smile. If you believe that the put-implied volatility was too high relative to the call-implied volatility, you could devise a long risk-reversal strategy by shorting the out-of-the-money call option and going long the out-of-the-money put option.
Question
In her statement to Patel, Cho is most likely correct regarding the:
Solution
A is correct. Cho correctly describes the volatility skew. Implied volatility for out-of-the-money (OTM) put options is higher than for at-the-money (ATM) put options and increases as the strike price moves further away from the current stock price. Implied volatilities for OTM call options are lower than for ATM call options and decrease as strike prices rise above the current stock price.
B is incorrect. Cho is incorrect about the volatility smile. The volatility smile occurs when OTM call and put option volatilities are higher than ATM option volatilities and are also higher than normal volatilities for OTM put and call options.
C is incorrect. Cho is incorrect about the long risk-reversal strategy; in fact, she describes a short risk-reversal strategy. If the put-implied volatility is too high relative to call-implied volatility, you would devise a long risk-reversal strategy by shorting the out-of-the-money put option and go long the out-of-the-money call option.
Options Strategies Learning Outcome
Discuss volatility skew and smile
Duane Armitage is a portfolio manager at LAMS Group, an independent investment advisory firm that offers portfolio management and investment advice to individual investors and institutional clients. Armitage is meeting with assistant portfolio managers Jessica Dufu and Emily Minkoff to review portfolios of clients Neha Kadakia and Maria Calzada.
Kadakia has been following Company XYZ and expects the price of its shares to decline sharply over the next month. Kadakia would like to use options to profit from this decline but also would like to limit losses if the expected share price decline does not materialize. Kadakia also indicates that she would like to minimize the cost of establishing the option position. Option information for XYZ shares is presented in Exhibit 1.
Exhibit 1.
November Expiration Option Information for Company XYZ: Current Share Price $117.43; Data as of 15 October 2019
Exercise Price
Call Premium
Put Premium
115
5.40
2.85
120
2.70
5.22
Dufu suggests that Kadakia can achieve her objective using either of the following strategies:
Strategy 1: Purchase November 120 call options and sell November 115 call options.
Strategy 2: Purchase November 120 put options and sell November 115 put options.
Are the strategies suggested by Dufu for Kadakia most likely correct?
Solution
C is correct. Strategy 1 is correct and Strategy 2 is incorrect. Given Kadakia’s expectations, the correct option strategy is a bear spread using calls. The bear spread can be implemented using call options or put options. In either case, it involves the purchase of the higher strike option and the sale of the lower strike option. Kadakia, however, has indicated that she would like to avoid a cash outlay. Given this constraint, the appropriate option strategy is to purchase November 120 call options and sell November 115 call options because doing so will result in an initial cash inflow of $5.40 – $2.70 = $2.70. Using put options would result in an initial cash outflow of $2.37 and a maximum profit of $2.63, which is less than the $2.70 maximum profit for the bear spread using calls. Net $2.63 if the stock falls below 115.
A is incorrect. Strategy 2 is incorrect because using put options would result in an initial cash outflow of $2.37.
B is incorrect. Strategy 1 is correct.
Options Strategies Learning Outcome
Discuss the investment objective(s), structure, payoffs, risk(s), value at expiration, profit, maximum profit, maximum loss, and breakeven underlying price at expiration of the following option strategies: bull spread, bear spread, straddle, and collar
Minkoff states, “I think a better strategy would be for Kadakia to undertake a calendar spread strategy, which is appropriate when there is an expectation for share prices to move in a certain direction but not immediately. Such a strategy focuses on taking advantage of the time value decay of stock options; however, it is only appropriate when implied volatility is expected to increase.
In her statement, Minkoff is least likely correct with regard to:
Solution
A is correct. Minkoff is incorrect in stating that calendar spreads are appropriate only if the expectation is for an increase in implied volatility. A short calendar spread is appropriate if the expectation is for a decrease in implied volatility or a big move in share prices that is not imminent. If a long calendar spread is implemented, the expectation is for a stable market or an increase in implied volatility. Minkoff is correct that a calendar spread strategy is appropriate when there is an expectation for share prices to move in a certain direction but not immediately and that such a strategy focuses on capturing the time value of stock options.
B is incorrect. Minkoff is correct about the capture of the time value of the option.
C is incorrect. Minkoff is correct about the direction and timing of the price move.
Options Strategies Learning Outcome
Describe uses of calendar spreads
Maria Calzada is a hedge fund manager and has asked Armitage for ideas on option trading strategies. Armitage suggests Calzada consider strategies built to profit from implied volatility and changes in implied volatilities. He presents implied volatilities by moneyness for Company ABC in Exhibit 2:
Exhibit 2.
Implied Volatilities by Moneyness: Three-Month Option for Company ABC
Stock
ATM
Put: 80%
Put: 90%
Call: 110%
Call: 120%
ABC
17.60
26.31
22.40
15.54
14.65
Armitage then makes the following statement: “Exhibit 2 depicts what we call a volatility smile. If the put implied volatility is considered to be too high compared with the call-implied volatility, then one way to take advantage of this situation is to enter a long risk reversal and delta hedge the option position by selling the underlying asset.”
In his statement to Calzada, Armitage is least likely correct with regard to:
Solution
B is correct. Exhibit 2 depicts a volatility skew in which implied volatility increases for out-of-the-money (OTM) put options and decreases for OTM call options. A volatility smile occurs when the curve is U-shaped––that is, implied volatility increases for OTM puts and calls.
C is incorrect. Armitage is correct about the long risk reversal strategy of selling the OTM put and buying the OTM call if the put implied volatility is considered to be too high compared with the call implied volatility.
A is incorrect. Armitage is correct about delta hedging the option position by selling the underlying asset.
Options Strategies Learning Outcome
Discuss volatility skew and smile
Calzada asks for recommendations on option strategies to implement if the market is expected to trade in a narrow range in the near term. Dufu responds, “The appropriate strategy in this scenario depends on your expectations for changes in implied volatility. If you expect a decrease in implied volatility, then you should write a straddle on the stock index. If your expectation is for implied volatility to increase, then you should enter a short risk reversal trade on the stock index. If your view is that implied volatility will remain unchanged, then you should buy call options and write put options on the stock index.”
In her response to Calzada, Dufu is most likely correct about:
Solution
A is correct. Dufu is correct about writing a straddle if the outlook is for the market to trade in a narrow range and an increase in implied volatility is expected. The strategy of buying call options on an index and writing put options on the index is incorrect; such a strategy would be implemented by an investor who has a bullish view of the market and an expectation that implied volatility will remain unchanged. The sale of puts is used to lower the cost of purchasing the calls. Dufu is incorrect about the short risk reversal strategy. This strategy would be implemented to benefit from an implied volatility skew. Specifically, one would enter this trade if call-implied volatility is viewed as being too high relative to put implied volatility––that is, one would sell the OTM call option and buy the OTM put option.
B is incorrect. Dufu is incorrect about the short risk reversal strategy. This strategy would be implemented to benefit from an implied volatility skew. Specifically, one would enter this trade if call implied volatility is viewed as being too high relative to put implied volatility––that is, one would sell the OTM call option and buy the OTM put option.
C is incorrect. Dufu is incorrect about buying calls and writing puts. The strategy of buying call options on an index and writing put options on the index is incorrect and would be implemented by an investor who has a bullish view of the market and an expectation that implied volatility will remain unchanged. The sale of puts is used to lower the cost of purchasing the calls.
Options Strategies Learning Outcome
Identify and evaluate appropriate option strategies consistent with given investment objectives
Wendy Manetti Case Scenario
Wendy Manetti is a risk manager at WTML Group, an investment management firm based in Miami. Manetti is running a training session for newly hired analysts, one of whom is Emily Fillizola.
Manetti begins the training session by noting that investors can modify the payoff profile of an investment position with synthetic derivative or equity positions. He provides the following examples:
Example 1: One can create a synthetic long position in a stock by purchasing calls and selling puts on this stock with the same strike and expiration date.
Example 2: A synthetic put option on a stock can be constructed by selling calls on the stock with the same strike and expiration date as the put and taking a short position on the stock.
Manetti presents the group with the option data for Company A in Exhibit 1. He describes the following scenario: “Assume a client owns 2,000 shares of Company A, which does not pay a dividend and is currently priced at $139.81. The client expects its price to remain stable over the next few months but does not want to sell the position.
Exhibit 1.
Option Data for Company A, 25 November 2019
Option
Expiration
Strike
Premium
Delta
Theta
Call
February 2020
140
5.40
0.510
–0.035
Call
July 2020
140
8.64
0.517
–0.021
Put
February 2020
140
6.15
–0.508
–0.034
Put
July 2020
140
10.55
–0.507
–0.019
Fillizola suggests that the client write 20 contracts of February 2020 call options with an exercise price of $140. The implied volatility of this option is 21.05%. Fillizola notes that if the share prices moves to $140 and the option is called, the client would effectively sell her shares at $145.40. If, however, shares prices move lower to $130 her effective sale price would be $135.40. Fillizola notes that this strategy would be appropriate if the expected stock’s volatility is higher than the implied volatility of 21.05%.
Manetti states, “Now consider a situation in which a client owns shares of Company A and wants to protect against a sudden decline in share price. A strategy to consider is the purchase of put options. I might suggest that the client purchase the February 2020 put option because it is cheaper than the July 2020 option and has the lowest time decay. If it were possible to purchase a February put option with a strike price lower than $140, it would be cheaper, but there would be a greater risk of loss in the position.”
Question
If the client executes Fillizola’s suggested strategy at the current price, her position delta will most likely be the same as the position delta of a portfolio that is:
A.
long 2,000 shares and short forward 980 shares.
B.
long 1,020 shares and short forward 980 shares.
C.
long 2,000 shares and short forward 1,020 shares.
Is Manetti most likely correct with regard to the strategy of purchasing put options?
Solution
B is correct. Although Manetti is correct that the February 2020 put option is cheaper, she is incorrect in stating that the February 2020 put option has the lowest time decay. This option has a theta of –0.034. In contrast, the July 2020 put option, although more expensive, has a theta of –0.019 indicating that it has the lowest time decay.
A is incorrect. Although Manetti is correct that the February 2020 put option with a strike price lower than $140 would be cheaper, this option exposes her to a greater risk of loss in the position because with a lower strike price, the put option would not protect against losses until the stock price falls below the lower strike price. She is incorrect in stating that the February 2020 put option has the lowest time decay.
C is incorrect. Manetti is correct that the February put option with a strike price lower than $140 is cheaper and is correct that it exposes her to a greater risk of loss in the position.
Options Strategies Learning Outcome
Discuss the investment objective(s), structure, payoff, risk(s), value at expiration, profit, maximum profit, maximum loss, and breakeven underlying price at expiration of a protective put position
If the client executes Fillizola’s suggested strategy at the current price, her position delta will most likely be the same as the position delta of a portfolio that is:
Solution
C is correct. The delta for the February 2020 $140 call strike option on Company A is 0.51. The delta for a long position in one share of Company A is 1. She is long 2,000 shares of Company A. The position delta for the covered call is (1 – 0.51) × 2,000 = 980. This position delta can be replicated by going long 2,000 shares and taking a short forward position in 1,020 shares. Forwards have deltas of 1.0 for non-dividend-paying stocks. Position delta for Option C = (2,000 – 1,020) = 980.
A is incorrect. The position delta for a portfolio that is long 2,000 shares and short forward 980 shares is (2,000 × 1) – (980 × 1) = 1,020. The position delta for the covered call is 980. The delta for the call option on Company A is 0.51. The delta for a long position in one share of Company A is 1. She is long 2,000 shares of company A. The position delta for the covered call is (1 – 0.51) × 2,000 = 980.
B is incorrect. The position delta for a portfolio that is long 1,020 shares and short forward 980 shares is 1,020 × 1 – 980 × 1 = 40. The position delta for the covered call is (1 – 0.51) × 2,000 = 980.
Options Strategies Learning Outcome
Compare the delta of covered call and protective put positions with the position of being long an asset and short a forward on the underlying asset
With regard to the strategy for Company A that Fillizola recommends, she is least likely correct regarding:
Solution
A is correct. Fillizola is incorrect regarding the expectation of volatility of the underlying compared with the implied volatility of 21.05%. The recommended strategy, a covered call, is appropriate if the expectation is that volatility of the underlying will be lower than the implied volatility of 21.05%. Fillizola is correct about the effective sale price if the stock is above $140. The stock gets called away at $140, and the effective sale price is $140 + $5.40 = $145.40. If the share price is $130, the client will sell at $130 and her effective sale price is $130 + $5.40 = $135.40.
B is incorrect. Fillizola is correct about the effective sale price. If the share price is $130, the client will sell at $130 and her effective sale price is $130 + $5.40 = $135.40.
C is incorrect. Fillizola is correct about the effective sale price if the stock is above $140. The stock gets called away at $140, and the effective sale price is $140 + $5.40 = $145.40.
Options Strategies Learning Outcome
Discuss the investment objective(s), structure, payoff, risk(s), value at expiration, profit, maximum profit, maximum loss, and breakeven underlying price at expiration of a covered call position
Are the examples of synthetic positions provided by Manetti most likely correct?
Solution
C is correct. Example 2 is incorrect. According to put–call parity, S0 + p0 = c0 + X/(1 + r)T. Accordingly, a synthetic put on a stock can be created by purchasing calls on this stock with the same strike and expiration date as the put and taking a short position in the underlying stock: p0 = c0 – S0+ X/(1 + r)T. Example 1 is correct. According to put–call parity, a synthetic long position is S0 = c0 – p0 + X/(1+r)T. A synthetic long position in a stock can be created by purchasing calls and selling puts on this stock with the same strike and expiration date.
A is incorrect. Example 1 is correct, but Example 2 is incorrect.
B is incorrect. Example 1 is correct.
Options Strategies Learning Outcome
Demonstrate how an asset’s returns may be replicated by using options