Solving Mixed Options Problems On The Series 7

By Investopedia Staff AAA

In Tips For Series 7 Options Questions, we discussed "pure" options strategies. Here, we will focus on the considerable number of questions on the Series 7 exam that test the candidates on strategies involving both options contracts and stock positions. (For everything you need to know for the Series 7 exam, see our Free Series 7 Online Study Guide.)

Solving "Mixed" Options Strategy Problems
The first strategy to use in solving these questions is deceptively simple: Read the questions carefully to determine the customer's primary objective:

  • If the question indicates that a customer needs to protect a stock position, then he or she must buy an options contract for protection.
  • If the customer is combining options with stock positions to create income, he or she must sell an options contract to produce the income.

As with the majority of options questions on the Series 7 exam, the scope of the questions is limited to maximum gain, maximum loss and breakeven. (To learn more, read Option Spread Strategies and Options Basics.)

A tool that you should use each time you calculate any of these is the $OUT/$IN cross. Don't take a chance by trying to keep track of the money flow in your head. The Series 7 exam is quite stressful for most people, so just write it down.

$ Out $ In
- -
- -
- -

A special note: In any strategy that combines stock with options, the stock position takes precedence. This is because options contracts expire - stocks do not.

Protecting Stock Positions: Hedging
Let's begin with hedging strategies. We will look at long hedges and short hedges. In each case, the name of the hedge indicates the underlying stock position. The options contract is a temporary form of insurance to protect the investor's stock position against adverse movements in the market. (For related reading, see A Beginner's Guide To Hedging.)

Long Hedges = Long Stock and Long Put
A long stock position is bullish. If the market in a stock turns down, the investor with the long stock position loses. Remember: If an investor needs to protect a stock position with options, the investor must buy the contract (like an insurance contract) and pay a premium. Puts go in-the-money (become exercisable) when the stock's market price falls below the strike price. The put is an insurance policy for the investor against a drop in the market. (To read more, check out Prices Plunging? Buy A Put! and Introduction To Put Writing.)

Let's look at few sample questions that illustrate one of the many approaches the exam may take to this subject. For these examples, we'll be changing only the multiple choice options that could be provided for the same question.

Example 1
A registered representative has a customer who bought 100 shares of XYZ stock at $30/share. The stock has appreciated to $40/share in the past eight months.The investor is confident that the stock is a good long-term investment with additional upside potential but is concerned about a near-term weakness in the overall market that could wipe out his unrealized gains. Which of the following strategies would probably be the best recommendation for this customer?
A. Sell calls on the stock
B. Buy calls on the stock
C. Sell puts on the stock
D. Buy puts on the stock
Answer: D.
Explanation: This is a basic strategy question. The customer wishes to fix, or set, his selling price for the stock. When he buys puts on the stock, the selling (or delivery) price for the stock is the strike price of the put until expiration. The long stock position is bullish, so to counter a downward movement, the investor purchases puts. Long puts are bearish.
Example 2
Now, using the same question, let\'s look at a different set of answers.
  1. Buy XYZ 50 puts
  2. Sell XYZ 40 calls
  3. Buy XYZ 40 puts
  4. Sell XYZ 50 calls

Answer: C.
Explanation: This set of answers goes a bit more deeply into the strategy. By purchasing puts with a strike (exercise) price of 40, the investor has set the delivery (selling) price of XYZ at 40 until the options expire.Why not buy the 50 put? When the market is at 40, a put with a strike price of 50 would be in the money by 10 points. Remember, puts with higher strike prices are more expensive. Essentially, the investor would be "buying his own money," if he purchased the 50 put in this case.

Let's try some others.

Example 3
An investors buys 100 shares of XYZ stock at $30/share and one XYZ 40 put @ 3 to hedge the position. Over eight months, the stock appreciates to $40/share.The investor is confident that the stock is a good long-term investment with additional upside potential, but is concerned about a near-term weakness in the overall market that could wipe out his unrealized gains. What is the maximum gain for this investor?
  1. $7/share
  2. $4/share
  3. $3/share
  4. Unlimited

Answer: D.
Explanation: This is a bit of a trick question. Remember: The stock position takes precedence. A long stock position is bullish, and it profits when the market rises. There is theoretically no limit as to how high the market can rise.

Now let's take a different look at this question:

Example 4
An investors buys 100 shares of XYZ stock at $30/share and one XYZ 40 put @ 3 to hedge the position. The stock has appreciated to $40/share in the past eight months.The investor is confident that the stock is a good long-term investment with additional upside potential but is concerned about a near-term weakness in the overall market that could wipe out his unrealized gains. If XYZ stock drops to $27 and the investor exercises the put, what is the profit or loss on the hedged position?
  1. Loss of $3/share
  2. Gain of $4/share
  3. Loss of $7/share
  4. Gain of $7/share

Answer: D.
Explanation: Track the money as shown in the graph below:

$ Out $ In
Purchase Price - $30 Exercising the Put - $40
Put Premium - $3 -
Total Out - $33 -
Net Gain/Loss - $7 Net Share Gain

Here's another common approach to this type of question:

Example 5
An investors buys 100 shares of XYZ stock at $30/share and one XYZ 40 put @ 3 to hedge the position. The stock has appreciated to $40/share in the past eight months. The investor is confident that the stock is a good long-term investment with additional upside potential, but is concerned about a near-term weakness in the overall market that could wipe out his unrealized gains. What is the investor\'s breakeven point for this position?
  1. $40
  2. $37
  3. $33
  4. $47

Answer: C.
Explanation: Look at the / cross in the previous question. The investor\'s original investment was $30, and then the investor bought the put for $3 ($30 + $3 = $33). To recover his original investment and the options premium, the stock must go to 33. By exercising the put, however, the investor showed a profit of $7/share or $700.

Now, let's look at the other side of the market.

Short Hedges = Short Stock and Long Call
We noted above that the stock position takes precedence. Remember: When an investor sells stock short, he or she expects the market in that stock to fall. If the stock rises, the investor theoretically has an unlimited loss. To insure themselves, investors may buy calls on the stock. The short stock position is bearish. The long call is bullish.

An investor who sells stock short is obligated to replace the stock. If the stock price rises, the investor loses. The investor buys a call to set (or fix) the purchase price. Until the options contract expires, the investor will pay no more than the call's strike price for the stock. (To learn more, read the Short Selling tutorial.)

Example 6
Suppose that an investor has sold 100 shares of MNO stock short at $75/share and feels confident that the stock\'s price will fall in the market in the near future. To protect against a sudden rise in price, a registered representative would recommend which of the following?
  1. Sell a MNO put.
  2. Buy a MNO put.
  3. Sell a MNO call.
  4. Buy a MNO call.

Answer: D.
Explanation: This is a direct strategy question. The basic definition of a short hedge is short stock plus a long call. The investor must buy the insurance to protect the stock position.

Now let's try a different approach.

Example 7
An investor has sold 100 shares of FBN stock short at 62 and buys one FBN Jan 65 call @ 2. If FBN stock rises to 70 and the investor exercises the call, what is the gain or loss in this position?
  1. $2/share
  2. $5/share
  3. $8/share
  4. Unlimited

Answer: B.
Explanation: Follow the money. The investor sold the stock short at $62, bought the call for $2, and then, when exercising the call, paid $65. The loss is $5/share.

$ Out $ In
Call Premium - $2 Short Sale Proceeds - $62
Exercise Price - $65 Total in Account/Share - $60
Net Gain/Loss - $5 Net Loss

Recap: As you can see, the long and short hedges are mirror image strategies. Remember, the stock position takes precedence and the investor must pay a premium (buy a contract) to protect the stock position. If the question refers to protection, hedging is the strategy.

Creating Income with Stock Plus Options
The first, and most popular of these strategies is writing covered calls. (To read more, see Come One, Come All - Covered Calls.)

Covered Call = Long Stock Plus Short Call
Writing (selling) covered calls is the most conservative of options strategies. Recall that when an investor sells a call, he or she is obligated to deliver the stock at the strike price until the contract expires. If the investor owns the underlying stock, then he or she is "covered" and can deliver if exercised.

The Series 7 exam may give you a hint by using the word, "income", as in Example 8, below.

Example 8
An investor owns 100 shares of PGS. The stock has been paying regular dividends but has shown very little growth potential. If the investor is interested in creating income while reducing risk, the registered representative should recommend which of the following strategies?
  1. Buy a call on PGS.
  2. Buy a put on PGS.
  3. Sell a call on PGS.
  4. Sell a put on PGS.

Answer: C.
Explanation: This is a "classic" covered call situation. The call premium received creates the income and, at the same time, reduces downside risk.

Let's add some numbers to the situation and ask some additional questions:

Example 9
The investor is long 100 shares PGS at $51 and writes one PGS May 55 call @ 2. What is the investor\'s maximum gain from this strategy?
  1. $2/share
  2. $3/share
  3. $5/share
  4. $6/share

Answer: D.
Explanation: Again, follow the money. See the / cross below:

$ Out $ In
Stock Price - $51 Call Premium - $2
- Excercise Proceeds - $55
Maximum Gain - $6
Example 10
Take the same situation as in Example 9 and ask the question: What is the investor\'s breakeven point?
  1. $55
  2. $53
  3. $49
  4. $45

Answer: C.
Explanation: The investor owned the stock at $51. When the investor sold the call at $2, the breakeven point was lowered to $49 because that is now the amount that the investor has at risk. $49 is also the maximum loss in this position.

A covered call increases income and reduces risk. Those are the two objectives of this conservative strategy. The strategy works best in a relatively flat to slightly bullish market. Investors must be made aware that:

Short Stock Plus Short Put
Another, and much riskier, strategy involves writing a put when the investor has a short position in the same stock. This position is a very bearish strategy. Remember, the stock position takes precedence.

Example 11
An investor sells 100 shares MPS short at 70 and simultaneously writes one MPS 70 put @ 3. What is the maximum gain in this strategy?
  1. $73/share
  2. $70/share
  3. $67/share
  4. $3/share

Answer: D
Explanation: The investor sold the stock at $70 and the put at $3. The investor now has $73/share in the account. If the market falls below $70, the put will be exercised and the stock will be delivered to the investor, who will pay the strike price of $70 for the stock and use the stock to replace the borrowed shares. The gain is $3/share.
Follow the money as in the / cross below:

$ Out $ In
Stock Price on Exercise of Put - $70 Short Sale Proceeds - $70
Put Premium - $3
Net Gain/Loss - $3 Gain
Example 12
Another question regarding this scenario: What is the maximum loss?
  1. Unlimited
  2. $3/share
  3. $70/share
  4. $63/share

Answer: A
Explanation: The investor who holds a short stock position loses when the market begins to rise. This investor will break even when the market goes to $73, because that is the amount in the account. Above $73/share, the investor has losses, which have the potential to be unlimited.

On the Series 7 exam, there are relatively few questions on this strategy. Recognize, however, the maximum gain, maximum loss and breakeven - just in case.

Summary
Options with stock positions have two basic objectives:

1. Protection of the stock position through hedging
2. Creating income by selling an option against the stock position.

The strategies outlined here may be either highly risky or very conservative. In the Series 7 exam, the candidate must first recognize which strategy recommendation is required and then follow the money to find the correct answer. (For everything you need to know for the Series 7 exam, see our Free Series 7 Online Study Guide.)

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