Index options
Over the following four chapters, we’ll discuss different types of non-equity options. Instead of stock being the underlying security, these options focus on the market value fluctuations of something else.
We’ll learn about these four non-equity options:
- Index options
- VIX options
- Foreign currency options
- Yield-based options
Non-equity option investors speculate on values going up or down, hedge themselves against adverse market movements, and create additional income opportunities, similar to regular equity option investors. The strategies are generally the same; for example, a long S&P 500 call is bullish on the S&P 500 index. The difference is the underlying asset connected to the option.
We’ll first focus on index options.
Index options
We briefly covered index options earlier in this unit, which derive their value from fluctuations in a specific index’s value. For example, you could invest in an S&P 500 index options contract that provides a return if the index value falls, is flat, or rises. Instead of investing based on stock price changes, index options investors bet on index value fluctuations. While there are numerous indices available to trade options on, these are most likely to appear on the exam:
SPX - S&P 500
- Tracks 500 large-cap U.S. traded companies
OEX - S&P 100
- Tracks 100 large-cap U.S. traded companies
- Subset of the S&P 500
DJX - Dow Jones Industrial Average
- Tracks 30 large-cap U.S. traded companies
RUT - Russell 2000
- Tracks 2,000 small-cap U.S. traded companies
VIX - Volatility index
- Tracks market volatility
Indices provide a “high-level” view of the market. You’ve probably watched the news cover the Dow Jones and the S&P 500, both commonly used to gauge the U.S. markets and economy. Various indices provide different perspectives on the market. For example, if the Russell 2000 is down, but the S&P 100 is up, it can be assumed small businesses are having a rough day in the market while large businesses are doing well.
Throughout this chapter, you’ll learn how index options are similar to equity options. However, there are two distinct differences you should be aware of.
First, you learned in a previous chapter that most index options are European style, meaning they can only be exercised at expiration. This is true for virtually all index options with one big exception - the OEX (S&P 100). The reason is unimportant, but the OEX is one of the only American style index options, meaning it can be exercised anytime. As a reminder, all equity (stock) options are American style.
The second difference relates to exercise. When an index option is exercised, shares are not bought or sold. Think about it - if an S&P 500 option worked the way equity options do, 500 shares of stock would be traded at exercise. Due to the size of indices, all index option exercises settle in cash. When a holder exercises their index option, the writer must deliver the “in the money” amount in cash. We’ll explore this concept later.
When an equity option is exercised, settlement occurs over one business day (T+1). With an index option, there are no shares traded at exercise, so index options also maintain a settlement of T+1.
Let’s jump into some math-based index option questions. Assume this position:
Long 1 SPX 4500 call at $20
Using your fundamental options knowledge, find the following:
- Maximum gain
- Maximum loss
- Breakeven
- Gain or loss at 4,550
- Gain or loss at 4,450
- Maximum gain = unlimited
Just like a regular equity option, long calls have unlimited gain potential. The investor maintains the “right to buy” at 4,500. The further the S&P 500 index rises above 4,500, the more the investor makes.
- Maximum loss = $2,000 (premium)
If the S&P 500 index goes below 4,500, the option is “out of the money” and will expire worthless. The worst-case scenario for an option holder is to lose the premium. A $20 option premium equals $2,000 ($20 x 100 multiple).
- Breakeven = 4,520 (strike + premium)
If the S&P 500 index rises to 4,520, the contract is “in the money” by $20. When the holder exercises the contract, the writer must deliver the “in the money” (intrinsic value) amount in cash. With the option $20 “in the money,” the writer must deliver $2,000 in cash ($20 x 100 multiple) to the holder, which offsets the original $2,000 premium paid.
- Gain or loss at 4,550 = $3,000 gain
At 4,550, the contract is “in the money” by $50. The writer must deliver $5,000 ($50 x 100 multiple) to the holder at exercise. The holder paid $2,000 upfront to buy the option, which partially offsets the gain from exercise. The investor is left with an overall $3,000 profit.
- Gain or loss at 4,450 = $2,000 loss
At 4,450, the contract is “out of the money” and expires worthless. The holder loses their $2,000 premium ($20 x 100 multiple), their maximum loss.
As you may have noticed, index options are very similar to equity options. In fact, you can use all the formulas from the long call chapter to answer the questions in the previous scenario.
Let’s try another example:
Short 1 RUT 2000 put @ $15
Using your fundamental options knowledge, find the following:
- Maximum gain
- Maximum loss
- Breakeven
- Gain or loss at 2,040
- Gain or loss at 1,960
- Maximum gain = $1,500 (premium)
The maximum gain on any short option is always the premium. Short puts are bullish, and the investor hopes the RUT stays above 2,000. If this occurs, the option is “out of the money,” expires worthless, and the investor keeps the $1,500 ($15 x 100) premium as a profit.
- Maximum loss = $198,500 (strike - premium)
Short puts lose more the further the market falls. If the RUT falls below 2,000, the contract goes “in the money” (gains intrinsic value). Theoretically, the index could go to zero, although this will probably never happen (all 2,000 businesses in the Russell 2000 index would have to go out of business).
A short put’s maximum loss is calculated by subtracting the premium from the strike price (2,000 - 15). At zero, the option would be “in the money” by $1,985, resulting in an overall loss of $198,500 ($1,985 x 100).
- Breakeven = 1,985 (strike - premium)
If the RUT falls to 1,985, the contract is “in the money” by $15. The holder (the long side) would exercise the contract, forcing the investor to deliver the “in the money” amount (intrinsic value) in cash. With the intrinsic value at $15, the investor must deliver $1,500 ($15 x 100) in cash to the holder. The $1,500 loss at exercise offsets the $1,500 premium received when this option was initially sold.
- Gain or loss at 2,040 = $1,500 gain
The contract is “out of the money” and will expire worthless. The investor keeps the $15 premium with no additional action required, which amounts to an overall gain of $1,500 ($15 x 100).
- Gain or loss at 1,960 = $2,500 loss
The contract is “in the money” by $40. When assigned (exercised), the writer must deliver $4,000 ($40 x 100) to the holder. The writer received $1,500 upfront to sell the option, which reduces the overall loss to $2,500.
Again, the fundamentals of options continue to apply. You can use all the formulas from the short put chapter to answer the questions from the previous scenario.
Investors commonly use index options to hedge against market risk, a type of systematic risk.
If you had money invested during the initial outbreak of COVID-19 (Coronavirus), you surely understand market risk. In March 2020 alone, the S&P 500 lost over 12%. A market loss of 12% over a year is bad enough, but a drastic decline in one month is devastating.
There are exceptions, but most investors experience losses during v broad market declines. Even well-diversified portfolios with exposure to various sectors and geographic locations would likely experience losses. This is an example of why investors cannot diversify out of market risk.
While investors can’t diversify out of market risk, it can be hedged against. As we learned in the hedging strategies chapter, an investor can protect themselves by going long an option that profits during an adverse market movement.
Investors with large diversified portfolios of investments could buy (go long) index puts to protect against market risk. If something like an unexpected recession occurs, the gains from a bearish long index put could offset the losses from other investments in the portfolio.
You may encounter a question regarding this topic on the exam. For example:
An investor owns a diversified portfolio of stocks currently worth $600,000. They want to fully hedge against market risk. Which of the following would best protect the portfolio?
A) Short 5 OEX 2000 puts
B) Long 5 OEX 2000 puts
C) Short 3 OEX 2000 puts
D) Long 3 OEX 2000 puts
First, let’s eliminate two answers that seem out of place. To hedge, it’s best investors buy (go long) an option. Selling options places the investor in a risky position where they must wait to see if they’ll be assigned (exercised). Also, short puts are bullish and will not offset losses as the market falls. Therefore, we can eliminate answer choices A and C.
Each index option hedges a specific amount of portfolio value. To find how much, multiply the strike price (2,000) by 100 (options multiple). Therefore, each OEX 2000 put hedges $200,000 of market value (2,000 x 100).
Last step - divide the portfolio value ($600,000) by the amount each option hedges ($200,000). The investor should buy three contracts to fully hedge a $600,000 portfolio with OEX 2000 puts. Therefore, the answer is D.
Let’s see if you can figure out one of these questions on your own:
An investor owns a well-diversified portfolio of large-cap stocks currently worth $1,400,000. They want to fully hedge against systematic risk. To adequately protect their portfolio, which investment should you recommend?
A) Long 40 DJX 350 calls
B) Long 40 DJX 350 puts
C) Long 20 DJX 350 calls
D) Long 20 DJX 350 puts
Answer = B) Long 40 DJX 350 puts
First, pick the option that will profit in a market decline. Long calls are bullish and will expire worthless if the market falls. Therefore, you can eliminate answer choices A and C.
Next, find how much each DJX 350 put hedges. With a multiplier of 100, each option covers $35,000 of portfolio value (350 strike price x 100 multiple).
Last, divide the overall portfolio value ($1,400,000) by the amount each DJX 350 put covers ($35,000). The investor should purchase 40 DJX 350 puts to properly hedge against a market decline (systematic risk).
There’s one more layer to protecting portfolios relating to a portfolio’s beta.
A portfolio with a beta of 1.0 has the same volatility as the market, historically speaking. Meaning, this portfolio has generally followed the market in the past. If the S&P 500 was up 10% last year, this portfolio should also be up 10% (10% x 1.0).
A portfolio with a beta above 1.0 is more volatile than the market. For example, a portfolio with a beta of 1.5 is expected to move 1.5 times faster than the market. If the S&P 500 was up 10% last year, this portfolio should be up 15% (10% x 1.5).
A portfolio with a beta between 0.0 and 1.0 is less volatile than the market. For example, a portfolio with a beta of 0.5 is expected to move at half the speed of the market. If the S&P 500 was up 10% last year, this portfolio should be up 5% (10% x 0.5).
A portfolio with a negative beta moves opposite to the market. For example, a portfolio with a beta of -2.0 is expected to move at twice the speed of the market, but in the opposite direction. If the S&P 500 was up 10% last year, this portfolio should be down 20% (10% x -2.0).
Here’s a table summarizing what we just discussed:
| S&P 500 return | Portfolio beta | Portfolio return |
|---|---|---|
| Up 10% | 1.0 | Up 10% |
| Up 10% | 1.5 | Up 15% |
| Up 10% | 0.5 | Up 5% |
| Up 10% | -2.0 | Down 20% |
Beta can involved in a portfolio hedging question. For example:
An investor owns a well-diversified portfolio of small-cap stocks with a beta of 1.4, currently worth $1,000,000. They want to fully hedge against systematic risk. To properly protect their portfolio, which investment should you recommend?
A) Long 7 RUT 2000 puts
B) Short 7 RUT 2000 calls
C) Short 5 RUT 2000 calls
D) Long 5 RUT 2000 puts
This portfolio moves 1.4 times faster than the market and needs extra protection in a market decline. The best way to initially approach this question is the same approach we used before:
Step 1: eliminate wrong answers
Although short calls are bearish, the maximum gain is the premium. If the market declines drastically, the investor is not protected beyond the money made on the premium. Investors should buy (go long) options to gain protection (hedge). Therefore, eliminate answers B and C.
Step 2: Find the amount of protection each option gives
Multiply the strike price (2,000) by 100 (option multiple). Therefore, each RUT 2000 put covers $200,000 of portfolio value.
Step 3: Divide portfolio value by option coverage
One long RUT 2000 put covers $200,000 of portfolio value. Therefore, a $1,000,000 portfolio with similar volatility to the RUT requires 5 long RUT 1000 puts for full protection.
If you got this far, you might have answered D. This is not the correct answer. There’s one more step!
Step 4: Multiply the contracts initially required by beta
The investor needs extra protection because this portfolio moves 1.4 times faster than the RUT. To obtain the answer, multiply the number of contracts initially required (5) by the beta (1.4). You are correct if you answered 7 long RUT 2000 puts (answer choice A)!
Let’s see if you can do one on your own:
An investor owns a well-diversified portfolio of large-cap stocks with a beta of 2.5, currently worth $800,000. They ask for your help in properly hedging against market risk. Which of the following should you recommend?
A) Long 4 SPX 2000 puts
B) Short 4 SPX 2000 puts
C) Long 10 SPX 2000 puts
D) Short 10 SPX 2000 puts
Answer = C) Long 10 SPX 2000 puts
First, we can eliminate the short puts because they’re bullish and won’t benefit the client if the market falls. Also, investors should buy options to hedge themselves. Eliminate answer choices B and D.
Second, find how much each put option covers. Multiply the strike price (2,000) by 100 (option multiple). Therefore, each option provides $200,000 of portfolio protection.
Third, divide the portfolio value ($800,000) by the contract coverage ($200,000 per option). An $800,000 portfolio that maintains similar volatility to the market requires 4 long SPX 2000 puts for a proper hedge.
Remember, this portfolio is two and a half times more volatile than the market! Last step - multiply the original number of long puts needed (4) by the beta (2.5). A portfolio with this level of volatility needs 10 long SPX 2000 puts to protect against a market decline.
When the market falls, portfolios with betas above 1.0 will likely fall faster and further than the market. This is why more volatile portfolios require more protection.
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