Options - COMM 101 Lecture Unit 8

Options An option is a form of derivative -- securities that *derive* their value from the value of another security, in this case, common shares. An option gives the holder the right to purchase or sell a common share at a specified price on or before a specified date. The key option terms are as...

Options An option is a form of derivative -- securities that *derive* their value from the value of another security, in this case, common shares. An option gives the holder the right to purchase or sell a common share at a specified price on or before a specified date. The key option terms are as follows: - **The premium** is the price or cost of the option - **A call** is the right to buy the asset - **A put** is the right to sell the asset - **Exercise price** is the price at which the underlying share will be bought or sold at - **The writer** is the seller of the option - **The holder** is the buyer of the option An **American style** option gives you the right to exercise the option at any time up to and including the expiration date. A **European style** option gives you the right to exercise only on the expiration date. Options traded in Canada and the U.S. are all American style. Example On May 3, 2019 TD Bank's common shares were trading at \$76.53. At the same time a June 21, 2019 call option at \$76.00 was trading at \$1.51. A put option on the same shares and same date, also at \$76.00, was trading at \$0.91. The call option gives the holder the right to *buy* TD Bank common shares at any time up to and including June 21, 2019 for \$76.00. - June 21, 2019 is the expiration date, \$76.00 is the exercise price and \$1.51 is the premium - The holder (buyer) must pay the premium whereas the writer (seller) receives the premium - [*If*] the call option is exercised, the holder pays the writer \$76.00 and the writer must deliver a common share to the holder The put option gives the holder the right to *sell* TD Bank common shares at any time up to and including June 21, 2019 for \$76.00. - Again, June 21, 2019 is the expiration date, \$76.00 is the exercise price, and in this case, \$0.91 is the premium. - The holder (buyer) must pay the premium whereas the writer (seller) receives the premium. - *[If]* the put option is exercised, the holder delivers a share to the writer who must pay \$76.00 for the share. Buying Options An investor who believes the price of a stock is going *up*, would buy a call option. As the price rises, the price of the call option will also rise. An investor who believes the price of a stock is going *down*, would buy a put option. As the price drops, the price of the put option will go up. Note that the option conveys the *right* to exercise, not the obligation. The holder does not have to exercise the option at any time, including at expiry. As a result if the investor who bought the option is wrong, the option expires worthless. The investor will have lost the premium paid, but no more. As we'll see in the next lesson, it's different for the writer (seller) of the option. An option is considered to be **in the money** when exercising it would produce positive cash flow. So a call option would be in the money when the market price of the common shares is \> the exercise price, and a put option would be in the money when the market price of the common shares is \< the exercise price. In the above example, the call option was in the money -- the holder of the call could exercise the option and buy TD Bank shares for \$76.00 and sell them in the market for \$76.53, generating positive cash flow of \$0.53. An option is said to be **out of the money** when it would not produce positive cash flow, and therefore no logical person would exercise it. For example, a put option is out of the money when the market price of the common shares is \> the exercise price (any logical person would sell at the higher market price). A call is out of the money when the market price of the common shares is \< exercise price (any logical person would buy at the lower market price). In the above example, the put option was out of the money -- if the holder of the put exercised it, they would be selling TD Bank shares for \$76.00 which is less than the market price -- no logical person would sell for less than they could receive in the market. An option is **at the money** when the market price = the exercise price. The situation from the holder's perspective is summarized in the following table. +-----------------+-----------------+-----------------+-----------------+ | At purchase | At or before | | | | | expiration date | | | +=================+=================+=================+=================+ | Belief about | Action | If price | If price | | stock price | | increases | decreases | +-----------------+-----------------+-----------------+-----------------+ | Will increase | Buy call option | Holder | Holder does not | | | | exercises call | exercise -- the | | | | option, buys | call option | | | | shares at the | expires | | | | exercise price | worthless | | | | and sells at | (premium lost). | | | | the higher | | | | | market price. | Option is **out | | | | | of the money.** | | | | Option is **in | | | | | the money.** | | +-----------------+-----------------+-----------------+-----------------+ | Will decrease | Buy put option | Holder does not | Holder | | | | exercise -- the | exercises put | | | | put option | option, buys | | | | expires | shares at lower | | | | worthless | market price | | | | (premium lost). | and sells at | | | | | the exercise | | | | Option is **out | price. | | | | of the money.** | | | | | | Option is **in | | | | | the money.** | +-----------------+-----------------+-----------------+-----------------+ *Concept Check* Alpha Corp.'s stock is trading at \$80. In the table below, place an X in the appropriate box to indicate whether the option is in the money, out of the money or at the money. ***Option*** ***In the money*** ***Out of the money*** ***At the money*** -------------------------------------------------- -------------------- ------------------------ -------------------- 6 month call option at an exercise price of \$90 3 month put option at an exercise price of \$85 1 month put option at an exercise price of \$75 1 week call option at an exercise price of \$80 1 week put option at an exercise price of \$80 3 month call option at an exercise price of \$75 **\ ** **Solution:** ***Option*** ***In the money*** ***Out of the money*** ***At the money*** ------------------------------------------------------ -------------------- ------------------------ -------------------- **6 month call option at an exercise price of \$90** **X** **3 month put option at an exercise price of \$85** **X** **1 month put option at an exercise price of \$75** **X** **1 week call option at an exercise price of \$80** **X** **1 week put option at an exercise price of \$80** **X** **3 month call option at an exercise price of \$75** **X** Exchange Traded Options Option contracts trade primarily on exchanges. In Canada, the Montreal Exchange trades all derivatives including options. In the US, options trade on the NASDAQ electronic exchange as well as on the Chicago Board of Exchange (CBOE). Note that since options are exchange traded, in addition to exercising the option, a holder could also sell the option at any time up to the expiration date. Exchange traded options are standardized by expiration dates and by exercise price. Each option provides the right to buy or sell *100 shares*, but quotes are given on a *per share* basis. Expiry dates are generally the third Friday of every month but in any month, the exchange will also open up weekly options (which expire on Fridays at the close of trading). Longer term options are also available, usually based on quarterly cycles and then a year out, maturing on the third Friday of January. Exercise prices are set by the exchange at the time the option is created; they are set so that investors have at least 5 choices around the then market price. For example, on Friday May 3, 2019, Royal Bank common shares were trading at \$106.84 (30 minutes before the close of trading). Investors could buy or sell the following options, all with an exercise price of \$105.00 (except where indicated) at the premiums indicated. Premiums for Royal Bank Options on Friday May 3, 2019: ***Expiry Date*** ***Call Option at \$105.00*** ***Put Option at \$105.00*** ------------------- ------------------------------- ------------------------------ May 3, 2019 1.84 0.05 May 10, 2019 1.96 0.11 May 17 2.14 0.25 May 24 2.43 0.50 May 31 2.58 0.63 June 21 3.05 1.00 July 21 3.50 1.29 Sept. 20 3.42\* 2.87\* Oct. 18 4.37 2.76 Jan. 17, 2020 5.22 4.20 Feb. 21, 2020 4.75\* 5.30\* Mar. 20, 2020 5.12\* 5.62\* Jan. 15, 2021 7.55 9.25 \* Exercise price is \$106.00 Although options are a supply and demand based market, one can see that the *further out* the maturity or expiration date is, the *higher* the price of the option when the exercise price remains the same. This makes sense in that there is a longer time period for the common shares to reach the exercise price. The investor must pay for this time value. The above call options are in the money and the put options are out of the money. Options are not available for all stocks, but rather, are written only for securities that are widely traded (i.e. the S&P/TSX 60, the Dow stocks and most in the S&P 500). Options are also written on equity index values, interest rates, foreign currencies, commodities, etc. In this course we are reviewing equity options only. Note also that an investor does not necessarily need to exercise an option to make money. Options are being traded up until expiry. Hence an investor can sell their options at any time up until expiry which creates another way for an option holder to profit. A not so obvious example follows. On November 30, 2023, Bank of Montreal shares were trading at \$111.49. A call option to purchase the shares for \$120 which expires on December 8, 2023 (i.e. 6 business days later) was trading for \$0.06. This reflects the fact that it is extremely unlikely that BMO shares will reach that level in such a short time. These options are referred to as "deep out of the money options" since the exercise price is so far away from the current market price. It is unlikely the holder will be able to exercise this option. However, if BMO shares rise to say \$114 (it is not uncommon for BMO shares to move by \$1 or \$2 in a day), this option will trade higher. It is still unlikely the option will be exercised but the price might increase to \$0.15 say, which means the investor has earned a 150% return on their investment. Some investors prefer investing in deep out of the money options since the returns can be much higher. Obviously the risk is also higher. For further information on options, the Montreal Exchange in Canada and the CBOE in the US have excellent educational material on their websites. ***\ *** Payoff and Profit The value of an equity option depends on the price the stock is trading at. Assume a stock is trading at \$20 and a two month call option with an exercise price of \$22 is priced at \$2.50. The option has value at any price over \$22 (i.e. the holder can exercise the option and buy the stock at \$22, then immediately sell the stock for a higher price) but the holder of the option will only earn a profit if the stock trades over \$24.50, since they need to recover the price of the option. Note that if the stock price never goes above \$22 in the next two months, the option would not be exercised and would expire worthless. Converting this to a general formula, if S~T~ is the price of the stock and X is the exercise price we can say that at expiration of an option (assuming it has not been exercised), , - There will be a **payoff** to the holder of the call option that is: S~T~ -- X if S~T~ \> X or 0 if S~T~ ≤ X - The holder **profits** when S~T~ -- X exceeds the premium paid. The holder of the option has a limited potential loss -- the maximum loss is the price of the option -- and unlimited potential profit -- there is no limit to how high the stock price can go. - The holder's **breakeven price** is the exercise price + the premium paid. Any price higher than the breakeven price results in a profit. Contrast this to the **writer** of the call option. Their potential profit is limited to the premium received. If they are writing the call naked, i.e. they do not own the shares but will purchase them if required at the expiration date, the potential loss is *unlimited*. No matter how high the stock price is at the expiry date, they must buy the shares at the market price and sell the shares to the holder at the exercise price. The writer's breakeven price is the same as the option holder's, i.e. the exercise price + the premium paid -- any price higher and they lose money. Payoff and Profit for Put Options For put options -- the right to sell a stock at the exercise price -- the holder believes the stock price will go down. For the \$20 stock mentioned above, assume a two month put option with exercise price of \$19 costs \$1.50. The option will have value when the market price is below \$19, i.e. the holder can buy shares in the market for less than \$19 and sell them to the option writer for \$19. However the holder will only earn a profit if the market price is below \$17.50, since they need to recover the cost of the option. Converting this to a general formula, if S~T~ is the price of the stock at expiration and X is the exercise price, - The **payoff** to the holder of the put option is: X - S~T~ if S~T~ \< X or 0 if S~T~ ≥ X - Again, the holder **profits** when X -- S~T~ exceeds the premium paid. The holder of the put option has limited loss potential (limited to the premium paid), but also limited profit potential, since the stock price can only go as low as zero. - The holder's breakeven price is the exercise price *less* the premium; any price *lower* than the breakeven price results in a profit. Writers of puts again have limited profit potential -- limited to the premium received -- and, assuming they are writing the puts naked, have limited loss potential -- their maximum loss, assuming the stock price goes to 0, is the exercise price less the premium received. The Potential Losses for Writers versus Holders It should be clear that the loss potential for option writers is greater than the loss potential for option holders. This is a critical difference. In theory, we could say that an investor who believes a stock price is going up could either buy a call or write a put. However, the consequences if the investor is wrong could be drastically different. Similarly, an investor who believes a stock price is headed lower could theoretically buy a put or write a call. However, the consequences of being wrong can be significantly higher for the call writer than for the holder of the put. *Concept Checks* 1\. Vanilla Inc.'s common shares are trading at \$100. An investor buys a six month put option with exercise price of \$95 for a premium of \$2. Fill in the table below to indicate the payoff and profit that will be realized for the various prices that the stock could be trading at in six months' time. Use negative numbers to indicate a loss. All numbers are in dollars -- do not add a dollar sign in your answer. ***Stock Price in 6 months*** ***75*** ***90*** ***100*** ***110*** ------------------------------- ---------- ---------- ----------- ----------- ***Payoff*** ***Profit*** **Solution:** ***Stock Price in 6 months*** ***75*** ***90*** ***100*** ***110*** --------------------------------- --------------- ------------- ------------ ------------ ***Payoff*** **95-75 =20** **95-90=5** **0\*** **0\*** ***Profit = payoff - premium*** **20-2= 18** **5-2 = 3** **0-2=-2** **0-2=-2** \*Option not exercised. 2\. Strawberry Inc.'s common shares are trading at \$40. An investor writes a six month call option with exercise price of \$44 for a premium of \$4. Fill in the table below to indicate the payoff and profit that will be realized for the various prices that the stock could be trading at in six months' time. Use negative numbers to indicate a loss. ***Stock Price in 6 months*** ***35*** ***40*** ***45*** ***50*** ------------------------------- ---------- ---------- ---------- ---------- ***Payoff*** ***Profit*** **\ ** **Solution:** ***Stock Price in 6 months*** ***35*** ***40*** ***45*** ***50*** ------------------------------------- ----------- ----------- --------------- -------------- ***Payoff*** **0\*** **0\*** **45-44 = 1** **50-44 =6** ***Profit = premium -- payoff^1^*** **4-0=4** **4-0=4** **4-1=3** **4-6=-2** \*Option not exercised ^1^ For the writer of an option, the profit is the premium they received, less any payoff they had to make Why Options? Why do investors buy options? In a word, it's leverage. An investor with a limited amount of funds to invest can gain much more exposure to a given stock using options than if they just bought the stock. Consider an investor with \$5,000 to invest. They have discovered ABC Corp., a company they're convinced has a stock price that is about to increase rapidly. Assume the stock is trading at \$50 per share. Six month calls to buy the shares at \$52.50, cost \$1. Assume three month treasury bills are yielding 1% compounded quarterly. The investor could use their \$5,000 as follows: 1. Buy all stock -- they have enough for 100 shares 2. Buy all options -- they have enough for 5,000 calls 3. Buy 100 calls and invest the remainder (\$4,900) in treasury bills Consider the **payoff** in 6 months of each strategy at various stock prices: +-------------+-------------+-------------+-------------+-------------+ | ***Price in | ***45*** | ***50*** | ***55*** | ***60*** | | 3 months*** | | | | | +=============+=============+=============+=============+=============+ | ***All | 100\*45 = | 100\*50 | 100\*55 | 100\*60 | | stock*** | 4,500.00 | =5,000.00 | | =6,000.00 | | | | | = 5,500.00 | | +-------------+-------------+-------------+-------------+-------------+ | ***All | 0.00 | 0.00 | 5000\*(55-5 | 5000\*(60-5 | | Options*** | | | 2.5) | 2.50) | | | | | | = 37,500.00 | | | | | = 12,500.00 | | +-------------+-------------+-------------+-------------+-------------+ | ***T-bills | 4900\*(1+.0 | 4,924.53 | 4,924.53 + | 4,924.53 + | | + | 1/4)^2^ | | 100\*(55-52 | 100\*(60-52 | | options*** | =4,924.53 | |.5) |.5) | | | | | = 5,174.53 | = 5,674.53 | +-------------+-------------+-------------+-------------+-------------+ The **profit** and breakeven stock price in 6 months are as follows: ***Price in 3 months*** ***45*** ***50*** ***55*** ***60*** ***Breakeven Price*** ------------------------- ------------------------- --------------------- ----------------------- ------------------------- ------------------------- ***All stock*** 100\*(45-50) = (500.00) 0.00 100\*(55-50) = 500.00 100\*(60-50) = 1,000.00 50.00 ***All Options*** 0-5000 = (5,000.00) 0-5000 = (5,000.00) 12500-5000 = 7,500.00 37500-5000 = 32,500.00 52.50+1 = 53.50 ***T-bills + options*** (75.47) (75.47) 174.53 674.53 52.50+75.47/100 = 53.26 The all option strategy has a larger loss potential but also a much larger profit potential than the all stock strategy. If the all option investor is wrong and the stock price stays the same or drops, they will lose their entire investment. In contrast, the all stock investor can only lose a portion of their investment (and only if they decide to sell -- in 6 months the options expire whereas the stock never expires). Hence the call option strategy has considerably more risk. However, if the investor is correct, the profit potential is significantly higher. If the stock moves to \$55, the all stock investor will have earned 10% on their investment. In contrast, the all option investor will have earned 150% on their investment. The all stock investor has used their \$5,000 to gain exposure to the performance of 100 shares. In contrast, the all option investor has used their \$5,000 to gain exposure to 5,000 shares. This is the leverage we spoke of earlier -- using available funds to get significantly more exposure to a stock. The treasury bills + option strategy is employed by investors who want to minimize their loss potential. In this case, the most they will ever lose is \$75.47 (the earnings on the t-bill less the premium on the calls). This loss is significantly less than either of the other strategies. In this case, the profit potential is also less. In practice, investors might seek to remedy this by buying riskier options. For example, in this case, instead of buying 100 options with a \$52.50 exercise price, they might buy options with a \$55 exercise price. The cost would be dramatically less -- say \$0.05 per option -- thus giving them a higher profit potential if the stock really does move higher (this would give them exposure to 2,000 shares and a breakeven price of \$55.05). Specific Option Strategies There are a myriad of option strategies that investors utilize. We are only going to review three of the more popular ones here but interested students should look through the education section of either the Montreal Exchange or the CBOE for more ideas. The Montreal Exchange explains 44 different option strategies with colourful names like condor, butterfly, strangle, calendar spread, and more. ***Covered Call*** A popular and reasonably conservative strategy for many investors is *to write call options on shares they already own,* referred to as a **covered call** (vs. writing the call naked, mentioned earlier). The options are written at an exercise price *above* where the shares are currently trading. Hence if the call gets exercised they will deliver shares they already own and receive a price higher than where the shares are trading at today, plus they will have received the premium. If the shares go down in value, the call option will not be exercised. At this point, they own shares with a lower value, but they will have received the premium from the call. For this reason, many investors write covered calls on shares they intend to hold for the long term, regardless of short term volatility. Example Canadian National Railways (stock symbol CNR) is considered by many Canadian investors to be a long term core holding of their portfolio. On May 3, 2019, CNR traded at \$125.35. A call expiring September 20, 2019 (4 ½ months later) at an exercise price of \$130 carried a premium of \$2.50. Owners of CNR stock could write this call and receive the \$2.50 premium on May 3. Obviously on that date they would not know if the call would be exercised or it wouldn't. If the call was exercised, they would be selling their shares for \$130 (which on May 3, happened to be above the highest the stock had traded for in the past year and was therefore an attractive price). Adding in the premium they received, means they effectively sold their shares for \$132.50, which was 5.7% above the level on May 3 (and they had the use of the \$2.50 premium for 4 ½ months). If the call was not exercised, the writer would still own the CNR shares and would have generated an extra \$2.50 or 2% on their investment. Note too that if the call was not exercised by September 20, CNR owners could then write another covered call, to generate even more premium. **Protective Put** An investor who wants to limit their loss potential on shares they already own, might decide to *buy a put exercisable at a price slightly less than their current market price,* referred to as a **protective put**. If the shares do go down, the investor can exercise the put and therefore limit their loss. Example Dollarama (stock symbol DOL) operates over 1,000 dollar stores in Canada. Although their stock has outperformed in recent years, in early 2019 they announced results that missed analyst expectations. On May 3, 2019 DOL traded at \$40.98. Owners of DOL who were concerned about the next quarter's results could have bought a put exercisable at \$40, expiring July 21, 2019, for \$1.25 (July 21 was approximately 3 weeks after DOL's next earnings release). By combining the put with their shares, they would limit their loss potential from the May 3 price. If the shares dropped below \$40, which is \$0.98 less than the May 3 price, the put would be exercised and the shares would be sold for \$40. Hence their loss on the stock + option strategy, could never exceed \$2.33 (the premium of \$1.25 plus the \$0.98 difference between the May 3 price and the exercise price). This was 5.4% of the May 3 investment, yet the investor still had the profit potential of owning the stock. They would have protected their stock investment against a drastic drop in stock price. Of course after July 21, the investor was no longer protected. Although this strategy does protect the investor, you can probably see it is considered a relatively expensive form of protection. Note that the same investor could have entered a stop-loss order on their DOL shares at \$40 at no cost. **Long Straddle** Would it make sense to buy both a put and a call on the same stock at the same exercise price, with the same expiry date? In theory the investor ought to make money on one of the options (i.e. the only scenario in which neither option has a payoff is if the stock price stays at the exercise price -- in practice highly unlikely). Would an investor undertake such a strategy and if so, why? Investors who believe a stock price is going up, buy calls. Investors who believe a stock price is going down, buy puts. What if the investor is unsure? In most cases, they will buy neither. But in some cases, it might make sense to buy both. Example Apple Inc. (stock symbol AAPL) is one of the most watched stocks in the world. In May, 2019 there were 42 analysts covering the stock and providing their estimate of future earnings. There were literally thousands of institutional investors who owned AAPL. On May 3, 2019 AAPL traded at US\$211.75. Its next earnings release date was scheduled for July 29, 2019. If AAPL missed the consensus estimate of earnings, its shares would most likely drop; if AAPL beat the consensus estimate, its shares would most likely rise. High tech stocks, including AAPL, have historically been very volatile stocks. Hence, an investor might take the position that they don't know if AAPL is going up or down, but they expect a big move either way. On May 3, 2019, a call option on AAPL at an exercise price of \$210 and expiration date of August 16, 2019 (about 3 weeks after the earnings release date) could be bought for \$11.05. A put option at the same exercise price and expiration date could be purchased for \$9.10. The investor was guaranteed to get a payoff on one of the options, no matter what the stock price is when exercised (S~T~). ***AAPL Price (***S~T)~ ***≤ 210*** ***AAPL Price (***S~T~***) \> 210*** ---------------------- ------------------------------------- -------------------------------------- ***Payoff on Put*** 210 -- S~T~ 0 ***Payoff on Call*** 0 S~T~ -- 210 ***Total*** 210 -- S~T~ S~T~ -- 210 Unfortunately however, the profit on the transaction is not always positive -- the cost of the strategy must be recovered. In this case, the cost was 11.05 + 9.10 =\$20.15. The stock price needed to move away from the exercise price by more than \$20.15 to realize any profit (i.e. above \$230.15 or below \$189.85) by August 16. Could this happen? At that time, the 52 week range for AAPL was \$142.00 - \$233.47. Clearly AAPL was a volatile stock and the prices at which this strategy would have turned a profit on, were within the one year range. In summary, investors can use options to accomplish a range of objectives. In some cases, both the risk and potential return are magnified, but in other cases, they can be a relatively conservative way to increase the yield on a portfolio, or reduce the risk of owning a stock.