This article will discuss how a value investor may want to take advantage of call options. It will discuss how options are typically priced. How value investors can use option pricing models in their favor. And conclude with an example revolving around Johnson & Johnson (ticker:JNJ). Supporting comments from Warren Buffett are also included via the 2008 Berkshire Hathaway Inc (ticker: BRK.A)(ticker: BRK.B) shareholder letter.
The first thing to understand is the pricing of options. Option pricing is coupled to the market value of the underlying company and a premium. The market value is just that, the current price being assigned to a stock on the open market. The key is on how this premium is determined. Premiums are calculated using a mathematical model called the Black-Scholes model. It is this mathematical model that value investors need to thank. The Black-Scholes model makes one big assumption. That markets are highly efficient (stocks are properly priced at all times). Of course, the reality is that markets are not efficient and this is how value investors can take advantage of call options on occasion.
The Black-Scholes assumption on efficient markets causes it's focus to be on volatility. Volatility is a horrible predictor of future share prices, especially with a long term investment window. In essence, the Black-Scholes model couples volatility to risk. Therefore the premium part of the options equation is tightly coupled to volatility of the more recent past.
From the 2008 Berkshire Hathaway annual report (full excerpt at bottom of article):
If the formula (Black-Scholes) is applied to extended time periods, however, it can produce absurd results. In fairness, Black and Scholes almost certainly understood this point well. But their devoted followers may be ignoring whatever caveats the two men attached when they first unveiled the formula.
This pricing model is the aspect that value investors can take advantage of. Specifically, long term call options can be used to profit off of this folly. More specifically, boring stocks that have become undervalued may present opportunity. Of course this is hit and miss since far out of the money call options are needed in addition to low volatility. Also, the risk associated with this is loss of capital (up to 100%).
So, the key is to find a good company that hasn't done much for an extended period of time. And a company that is simply undervalued by atleast 33%. In practice, you should be hunting for undervalued stocks and the fact that it has low volatility (and small option premiums) should be more of a coincidence. A coincidence worth looking for while researching companies. It is hard to seek out these companies specifically. Good call option opportunities may arise only once every few years. The harder you look though, the more often opportunities will appear. 6 or more months of low volatility is typically required for minimal premium assignment.
As a current example, take Johnson & Johnson (ticker:JNJ) which is a high quality company trading at $63.45 per share. It's share price has also traded in a small range for an extended period of time (6+ months). Over the past year, it's price has stuck between $46.25 and $65.95 with very few spikes and it has tightly tracked the Dow. Because of this, the Black-Scholes formula assumes that JNJs options deserve a small premium. Currently, January 2012 call options at the $90 strike are only worth about 25 cents. The assumption here is that JNJ is undervalued and worth over $100. Assuming that JNJ is a truly good company, it will probably be worth even more in 2012. After all, price follows value over the long term.
This proposed strategy recommends one immediate action be taken after purchasing the call options. Place a limit order to sell about 1/3 of the options for 3 times or more than the price that was paid for them. The portion and limit order price doesn't really matter as much as its purpose. The purpose is to set up a limit order that will recoup the investments costs after commissions as soon as possible. Remember, loss of 100% of your investment can happen with call options so breaking even is always a good idea. Even if something is undervalued, it can take years for Mr Market to agree. Even if only 50% is recouped up front, this will minimize the potential loss to 50%. These are options though, and this may never happen. A 100% loss could still occur. Trying to sell 1/3 of the options for 80 cents a piece, for example, is of the utmost important.
The remaining call options is where the money may or may not be made. If Mr Market plays nice, and JNJ does reach $100 per share within 2 years, those options will be worth $10 or more a piece. This represents a handsome gain! Depending on timing and premiums assigned (thanks to the Black-Scholes formula), the call options might be worth $10 each when JNJ is at $90 per share. The gains possible are clearly great and this is what value investors may decide to try and exploit. However, losses are also possible and a 100% loss could also occur. Never forget that the greatest risk is the risk of loss of capital. Minimize your exposure to options as much as possible. Doing call options with less than 5% of ones portfolio is highly recommended since a 5% loss loss is not catastrophic. This strategy is a risk/reward proposition where one must be convinced that the typically outcome is positive.
A follow up discussing a naked put strategy can be found here
DISCLOSURE: The author of this article owns JNJ stock and 2012 LEAP options at the $90 strike. Options are a high risk strategy in which a 100% loss of capital can occur. The author of this article takes no responsibility regarding actions taken by readers of this article.
Excerpt from the 2008 Berkshire Hathaway annual report (page 20, 21):
The Black-Scholes formula has approached the status of holy writ in finance, and we use it when valuing our equity put options for financial statement purposes. Key inputs to the calculation include a contract’s maturity and strike price, as well as the analyst’s expectations for volatility, interest rates and dividends.
If the formula is applied to extended time periods, however, it can produce absurd results. In fairness, Black and Scholes almost certainly understood this point well. But their devoted followers may be ignoring whatever caveats the two men attached when they first unveiled the formula.
It’s often useful in testing a theory to push it to extremes. So let’s postulate that we sell a 100- year $1 billion put option on the S&P 500 at a strike price of 903 (the index’s level on 12/31/08). Using the implied volatility assumption for long-dated contracts that we do, and combining that with appropriate interest and dividend assumptions, we would find the “proper” Black-Scholes premium for this contract to be $2.5 million.
To judge the rationality of that premium, we need to assess whether the S&P will be valued a century from now at less than today. Certainly the dollar will then be worth a small fraction of its present value (at only 2% inflation it will be worth roughly 14¢). So that will be a factor pushing the stated value of the index higher. Far more important, however, is that one hundred years of retained earnings will hugely increase the value of most of the companies in the index. In the 20th Century, the Dow-Jones Industrial Average increased by about 175-fold, mainly because of this retained-earnings factor.
Considering everything, I believe the probability of a decline in the index over a one-hundred-year period to be far less than 1%. But let’s use that figure and also assume that the most likely decline – should one occur – is 50%. Under these assumptions, the mathematical expectation of loss on our contract would be $5 million ($1 billion X 1% X 50%).
But if we had received our theoretical premium of $2.5 million up front, we would have only had to invest it at 0.7% compounded annually to cover this loss expectancy. Everything earned above that would have been profit. Would you like to borrow money for 100 years at a 0.7% rate?
Let’s look at my example from a worst-case standpoint. Remember that 99% of the time we would pay nothing if my assumptions are correct. But even in the worst case among the remaining 1% of possibilities – that is, one assuming a total loss of $1 billion – our borrowing cost would come to only 6.2%. Clearly, either my assumptions are crazy or the formula is inappropriate.
The ridiculous premium that Black-Scholes dictates in my extreme example is caused by the inclusion of volatility in the formula and by the fact that volatility is determined by how much stocks have moved around in some past period of days, months or years. This metric is simply irrelevant in estimating the probabilityweighted range of values of American business 100 years from now. (Imagine, if you will, getting a quote every day on a farm from a manic-depressive neighbor and then using the volatility calculated from these changing quotes as an important ingredient in an equation that predicts a probability-weighted range of values for the farm a century from now.)
Though historical volatility is a useful – but far from foolproof – concept in valuing short-term options, its utility diminishes rapidly as the duration of the option lengthens. In my opinion, the valuations that the Black-Scholes formula now place on our long-term put options overstate our liability, though the overstatement will diminish as the contracts approach maturity.
Even so, we will continue to use Black-Scholes when we are estimating our financial-statement liability for long-term equity puts. The formula represents conventional wisdom and any substitute that I might offer would engender extreme skepticism. That would be perfectly understandable: CEOs who have concocted their own valuations for esoteric financial instruments have seldom erred on the side of conservatism. That club of optimists is one that Charlie and I have no desire to join.
-The 2008 Berkshire Hathaway shareholder letter
The first thing to understand is the pricing of options. Option pricing is coupled to the market value of the underlying company and a premium. The market value is just that, the current price being assigned to a stock on the open market. The key is on how this premium is determined. Premiums are calculated using a mathematical model called the Black-Scholes model. It is this mathematical model that value investors need to thank. The Black-Scholes model makes one big assumption. That markets are highly efficient (stocks are properly priced at all times). Of course, the reality is that markets are not efficient and this is how value investors can take advantage of call options on occasion.
The Black-Scholes assumption on efficient markets causes it's focus to be on volatility. Volatility is a horrible predictor of future share prices, especially with a long term investment window. In essence, the Black-Scholes model couples volatility to risk. Therefore the premium part of the options equation is tightly coupled to volatility of the more recent past.
From the 2008 Berkshire Hathaway annual report (full excerpt at bottom of article):
If the formula (Black-Scholes) is applied to extended time periods, however, it can produce absurd results. In fairness, Black and Scholes almost certainly understood this point well. But their devoted followers may be ignoring whatever caveats the two men attached when they first unveiled the formula.
This pricing model is the aspect that value investors can take advantage of. Specifically, long term call options can be used to profit off of this folly. More specifically, boring stocks that have become undervalued may present opportunity. Of course this is hit and miss since far out of the money call options are needed in addition to low volatility. Also, the risk associated with this is loss of capital (up to 100%).
So, the key is to find a good company that hasn't done much for an extended period of time. And a company that is simply undervalued by atleast 33%. In practice, you should be hunting for undervalued stocks and the fact that it has low volatility (and small option premiums) should be more of a coincidence. A coincidence worth looking for while researching companies. It is hard to seek out these companies specifically. Good call option opportunities may arise only once every few years. The harder you look though, the more often opportunities will appear. 6 or more months of low volatility is typically required for minimal premium assignment.
As a current example, take Johnson & Johnson (ticker:JNJ) which is a high quality company trading at $63.45 per share. It's share price has also traded in a small range for an extended period of time (6+ months). Over the past year, it's price has stuck between $46.25 and $65.95 with very few spikes and it has tightly tracked the Dow. Because of this, the Black-Scholes formula assumes that JNJs options deserve a small premium. Currently, January 2012 call options at the $90 strike are only worth about 25 cents. The assumption here is that JNJ is undervalued and worth over $100. Assuming that JNJ is a truly good company, it will probably be worth even more in 2012. After all, price follows value over the long term.
This proposed strategy recommends one immediate action be taken after purchasing the call options. Place a limit order to sell about 1/3 of the options for 3 times or more than the price that was paid for them. The portion and limit order price doesn't really matter as much as its purpose. The purpose is to set up a limit order that will recoup the investments costs after commissions as soon as possible. Remember, loss of 100% of your investment can happen with call options so breaking even is always a good idea. Even if something is undervalued, it can take years for Mr Market to agree. Even if only 50% is recouped up front, this will minimize the potential loss to 50%. These are options though, and this may never happen. A 100% loss could still occur. Trying to sell 1/3 of the options for 80 cents a piece, for example, is of the utmost important.
The remaining call options is where the money may or may not be made. If Mr Market plays nice, and JNJ does reach $100 per share within 2 years, those options will be worth $10 or more a piece. This represents a handsome gain! Depending on timing and premiums assigned (thanks to the Black-Scholes formula), the call options might be worth $10 each when JNJ is at $90 per share. The gains possible are clearly great and this is what value investors may decide to try and exploit. However, losses are also possible and a 100% loss could also occur. Never forget that the greatest risk is the risk of loss of capital. Minimize your exposure to options as much as possible. Doing call options with less than 5% of ones portfolio is highly recommended since a 5% loss loss is not catastrophic. This strategy is a risk/reward proposition where one must be convinced that the typically outcome is positive.
A follow up discussing a naked put strategy can be found here
DISCLOSURE: The author of this article owns JNJ stock and 2012 LEAP options at the $90 strike. Options are a high risk strategy in which a 100% loss of capital can occur. The author of this article takes no responsibility regarding actions taken by readers of this article.
Excerpt from the 2008 Berkshire Hathaway annual report (page 20, 21):
The Black-Scholes formula has approached the status of holy writ in finance, and we use it when valuing our equity put options for financial statement purposes. Key inputs to the calculation include a contract’s maturity and strike price, as well as the analyst’s expectations for volatility, interest rates and dividends.
If the formula is applied to extended time periods, however, it can produce absurd results. In fairness, Black and Scholes almost certainly understood this point well. But their devoted followers may be ignoring whatever caveats the two men attached when they first unveiled the formula.
It’s often useful in testing a theory to push it to extremes. So let’s postulate that we sell a 100- year $1 billion put option on the S&P 500 at a strike price of 903 (the index’s level on 12/31/08). Using the implied volatility assumption for long-dated contracts that we do, and combining that with appropriate interest and dividend assumptions, we would find the “proper” Black-Scholes premium for this contract to be $2.5 million.
To judge the rationality of that premium, we need to assess whether the S&P will be valued a century from now at less than today. Certainly the dollar will then be worth a small fraction of its present value (at only 2% inflation it will be worth roughly 14¢). So that will be a factor pushing the stated value of the index higher. Far more important, however, is that one hundred years of retained earnings will hugely increase the value of most of the companies in the index. In the 20th Century, the Dow-Jones Industrial Average increased by about 175-fold, mainly because of this retained-earnings factor.
Considering everything, I believe the probability of a decline in the index over a one-hundred-year period to be far less than 1%. But let’s use that figure and also assume that the most likely decline – should one occur – is 50%. Under these assumptions, the mathematical expectation of loss on our contract would be $5 million ($1 billion X 1% X 50%).
But if we had received our theoretical premium of $2.5 million up front, we would have only had to invest it at 0.7% compounded annually to cover this loss expectancy. Everything earned above that would have been profit. Would you like to borrow money for 100 years at a 0.7% rate?
Let’s look at my example from a worst-case standpoint. Remember that 99% of the time we would pay nothing if my assumptions are correct. But even in the worst case among the remaining 1% of possibilities – that is, one assuming a total loss of $1 billion – our borrowing cost would come to only 6.2%. Clearly, either my assumptions are crazy or the formula is inappropriate.
The ridiculous premium that Black-Scholes dictates in my extreme example is caused by the inclusion of volatility in the formula and by the fact that volatility is determined by how much stocks have moved around in some past period of days, months or years. This metric is simply irrelevant in estimating the probabilityweighted range of values of American business 100 years from now. (Imagine, if you will, getting a quote every day on a farm from a manic-depressive neighbor and then using the volatility calculated from these changing quotes as an important ingredient in an equation that predicts a probability-weighted range of values for the farm a century from now.)
Though historical volatility is a useful – but far from foolproof – concept in valuing short-term options, its utility diminishes rapidly as the duration of the option lengthens. In my opinion, the valuations that the Black-Scholes formula now place on our long-term put options overstate our liability, though the overstatement will diminish as the contracts approach maturity.
Even so, we will continue to use Black-Scholes when we are estimating our financial-statement liability for long-term equity puts. The formula represents conventional wisdom and any substitute that I might offer would engender extreme skepticism. That would be perfectly understandable: CEOs who have concocted their own valuations for esoteric financial instruments have seldom erred on the side of conservatism. That club of optimists is one that Charlie and I have no desire to join.
-The 2008 Berkshire Hathaway shareholder letter
