ATESTOCK ANDOPTIONS
T
he “equity culture” of the late nineties led to manychanges in employee compensation as stock purchaseplans and option grants worked their way down the foodchain. We’ve all heard the good stories (the hourlyworker at Wal-Mart retiring a millionaire through theregular purchase of company shares), the bad (piles of options indot-bomb companies, accepted as a trade-off for a lower salary,expiring worthless), and the ugly (Enron employees losing their jobsthe same week as their 401(k), loaded with company stock,201Copyright 2003 by The McGraw-Hill Companies, Inc. Click Here for Terms of Use.
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imploded). Increased ownership of company stock and stockoptions presents new challenges and investment dilemmas in addition to their well-known beneﬁts. This chapter will address some ofthese issues.Before taking any action, investors who own shares of or optionson their employer’s company should verify what is and is not permitted under their company’s rules. Some of these rules are explicit(the interdiction to sell designated shares before you are 47 yearsold), others maybe less so (the prohibition of writing covered callsagainst company stock). Double-check before taking any action.
Equity CollarsCan one have too much of a good thing? If the good thing is a stock,the answer is yes. Consider these two examples:■
Mrs. Jones has been buying her company’s shares for the last 14years. It’s the only stock she owns, and it represents a substantial percentage of her net worth.
■
Mr. Smith has just sold the company he founded 12 years ago toa multinational that paid him with its stock, rather than cash.
Sometimes it is difﬁcult or impossible for an investor to reduce anoversized position. The obstacle may be real (the investor is prohibited from selling) or psychological (an employee is afraid of jeopardizing future career prospects if the company interprets the saleof its stock in a negative light). In either case, there may come a pointwhere protection of capital becomes a priority.It’s hard to argue against the advantages of going long some putoptions to protect an equity position: they limit the downside risk,maintain the stock’s upside potential, and help the holder sleep atnight. The problem is, buying these puts costs money. Someone whohas accumulated a substantial position in the shares of Costco(COST) might hesitate to pay $1.30 to purchase the April 40 puts(with eight weeks until expiration) when the stock is trading at$42.09. The cost of two months’ protection is more than 3% of thestock price and could represent a serious cash drain for someonewith a substantial number of shares.
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$3
Profit/(Loss)
$2$1$0($1)($2)($3)$30
$35
$40
$45
$50
$55
Price of COST at Expiration
Figure 8.1 COST Collar
But for someone whose main concern is preservation of capitaland who may be willing to give up something besides cash, anequity collar may be a viable solution. This strategy consists of purchasing a protective put, for example the April 40 put at $1.30 mentioned above, and ﬁnancing the purchase by writing a call option,maybe the April 45 call at $0.90. Writing the call does limit the proﬁtpotential on the stock, but it also cuts the cost of the hedge to $0.40per share.The collar, in fact, accomplishes two things. First, it limits thedownside risk on the stock since the put gives the investor the rightto sell COST at $40. Second, it limits the upside on the stock fromthe current price of $42.09 to the call’s strike price of $45. Quantifying these numbers we get a risk of $2.49 (the loss from $42.09 to theput’s $40 strike plus the $0.40 cost of the position) and a proﬁtpotential of $2.51 (the stock’s appreciation from $42.09 to the call’sexercise price of $45 less the $0.40 cost of the collar). This resultingrisk-reward proﬁle is illustrated in Figure 8.1.What if our investor wants to hedge the position for longer thaneight weeks? To determine the cost, let’s look at COST optionquotes, with the stock at $42.09:
AprilJulyOctoberJanuary
45 Call$0.90–$0.95$2.00–$2.10$3.20–$3.30$4.40–$4.60
40 Put$1.15–$1.30$2.15–$2.25$3.10–$3.30$4.00–$4.20
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Table 8.1Buy 40 Put
Write 45 Call
Cost of Collar
April
$1.30
$0.90
$0.40
July
$2.25
$2.00
$0.25
October
$3.30
$3.20
$0.10
January
$4.20
$4.40
($0.20)
Table 8.1 calculates the cost of the 40–45 collar for various expiration dates.It may come as a bit of a surprise that the longer-dated collarsactually cost less than the shorter-dated ones. In fact, the January40–45 collar can be established for a small credit. Many investorsstructure their collars so that the premium received from writingthe call fully offsets the cost of the put. This is known as a zero-costcollar. This may seem advantageous—more time for less money—but there is another side to the coin, as you will see in the nextsection.Anyone who decides to collar his corporate shares should remember that it involves writing a call, and for this call to be covered, thestock cannot be hindered by any selling restrictions. In most cases,the stock needs to be deposited with the broker executing the collar to margin the short call position.
Reality Interferes with TheoryWhen we pulled up the COST option quotes for our collar example,the risk-free interest rate, as deﬁned by Treasury bills, was hovering somewhere below 2%. Cash was trash. This fact (reality) interfered with a phenomenon (theory) that is usually observed withcollars but was not in evidence here. We offer some theoreticaloption prices in Tables 8.2 and 8.3 to illustrate this point. We createdscenarios with 3% and 6% risk-free rates for two stocks, one with25% volatility (blue-chip range) and one with 50% volatility (hightech range). Both tables assume a stock price of $42.50. Here is whatwe found.
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Table 8.2Volatility ⫽ 25%3 Months
6 Months
9 Months
1 Year
2 Years
$1.26
$2.22
$3.04
$3.75
$6.06
$0.96
$1.61
$2.14
$2.57
$3.76
$0.30
$0.61
$0.90
$1.18
$2.30
$1.37
$2.47
$3.44
$4.31
$7.20
$0.88
$1.44
$1.87
$2.21
$3.06
$0.49
$1.03
$1.57
$2.10
$4.14
With 3% 45 CallRisk-free 40 PutRateDifferenceWith 6% 45 CallRisk-free 40 PutRateDifference
Let’s start with Table 8.2, looking at the 40–45 collar under the 3%risk-free interest rate assumption. The 3-month collar can be established for a $0.30 credit. This is usually the case for collars when thestock is sitting halfway between the two strike prices, as the call willgenerally be worth slightly more than the put. As the time to expiration increases, the credit becomes larger, to the point where thetwo-year collar can be initiated for a $2.30 credit, virtually eliminating all risk from the position. Remember that the worst-case scenario has the stock falling below $40, in which case a $2.50 loss isrealized on the stock. If the collar was initiated for a $2.30 credit itvirtually absorbs all of this loss.Moving down to the same collar under the 6% interest rateassumption, we ﬁnd larger credits, to the point where the two-yearcollar is not only risk-free, but is generating a proﬁt under all possible outcomes. The $4.14 credit more than makes up for the maximum $2.50 loss realized if the stock goes below $40, leaving a $1.64proﬁt under the worst-case scenario. A rise of the stock to $45 orhigher would generate a $2.50 proﬁt on the stock that, added to theinitial $4.14 credit, produces a total gain of $6.64. An ideal “can’tlose” situation.Or is it? An investor who initiates a two-year collar has eliminatednot only all of the downside risk, but also most of the proﬁt potential. This investor has, in fact, turned the stock position into something that looks a lot like a ﬁxed-income instrument. There is noout-of-pocket cost to establish the option position, but there are
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Table 8.3Volatility ⫽ 50%3 Months
6 Months
9 Months
1 Year
2 Years
$3.36
$5.26
$6.73
$7.98
$11.82
$2.88
$4.40
$5.53
$6.46
$9.06
$0.48
$0.86
$1.20
$1.52
$2.76
$3.49
$5.15
$7.11
$8.48
$12.75
$2.77
$4.17
$5.17
$5.98
$8.16
$0.72
$0.98
$1.94
$2.50
$4.59
45 Call
With 3%Risk-free 40 PutRateDifferenceWith 6% 45 CallRisk-free 40 PutRateDifference
plenty of opportunity costs. Of course, moving synthetically froman equity position to something that looks like cash may be whatsomeone with an overexposure to one stock is trying to accomplish.(Note that this type of position—where an investor eliminates allrisk and virtually all proﬁt potential—has caught the attention ofpeople at the U.S. Treasury. See the section on taxes in Chapter 10before trying this at home.)Moving down to Table 8.3, we ﬁnd results that once again mayappear counterintuitive: collars on a 50% volatility stock generatea higher credit than those on a 25% volatility equity. In fact, underthe 6% interest rate assumption, the $2.50 credit obtained in establishing the one-year collar is sufﬁcient to completely eliminate theposition’s risk. Using two-year options generates a $4.59 credit,guaranteeing a $2.09 proﬁt no matter what the stock price at expiration. This, of course, is great news for those looking to reduce oreliminate the risk of a stock position: the hedged position will return4.9% in the event that the stock drops below $40 and 16.7% if it risesabove $45—roughly 2.43% annualized and 8.0% annualized if oneassumes annual compounding. One associates returns like thesewith cash, not with a 50% volatility stock.Other Potential Collar BuyersBuying a collar might be of interest to traders and investors who arenot necessarily overweighed in one stock. Consider the case of a
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207
trader who has held a stock for 11 months, during which time thestock has doubled in value. Selling now would generate a nice proﬁtbut would also incur a tax bill based on the short-term capital gainsrate. Holding on for one more month would substantially reducethe tax bill, but the reduction could be the result of the stock goingdown as much as the result of the more favorable tax treatment. Theappropriate collar could help reduce the downside risk of the position while the holding period meter keeps running.An equity collar would also do the job for an investor who ﬁndsherself with a substantial long-term capital gain in November orDecember but wants to postpone the gain until the following taxyear, even though she will beneﬁt from the lower tax rate. Beforeinitiating a collar for tax reasons, see Chapter 10 and make sure youhave up-to-date information on the tax treatment of collars becausethe rules change faster than a book can be printed.
The Two Half-Collars: Buying Puts,Writing CallsIf collars can be used to hedge an overweighed stock position, socan half-collars—either writing the calls or purchasing the puts. Ifan investor owns some shares without any restrictions, she candeposit them with her broker and write covered calls. Anotherinvestor might be receiving unrestricted shares in a few months andwould still like to write calls against those shares. The only solutionfor this second investor is to get approval from her broker to writeuncovered calls, provide the margin necessary to maintain this position, and monitor the position closely to avoid early assignment. Ofcourse, this assumes she is not prohibited from writing calls on hercompany’s stock. Very few investors will want to put up with allthese restrictions. Furthermore, writing covered calls against anoverweighed stock position only provides partial downside protection; this is where the strategy falls short of the desired riskreduction.The last avenue left to explore is the purchase of protective puts.These have the double advantage of offering as much downside protection as an investor desires (through strike price selection) andmaintaining the underlying stock’s full upside potential. They also
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can be quite expensive, and we have seen many investors decide totake their chances when we pulled up quotes on put options andtold them how much it would cost to insure their holdings.Buying Partial InsuranceThere is no need for an investor with a large stock position to insureevery share held. Insurance can be purchased on part of the position to protect the core of the holdings, and the balance of the sharescan be held unhedged. It is easy to understand how one would buyputs on only a half, a third, or a quarter of a stock held. In this section, we want to highlight options’ ﬂexibility and show that buyingpartial insurance can mean more than buying 50 puts to hedge halfof a 10,000 share position.Take the situation of a longtime employee who has accumulated5,000 shares of Plodding Along (PAL), now trading at $100. Thisemployee will be retiring in one year, at which point she will be freeto sell any or all of her PAL shares. Having half a million dollars tiedup in one security makes her somewhat nervous, especially whenthis represents the core of her retirement nest egg. Looking at oneyear LEAPS she ﬁnds the following:PAL:100 put:95 put:90 put:85 put:80 put:75 put:
$100$12.10$9.80$7.60$5.70$4.10$2.85
Fully insuring her holdings would entail purchasing 50 of the 100puts, at a cost of $60,500 ($12.10 ⫻ 50 ⫻ 100). This choice insures allof her shares, with no deductible, but at a cost of 12% of her stockposition’s value. This is where a lot of would-be hedgers back off:they are all in favor of insurance, but not at this cost.Our investor needs to determine how much she is willing tospend for insurance. If 12% is too high, what about 6%? There isobviously no correct answer here, but for the purpose of our example, let’s see what type of insurance she can buy with a 5% limit.
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Hedging fewer than 5,000 shares: in dollar terms, 5% of the valueof our investor’s holdings represents $25,000. This sum could beused to purchase 20 of the 100 puts, 25 of the 95 puts, 43 of the 85puts, or 50 of the 80 puts. This last alternative would cost only$20,500 and insure all of her shares; but the amount by which theseoptions are out-of-the-money would force our investor to absorb theﬁrst 20% drop in the price of PAL. For argument’s sake, let’s assumeshe is most comfortable purchasing 25 of the 95 puts. These insurehalf of her holdings, and she can easily cope with the options beingonly 5% out-of-the-money.Another way for this investor to obtain partial insurance wouldbe to insure all of her shares but to obtain coverage over only a limited range. For example, she could purchase 50 of the 95 puts at$9.80 each and simultaneously write 50 of the 80 puts at $4.10 percontract. Her insurance cost would then be $5.70 per share, slightlyhigher than her 5% limit. Let’s explore this further before beggingoff because the spending cap has been breached.Readers will have recognized the long 95/short 80 put positionas a bear put spread, described as a trading strategy in Chapter 6.Here we are using what was previously described as a trading strategy to hedge. First let’s do a quick analysis in terms of rights andobligations. Our investor purchases 50 of the 95 puts: this gives herthe right to sell her 5,000-share position at $95. She can consider herself to be fully insured. She also wrote 50 of the 80 puts, obligatingherself to purchase 5,000 shares of PAL at $80. Should she be forcedto reestablish her stock position at $80, her newly acquired shareswould then be held without any downside protection. In otherwords, the bear spread insures our investor from $95 down to $80,but no further.Since this bear spread is purchased on a share-to-share basis withthe stock held, the overall position can be easily summarized, as inTable 8.4.A few comments on Table 8.4. The value of the 80 put appears asa negative number since the investor is short this option and willhave to repurchase it at expiration if she does not want to beassigned. The far-right-hand column is the overall proﬁt and lossbased on a starting stock price of $100 and the ending value of thebear put spread. We have not asked our investor the average cost ofher PAL shares, but we can probably safely assume that since these
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The Options Strategist
Table 8.4PAL atOptionExpiration
Proﬁt/(Loss)on Stock
Value of95 Put
Value of80 Put
Cost ofPutSpread
TotalProﬁt/(Loss)
$110
$10
$0
$0
($5.70)
$4.30
$105
$5
$0
$0
($5.70)
($0.70)
$100
$0
$0
$0
($5.70)
($5.70)
$95
($5)
$0
$0
($5.70)
($10.70)
$90
($10)
$5
$0
($5.70)
($10.70)
$85
($15)
$10
$0
($5.70)
($10.70)
$80
($20)
$15
$0
($5.70)
($10.70)
$75
($25)
$20
($5)
($5.70)
($15.70)
$70
($30)
$25
($10)
($5.70)
($20.70)
have been accumulated over many years it is signiﬁcantly below thecurrent $100 stock price.Figure 8.2 compares an unhedged equity position, a partial hedgecreated by purchasing 95 puts on half the shares held, and a partialhedge created by purchasing the 95–80 bear put spread. Proﬁts andlosses are calculated on a per share basis. The result shown for the
Profit/(Loss) per Share
$20$10$0
PAL95 PutPut Spread
($10)($20)($30)($40)$60
$70
$80
$90
$100
PAL Price at Expiration
Figure 8.2 Hedging PAL
$110
$120
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211
long 95 put strategy is actually an average of half hedged shares andhalf unhedged shares.This ﬁgure gives us a visual representation of how two of the possible hedges perform. If PAL’s price is up from the current $100 atoption expiration, they have very comparable costs: the equivalentof $4.90 per share for the 95 puts (the cost of each put was $9.80, butonly half the number of contracts necessary to cover the stock position was purchased), and $5.70 per share for the bear spread. Below$95, the bear spread, at least initially, offers better protection, as thelong 95 puts fully hedge the long stock. Below $75, since the bearspread only offered protection down to $80, the half-position in the95 puts offers a more efﬁcient hedge than the bear spread. Twoinsurance strategies with similar initial costs but different downsideprotection. We view this choice as an illustration of the ﬂexibility ofoptions, not as an additional headache.The bear spread we chose was one of many that are possible. Wecould also have purchased the 100 puts and written the 80s (for an$8 debit), or bought the 90s and written the 75s for a $4.85 cost. Howdoes one choose which option to buy and which one to write, or atleast narrow down the ﬁeld? We like to start with the approximateamount we are willing to spend on a hedge. In the above example,this was 5% of the stock’s value for 12 months of protection. We thenlook at which spreads such an amount will buy. In addition to the95–80 spread at $5.70, the 100–90 spread was $4.50. The 100–90spread was a little less expensive, at-the-money, but the two strikeprices were only $10 apart. Spending an additional $1.20 gave us afull extra $5 of protection (when the goal is insuring a long stockposition, the wider the spread, the better). Once again, the ﬁnal decision becomes a function of personal preference, risk aversion, andwhich spread feels best given what we know of PAL and our perception of potential risk over the next 12 months.Finally, for those investors who may have skimmed over thespreading strategies in Chapter 6, we would strongly recommendgoing back and paying special attention to the price behavior ofspreads over time and how they tend not to reach their maximumtheoretical value until very close to option expiration. Time spentreviewing that section may eliminate some unexpected frustrationsdown the road.
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Hedging Corporate Stock OptionsAnyone who is looking to hedge a position in corporate optionsshould begin by verifying what is permissible under corporate policy and that it will not be a “career limiting move.”
A Note on NomenclatureWhen dealing with exchange-traded options, the standard is to talkin terms of contracts, each covering 100 shares of underlying stock.In the world of corporate options, if someone is granted 5,000options this refers to options on 5,000 shares, not 500,000. We willtry and keep this distinction clear in our discussion.Also, executive options usually vest after a set time period. Beforethey are vested, options are, for this discussion, worthless becausethey cannot be exercised. Needless to say, we assume that theoptions being hedged have vested.
What and When to HedgeHedging corporate stock options seems like a redundancy: optionsprovide a natural hedge with limited risk and full upside potential.And because corporate options are generally granted at no cost tothe employee (employees do not have to pay the option’s premium,although they will have to pay an amount equal to the option’sstrike price in order to purchase the stock upon exercise), the limited risk aspect turns out to be no risk, while the full upside potential is obtained. To make the option holders’ life even easier, mostcorporations provide a cashless exercise feature, where the stockunder option can be purchased through exercise and sold immediately without the option holder having to put up any capital. Sowhat is there to hedge?Not the options themselves, but the options when they start acting like the underlying stock; in other words, when they are in-themoney by a substantial amount. In-the-money options representunrealized gains, and although the gains cannot turn into losses,they can easily disappear. And this is the object of our attention:in-the-money call options that represent accrued but unrealizedproﬁts.
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If It Looks Like Stock . . .If an in-the-money call option looks like the underlying stock,behaves like stock, and goes up and down in value like stock, thenit is probably wise to treat it like stock. This means that the equityhedging strategies discussed above should apply. The problem isthat the option holder is not in possession of the stock, even thoughhe may be free to exercise his options at any point in time. Writingcalls, or purchasing a collar (which involves writing calls), wouldentail margining uncovered options, which is not a very attractiveproposition. So are we back to square one?Studies show that executives place a lower value on their corporate options than the market does. The likely explanation is that tothe executives these options represent more of the same: they areemployed by the ﬁrm, probably own shares of stock, and now aregetting options. The end result is too many eggs in the employer’sbasket, so it is not surprising that an outside investor, whose portfolio is otherwise well diversiﬁed, would place a higher value onthese same options.Another possible explanation is that executive options are not allthey appear to be. In Chapter 1 we noted that the buyer of a call hasto take one of three actions: let the option expire, exercise it, or sellit to close the position. When someone is granted company options,the third choice is not available: the options have to be exercised or,if they are out-of-the-money, kept until they expire worthless. Thisrestriction means corporate options should be discounted whencompared to equivalent listed options. This also is illustrated in thefrequency of early exercise. With listed options it very seldommakes any economic sense to exercise a call early. But with corporate options, this occurs frequently. To gauge the cost of exercisingoptions early, look at Table 8.5, which calculates the theoretical values of different in-the-money call options with a $50 strike price.Assume corporate options were granted quite a few years ago,when the stock was at $50 (the price that became the options’ strikeprice). The stock has risen to $75, but the options still have two yearsuntil expiration. An employee who wants to lock in some of thestock’s gains could exercise and would net $25, assuming a cashlessexercise. But if this employee could simply sell her options, shewould pocket a little over $30, assuming the options are priced witha 30% volatility. Some would see her as “leaving $5 on the table,” or
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Table 8.5
One-Year Option
30%Volatility Two-Year OptionOne-Year Option45%Volatility Two-Year Option
Stock at $75
Stock at $100
$27.51
$52.01
$30.42
$54.23
$29.26
$52.61
$33.55
$56.04
20% of her realized gain. If the underlying stock is riskier and itsoptions are priced with a 45% volatility, the opportunity loss is morethan $8.50, or about 34% of her realized gain. Even with the stock at$100 (and the options 100% in-the-money), early exercise results inan apparent opportunity loss.Of course, no money is being left on the table because the difference outlined here really represents that between listed and corporate options. But it does open up an interesting strategy. Assume anexecutive holds some in-the-money options with two years remaining until they expire. If his goal is to generate cash to pay for a newhouse, a bigger boat, or a divorce settlement, his choice is limited:exercise the option and take the money. But if his primary goal is tolock in the accrued gain, and there is no immediate need for thecash, he could write uncovered call options with an expiration dateand strike price as close as possible to those of his corporate options.There will be two obstacles to writing the exchange-traded options:convincing his brokerage ﬁrm to approve his account for uncoveredcall writing and margining the position until expiration.If our executive holds any ﬁnancial assets, these can probably beused to margin the uncovered call position. Stocks, bonds, andmutual funds are all marginable, and it should be remembered thatmargining a short option position does not involve borrowingfunds and accruing interest expenses, but simply putting up sufﬁcient assets to show the ability to meet the obligation assumed inwriting options. He should be aware of the risks of early assignmenton short call options, as discussed in Chapter 4.Assuming these two obstacles can be overcome, writing uncovered calls against corporate options will have a double beneﬁt: theﬁrst is easily measurable in that the premium received from writing
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215
Table 8.6
One-Year Option
30%Volatility Two-Year OptionOne-Year Option45%Volatility Two-Year Option
Stock at $75
Stock at $100
$19.36
$42.65
$23.44
$45.78
$22.46
$44.11
$27.73
$48.99
the exchange-traded calls will be greater than the amount thatwould be obtained by exercising the corporate options. The secondadvantage may turn out to be tax related. Exercising corporateoptions immediately creates a tax liability. Writing uncovered callsagainst corporate options may or may not trigger a taxable event.The tax treatment may hinge on how similar in terms both optionsare. If they are deemed to be “essentially the same security,” thewriting of uncovered calls may trigger a taxable event.Which argues in favor of writing a materially different option. Tojudge if this makes economic sense, look at Table 8.6, which calculates the theoretical prices of options with a $60 strike price.To recap, we have an executive with the right to purchase company stock at $50, two years left on his corporate options, and thestock trading at $75. If he exercises his calls, he nets $25. If he writesan uncovered call, with