Is it frequently wrong to exercise employee stock options?

I've been thinking about the valuation of employee stock options lately. One of the key questions options-holders often ask themselves is when to exercise. Usually their main focus is the mostly fruitless question of timing the market - will the stock price go up? Will it go down?

My analysis, however, suggests that in certain circumstances, there is a much more important factor which always points towards holding. I would think that, if this were correct, it would be well known, so I may well be wrong, and if so I look forward to your enlightening comments. But if I'm right, it seems possible that a lot of people have made a lot of poor financial decisions.

First, it my help to acquaint yourself with my previous post on stock valuation. The gist is that a growth company which does not issue dividends should, on average, have its stock price grow at the prevailing interest rate for its level of risk. Next, it is important to note that employee stock options here are "American-style", meaning they can be exercised at any time before the expiration date. Furthermore, the expiration date is usually long after the vesting date (first date at which the option can be used), ie by 5-10 years.

Now a small example should be all it takes to demonstrate the relevant principle. Suppose I hold 2 options with a strike price of $100 for a stock whose current value is $200. My position is worth 2 x ($200-$100) = $200. The interest rate is 10%. Suppose I hold these options, what will happen in a year? The stock price should, on average, go up 10% to $220. My position will now be worth 2 x $120 = $240. Suppose instead I sell, and then invest in a broad index. I get $200 for selling. Now I invest @10%, and at the end of the year I have $220.

Where is the missing $20? It is the interest rate on the $200 in capital whose use I have foregone. By holding the options, I earn the interest rate on $400 of stock, whereas by exercising them, I earn the interest rate on $200 of an index fund. In other words, these 2 options (once we're well into the money) function as a *loan* of $200 in capital, at an interest-rate of zero, whose earned interest is all mine.

Now, this analysis was done on average. Clearly the *risk* of holding onto the option is much higher than the risk involved in an index fund. Yet I think one can reasonably argue that having to chop one's interest-bearing capital in half is rather a high price to pay for diversification. Furthermore, we can assume that the return on the individual stock is not just the market rate of return, but the *risk-adjusted* market rate of return, so it already includes some extra compensation for its riskiness. On the other hand, this stock is even riskier for you than for the market because your salary and job are correlated with its performance, hence this extra compensation would not be enough, by itself, to make it worth holding the stock, if it weren't for this extra facet.

Obviously as time goes on and the stock rises, the "base value" (strike price x number of options) becomes smaller and smaller relative to the appreciated value. Hence the extra return becomes smaller compared to the extra risk. But (on average) it should take 5 years to get to where the base value is only half of the productive capital. At this point, the hit in long-term earning potential from exercising is still huge - yet I get the feeling that most employees vest and exercise long before then.

It should be emphasized that this analysis only holds for certain situations. The necessary conditions for include, but are not limited to:

  • "Lent" capital must be large. Often employees of early-stage startups get their options at close to zero strike price, hence this principle does not apply.
  • The company must not be issuing, or planning to issue, substantial dividends. (Dividends transfer value away from the option-holder, as my earlier post discussed)
  • The current price must be reasonably fair, ie if you work for a 1999 dot-com with a huge stock price, little revenue, and no profits, you should probably get out while the getting out is good. (And also, let me know how you're reading this post - neat trick!)
  • You must not have a strongly-downward-sloping marginal utility of money. Alternately, you must not be extremely risk-averse. With enough risk-aversion, it may be correct to shift to much less profitable, but safer investments.
  • You must be willing to bear the pyschological costs (and "I told you so"-s) if your company's stock takes a nosedive.
  • You must not be planning to blame me if it turns out poorly.

Despite these caveats, it seems to me that far fewer people execute this strategy than meet these conditions situation. For example, this analysis suggests that its terrible to exercise options with a high strike price and only modest appreciation, yet I'm sure people do it. (Before I worked out this example, I would probably have done it myself, as part of fetishizing diversification). Is it extreme risk-aversion, ignorance of the relevant economics, or have I totally missed something?

UPDATE: This looks very relevant. Apparently there is a decent financial literature on exactly this subject.

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Besides the fact that you're

Besides the fact that you're completely ignoring the role of corporate earnings (not to mention the equity risk premium) in equity valuation, you're also overlooking that the very purpose of stock options is to enable leverage and hedging (i.e., to vary the potential upside/downside relative to your initial investment, or to customize your potential payoff function to your particulat risk profile). Why do you consider this mysterious?

Suppose the stock price, rather than rising to $220, fell to $100. The owner of stock loses 50% of his investment, the option holder loses 100%. Greater upside and greater downside. Again, why do you consider this mysterious?

There is no need to assume only increases in stock prices and no decreases, or to use your "loan" analogy or to make any of the quite limiting assumptions you make in the bullets. All you need is an investor/speculator seeking to craft an optimal payoff function given his risk profile and his expectations of a stock's future volatility (and of course the counterparties to enter into the derivatives contracts to make it possible).

Some thoughts: 1. Risk is

Some thoughts:

1. Risk is generally compensated for only when it can't be diversified away. Other investors can do this, but you can't, so you get the risk, but no risk premium. Of course, you do get the leverage, but...

2. The leverage cuts both ways. If the stock goes up, you make a lot of money, but if it drops sharply, you can lose a lot of money very quickly. And when a stock's trading at 80 times earnings, a disappointing earnings report can do just that.

3. Stocks are historically overvalued right now, which tilts the calculus in favor of taking the money and running.

4. I should have gone over to Google.

Brandon, 3. Stocks are

Brandon,

3. Stocks are historically overvalued right now...

In general? Not having any significant evidence either way, my expectation would have been that a significant majority of stocks have had significantly higher levels of overvaluation at some point in the last five years or so.

One test might be how many of the S&P500 stocks have fallen less in price from their historical peak than their EPS has over the same time frame. Alternately, look at charts of PE ratios.

Regards, Don

Brandon, Just looking at the

Brandon,

Just looking at the DOW30 stock prices and approximately comparing the current price vs the peak price between 1998 and 2002 --

5 stocks showed gains of 14% to 54%(CAT)

5 showed losses of 20% or less

9 showed losses of 35% to 49%

11 showed losses of 50% to 70%(INTC,MRK,GM)

Regards, Don

Don: Sorry; my phrasing was

Don:

Sorry; my phrasing was a bit ambiguous. I meant that stocks are overvalued by historical standards, not that their valuations are historical in their excesses.

I think your analysis leaves

I think your analysis leaves out one further advantage to holding--the consequence of being protected against extreme downside risk.

Assume a strike price of $100, a market price of $200, and an interest rate of 10%--ignore risk aversion, since it isn't central to the point I want to make. On average, the stock is worth $220 a year later. That average includes some probability that it will be worth less than $100, balanced by some probability of gains large enough to bring the average to $220.

If you hold the option you get the full value of any gains but bear only part of the loss, since if the price falls below $100 you don't exercise the option. So on average your return is more than 10%.

Dr. Friedman: It's true that

Dr. Friedman:

It's true that holding the option is safer than exercising the option and holding the stock, and I don't see that there's any good reason ever to do the latter unless the options are about to expire. But there's a third alternative which is safer than either, namely to exercise the option and sell the stock. Holding the options still has considerable downside risk compared to cashing out.

Brandon writes: The leverage

Brandon writes:

The leverage cuts both ways. If the stock goes up, you make a lot of money, but if it drops sharply, you can lose a lot of money very quickly.

Yes, but the thing is that this is not value-neutral leverage, its leverage on a significantly +EV bet.

David - Yes, that is additional value to the option.

All: Tax consequences are a significant additional effect as well. Let's add taxes to the example. I can hold my 2 options, and expect to make $40 next year. Or I can exercise, for a profit of $200, taxed as ordinary income, and keep $120 of it, which earns on average $12 next year. Yeah, its a leveraged bet, and yeah, there is more risk, but *look at that huge difference in EV* Call me a gambler, but $40 vs. $12 average return is enough to make me willing to take on quite a bit of risk!

As a personal financial

As a personal financial advisor, I have frequently had new clients come to me faced with this situation, and in the overwhelming majority of cases, I've advised immediate exercise and sale of most or all of the vested options until the client has realized enough money to achieve financial independence (assuming the stock was at least, say, 50% higher than the exercise price). The studies of wealth and happiness as well as my own experience with clients suggest that having enough to comfortably pay for basic food, clothing, and shelter has tremendous marginal utility over not being able to do so, but that incremental wealth beyond that adds comparatively little to expected happiness.

Acting rationally, if we had the opportunity to make a triple-or-nothing bet on the flip of a coin, we'd do it ... but not if the bet was for our entire net worth. Granted that my sample is a very biased one, the people seeking my advice on this question virtually always have the majority of their liquid net worth in these options, and many have 90% or more.

I was fortunate, in late 1999, to have a couple come to me seeking advice on how to minimize the income tax consequences of employee options in an Internet stock that had made them millionaires on paper. I suggested they simply hold onto the options for another year or two, since there was a good chance the stock would come down to earth, wiping out most or all of their gain and eliminating the income taxation problem. They got the point and cashed in enough of their lottery tickets to give them around $1 million after paying taxes before the bottom dropped out on their stock and their unvested options found themselves underwater. We then reinvested the proceeds in a thoroughly diversified portfolio that has continued to grow at a reasonable rate. Their colleagues, virtually without exception, netted little or nothing because they waited too long (and a few got really clobbered by exercising and holding their incentive stock options with the intention of holding them just over a year for long-term capital gains treatment, and ended up losing all the profits but owing taxes on them anyway because of the alternative minimum tax).

Assuming the options represent a small enough portion of the employee's net worth that the marginal utility of the unrealized gain at this point doesn't dwarf the marginal utility of doubling that amount, I do believe your thoughts are valid, since the premium that ought to be attached to the current option price for time remaining until expiration is not realizable on employee stock options that cannot be sold. But I believe this calculus doesn't apply to the overwhelming majority of employees in this situation, who will not yet have achieved basic financial independence with the rest of their net worth at the time the decision has to be made.

Of course, you cited this in your piece both in the acknowledgment of the diminishing marginal utility issue and your concession of the point that a broadly based index fund is less volatile than a leveraged holding in a single stock (boy, is THAT the understatement of the year!). When you consider that it is a leveraged investment in the stock of the company that also provides the employee's salary, it becomes even more obvious that this is not something to consider until enough money is off the table to make the balance a sporting wager and not a serious threat to the employee and their family.

But once it IS a sporting wager, I think your argument is entirely correct, and with clients who have enough in a diversified portfolio to assure their financial independence, I usually do suggest they hang onto their options until just before expiration based on the the same logic you provided (setting some reasonable limit such as 25% of their net worth so that a total loss won't be a personal disaster).

Given the history in recent

Given the history in recent years of catastrophic failures and devaluations of companies, things like Enron should teach everyone to have some kind of plan to exercise options, then sell to diversify their holdings. It's OK to keep some of the original stock for whatever reason.

You have to do this while the company looks good, so you don't risk a sudden halt in your ability to sell your stock or possibly be charged with trading based on insider information.

Patri, I think that in many

Patri, I think that in many cases your lack-of-risk-aversion criterion will fail, not because the absolute level of aversion is so extreme, but because of the *type* of aversion: an aversion to being very highly leveraged. Even when people can go into debt in a big way so as to increase their expected return (which is not always), they may not want to do so.

To take an example completely unrelated to any real situation: suppose you work for a tech company in the SF Bay Area and the value of your options is sufficient to allow you to make a reasonable (or more than reasonable) down payment on a ludicrously expensive Bay Area house. Suppose further that you would really like to buy such a house soon and to hold secure title to it so as to, say, settle down and raise a kid or two there.

Rather than exercising your options, you could hold onto them and go into more debt to get your house, perhaps taking out one of those fancy interest-only mortgages. Your analysis suggests that, as long as you expect the appreciation rate of the stock to be greater than that of real estate, this approach would increase your expected return. But I suggest that a lot of people would rather take the cash, get equity in their house, and sleep more soundly at night.

Brandon: It’s true that

Brandon: It’s true that holding the option is safer than exercising the option and holding the stock, and I don’t see that there’s any good reason ever to do the latter unless the options are about to expire. But there’s a third alternative which is safer than either, namely to exercise the option and sell the stock. Holding the options still has considerable downside risk compared to cashing out.

But what do you do with that capital? If you invest it at the risk-free rate, you may be protecting your capital, but at a huge cost in future earn. Suppose the risk-free rate is 5% in my example, now with taxes as mentioned above, you can expect to earn $6 next year instead of $40, just to protect $120 in capital. Does that really seem like its worth it? Even to expect to earn $12 instead of $40 to give your $120 in capital the risk of a broad index instead of a single stock seems pretty questionable.

If your goal is to live on the capital, ok sure, you don't want to face the risk. But if your goal is to accumulate wealth, say to retire early, then this seems like a horrible tradeoff to make.

Less - You make a number of good points, but I think many were covered by my caveats. For example, I specifically mentioned your high-flying stock example, if you think the stock will drop sharply then of course you should exercise. I also mentioned the declining marginal utility of money. If you can exercise enough to be "set for life" right then, then it makes sense to do so.

But I believe this calculus doesn’t apply to the overwhelming majority of employees in this situation, who will not yet have achieved basic financial independence with the rest of their net worth at the time the decision has to be made.

But this is exactly when it is the most important to hold! You will take many more years, on average, to achieve financial independence if you exercise. Just look at the math of my example, especially with taxes. You can expect to earn less than a third the investment return if you exercise as if you hold. How does it make any sense to tell someone that the way to achieve financial independence is to dramatically decrease their investment income?!

I guess it all comes down to beliefs about risk, and your alternative income options. If you have the nest egg and the earning power to be able to recover from your options being wiped out, then its a lot easier to gamble.

Patri, I think that in many

Patri, I think that in many cases your lack-of-risk-aversion criterion will fail, not because the absolute level of aversion is so extreme, but because of the type of aversion: an aversion to being very highly leveraged. Even when people can go into debt in a big way so as to increase their expected return (which is not always), they may not want to do so.

Yes, but there is no debt here. The more analogous situation is that you've been offered free leverage, but just once. You've been given an interest-free loan to buy stock in one company (unfortunately the company you work for). Not only is the loan interest free, but if the stock is down, you don't have to pay back the loan. If the stock appreciates, you get to call it quits and get the appreciation, but then the loan disappears. Throwing away the use of that capital is just such a *huge* cost, especially when you consider the tax consequences.

To take an example completely unrelated to any real situation: suppose you work for a tech company in the SF Bay Area and the value of your options is sufficient to allow you to make a reasonable (or more than reasonable) down payment on a ludicrously expensive Bay Area house. Suppose further that you would really like to buy such a house soon and to hold secure title to it so as to, say, settle down and raise a kid or two there.

Rather than exercising your options, you could hold onto them and go into more debt to get your house, perhaps taking out one of those fancy interest-only mortgages. Your analysis suggests that, as long as you expect the appreciation rate of the stock to be greater than that of real estate, this approach would increase your expected return. But I suggest that a lot of people would rather take the cash, get equity in their house, and sleep more soundly at night.

I dunno, I think there are some issues with this. For one thing, whether you make a down payment or do an interest-only mortgage, either way you are making a highly leveraged bet on local real estate. So you've greatly increased your risk either way you do it. Is the difference in risk by having the higher down payment really so high? It seems to me that its actually a fairly small difference in leverage. Whereas exercising is a huge difference in future earning power (a factor of 3.33x when the stock has doubled).

I think its important to remember here that diversification and sleeping well at night are all well and good when the differences in earning power are small. But here the difference in earning power is *HUGE*. Call me a gambler, but I'd sleep better at night knowing that my vested options are earning 3.33x as much as if I'd exercised them.

(Also, stepping away from efficient markets, I guess I see Bay Area real estate prices as much more likely to be in a bubble, and fall, than Bay Area tech company stock prices.)

Patri: It depends on how

Patri:

It depends on how much the options are worth. If I had, say, a million dollars, you would have to give me very good odds to convince me to risk that money for any amount, because that's already enough to give me all the material goods I really want out of life, or at least close enough that I could make up the rest in a few years. Sure, ten million would be great, but if it was all I had, I wouldn't bet one for ten on the flip of a coin, because that first million is worth more to me than the other nine. On the other hand, if I had two million in options, and I didn't have good reason to believe the stock was headed south, I might only exercise half and hold the rest.

All of your arguments make sense for someone with a minority---or maybe even a slight majority---of his wealth in ESOs. But they don't make sense for an even moderately risk-averse person with 90% of his wealth riding on them.

One way to protect your profits while leaving open the possibility for more gains might be to buy out-of-the-money put options on the underlying stock (assuming your employer allows it). This would reduce your gains (I'm not sure by how much), but it would protect you against a catastrophic drop in the stock price. At the very least, I would use some kind of trailing stop strategy, such as cashing out some or all of my options if they ever dropped, say, 30% below their peak value.

Brandon - You can't buy puts

Brandon - You can't buy puts on the stock of the company when you are holding employee stock options in the company, but you CAN do so on an industry index. To protect unvested options for some clients in one particularly Internet company, I recommended they buy puts on an Internet index (which included their company). Again, just to the extent necessary to guarantee financial independence. Like all insurance, buying out-of-the-money puts is not expected to be a profitable act, but is designed to protect against a calamity the insured can't handle.

Patri - It really does boil down to how much you're willing to risk on one flip of a coin. As I noted, the limit I've normally suggested to clients was 25% of their net worth. You can't just speak of $40 vs $12 as if that were the end of the argument. If you had the choice of a net worth of $12 million or a 50% chance of a net worth of $80 million and a 50% chance of being flat broke, would you go for it on the grounds that the expected return was $40 million vs $12 million?

Less - no, I would not go

Less - no, I would not go for that gamble. But I see this gamble as very different. Suppose that your stock options are significantly less than the amount you need to retire - say $250K and you need $1M. What I'm saying is that you will get to $1M much faster, on average, if you don't exercise, and earn the much higher interest rate. If you exercise, it will take you many more years to get to $1M, because you are earning so much less.

I don't see why this argument fails to hold even if the $250K is 90% of your savings. You are still going to get to retirement much faster, on average, by not exercising. I guess the worst-case TTR (time to retirement) becomes longer, but it still seems like a hella better distribution of TTRs.

This is more than a

This is more than a theoretical exercise for me: I actually advise clients on such matters and feel a strong fiduciary duty to give advice that is in their best interests. We usually adopt a simple heuristic in which we exercise about half the options when the stock price is 150% of the exercise price, and most of the remainder when the stock price is double the exercise price, holding the rest until near expiration. We hold some because your calculations are right, but exercise most because your trivialization of the diminishing marginal utility issue ignores the calculus of the typical person's situation.

You don't have to convince me that holding the options until expiration will, on average, get you to $1 million faster. You will also, on average, get rich faster if you dispense with all forms of insurance (life, home, disability, health, liability). But when a result two standard deviations worse than expected means poverty, you can't treat it casually.

We also agree on the calculation of expected returns. There is absolutely no question that, once we ignore the diminishing marginal utility of wealth, the numbers favor holding the options until the last possible day. So long as an employee is not permitted to sell the options, there is no way to realize the premium that ought to be added to the option's intrinsic value to reflect its true worth. Exercising an option prior to the last day is ALWAYS a mathematical mistake.

But having 1/4th of the money you'll need for financial independence means you're only around 15 years away from total independence with modest additions to your investment stake (participating in the company 401(k) plan, for example) and a 100% diversified equity investment strategy. And if 90% of your net worth is being risked, the downside of the option gamble is that you'll be left with 1/40th of the money you need, leaving you more than twice as many years from financial independence.

I also think we need to bring out explicitly an implicit belief that often enters into the calculation. Some of us have the unspoken awareness in the back of our mind that broke doesn't actually mean broke, since we have parents and/or grandparents with enough wealth that we are ALREADY basically assured of financial independence. We're not really risking it all on one roll of the dice. Furthermore, the biggest asset of a typical 30-year-old is the present value of their own future expected earnings. Young and broke isn't even remotely the same as old and broke. So the young worker with well-to-do parents who is stuffing the maximum into 401(k) plans and Roth IRAs might well take a flyer on the options that is 90% of their formal net worth but a trivial percentage of a more complete balance sheet (of course, if the balance sheet were truly complete, it would include the value of love, friendship, liberty, and their Google search engine, which is probably the main reason financial wealth beyond the necessities is so unimportant to the question of personal happiness).

BTW, as long as we are talking about the real world, let me point out that the typical person with vested stock options has lots of unvested options, since most companies who use them issue new ones on a regular basis with staggered exercise dates. Even when my clients have exercised ALL the options they could, they typically had plenty more unvested options that left the big bet substantially intact as long as they remained with the company. So the person who exercises ALL their options is often just exercising 10% or 20% of them (the vested ones), meaning they're going to hit $1 million only a few days later than you do if you're right (but years sooner if you're wrong).

Patri: Yes, that does make

Patri:

Yes, that does make sense. I'd be more inclined to risk the money if I didn't have enough to retire already.

But if you want leverage, what about cashing out some of your ESOs and buying calls (or puts) on other stocks? You still take the tax hit, but this strikes me as a lot safer than betting the farm on one stock. Which is not to say that it doesn't still sound pretty risky to me.

Brandon - You're right about

Brandon - You're right about there being others ways to leverage. The difference is that the employee has an option without having to pay a premium for the time value of the period until expiration (nor is it an opportunity cost of holding them, since employees are not permitted to sell employee stock options on the open market). Thus, there is probably no alternative with as high an expected return as the employee stock option, even if a person is willing to create the same leverage ratio with other available investments.

Brandon - what Less said.

Brandon - what Less said. It's not about leverage, its about being given a riskless, interest free loan to leverage with. You don't get that deal for free.

Less - you say lots of

Less - you say lots of sensible things here, and we pretty much agree. I think the key thing driving my insensitivity to the risk of holding here is "Furthermore, the biggest asset of a typical 30-year-old is the present value of their own future expected earnings. Young and broke isn’t even remotely the same as old and broke.". As a 29-year-old, if my options became worthless, I would still have some assets, plus a great job, and a great resume to go get a great job. My future would still be plenty bright, hence my willingness to make the hugely +EV but risky gamble.

Gravity, Suppose you hold

Gravity,

Suppose you hold two options with a strike price of $100 for a stock whose current value is $100. Using your valuation formula, these options are worthless because current value = strike price. This is clearly wrong because, if the stock goes up, they’re worth money. If the stock price goes up a lot, the options will be worth a lot of money. That’s why they use the Black-Scholes equation to value options. Basically, Black-Scholes involves taking an estimate of the stocks variance, the expiration date of the options, the current price, the strike price, and integrating over the possible values of the stock at the expiration date.

This has already been covered above, but the options you describe have only time value. Since employees cannot sell the options, or, presumably even create equivalent synthetic options to sell, time value cannot be realized by the employee.

Regards, Don

Suppose you hold two options

Suppose you hold two options with a strike price of $100 for a stock whose current value is $100. Using your valuation formula, these options are worthless because current value = strike price. This is clearly wrong because, if the stock goes up, they're worth money. If the stock price goes up a lot, the options will be worth a lot of money. That's why they use the Black-Scholes equation to value options. Basically, Black-Scholes involves taking an estimate of the stocks variance, the expiration date of the options, the current price, the strike price, and integrating over the possible values of the stock at the expiration date.