Got Employee Stock Options? Grok's rule for when to exercise

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Got Employee Stock Options? Grok's rule for when to exercise

Postby grok87 » Fri Feb 26, 2010 12:19 am

Many folks may have employee stock options. These often present one with a puzzle: when is the best time to exercise them? Employee stock options are different than regular exchange traded stock options because they cannot be sold, only exercised.

1) Exercise too soon and you lose the "time value" of the options (i.e. the value beyond how much they are currently "in the money")
2) Wait too long to exercise and you risk their value going to zero if the stock price drops below the strike price of the options.

Here is a rule of thumb I worked out a couple of years ago:

Keep the value of your options to no more than p% of your portfolio- i.e. if they exceed this value, exercise enough options to reduce the value of the remaining options to p% of your portfolio:

current value of options = (number of options)*(S-X)

p = i*T / (S/X -1)

where i = current risk free interest rate
T = Time in years till expiration
S = stock price
X = strike price of option

So for example lets say you have 1000 options with 2 years till expiry and have an strike price of $20 a share, and the stock is currently trading at $50 then:

p= 0.83%*2/(50/20-1) = 1.1%

(since the two year treasury is at 0.83%)

Let's say you have a $500,000 portfolio then you want to reduce your options to 1.1%*$500,000 = $5,500. Since the options are currently worth $30 each (=$50-20) that means you should keep 183 of the 1,000 options and exercise the other 817.

Here's some background on the rule of the thumb and discussion:

viewtopic.php?t=13534&highlight=options

hope this helps,
cheers,
grok, CFA
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Postby dbr » Fri Feb 26, 2010 1:26 pm

Thanks, hope a couple of readers of recent threads on the subject find this.
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Re: Got Employee Stock Options? Grok's rule for when to exer

Postby Wagnerjb » Sat Feb 27, 2010 4:09 pm

grok87 wrote:So for example lets say you have 1000 options with 2 years till expiry and have an strike price of $20 a share, and the stock is currently trading at $50 then:

p= 0.83%*2/(50/20-1) = 1.1%

(since the two year treasury is at 0.83%)

Let's say you have a $500,000 portfolio then you want to reduce your options to 1.1%*$500,000 = $5,500. Since the options are currently worth $30 each (=$50-20) that means you should keep 183 of the 1,000 options and exercise the other 817.

Here's some background on the rule of the thumb and discussion:

viewtopic.php?t=13534&highlight=options

hope this helps,
cheers,


Hi Grok: I made some comments in the linked thread, but I would like to repeat a few of them:

a) Your formula does a good job of addressing the relevant issues, including diversification.

b) In my opinion, your formula is very conservative. The example you posted showed individual for whom the options represented 6% of his net worth. That's less than the level of "play money" that many Bogleheads accept. However, your formula would have him exercise over 80% of his options....which I feel is not necessary.

c) I prefer this model when making the decision on company stock options:

http://www.parametricportfolio.com/down ... ptions.pdf


There is no "right" answer to this decision, and (changes in) income taxes are also a factor....but not one that can be modeled very well in such a formula. Bottom line is that both your formula and the attached link provide a framework for an employee to decide on when to exercise and how much to exercise.

Best wishes.
Andy
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Re: Got Employee Stock Options? Grok's rule for when to exer

Postby dtcrisp » Sat Feb 27, 2010 5:04 pm

Keep the value of your options to no more than p% of your portfolio- i.e. if they exceed this value, exercise enough options to reduce the value of the remaining options to p% of your portfolio


That's what I settled on working at m$ (the other m$) in the 90's. In this case the value of p held at 50% for years, until arbitrarily dropping to 0 in late 1999.

For a stock like msft over that time period, the difference between p=10% and p=90% was staggering. As well of course the choice of year to walk away. There's no right answer - it is an interesting, and quite personal, game.
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Re: Got Employee Stock Options? Grok's rule for when to exer

Postby grok87 » Sun Feb 28, 2010 12:04 am

Wagnerjb wrote:
grok87 wrote:So for example lets say you have 1000 options with 2 years till expiry and have an strike price of $20 a share, and the stock is currently trading at $50 then:

p= 0.83%*2/(50/20-1) = 1.1%

(since the two year treasury is at 0.83%)

Let's say you have a $500,000 portfolio then you want to reduce your options to 1.1%*$500,000 = $5,500. Since the options are currently worth $30 each (=$50-20) that means you should keep 183 of the 1,000 options and exercise the other 817.

Here's some background on the rule of the thumb and discussion:

viewtopic.php?t=13534&highlight=options

hope this helps,
cheers,


Hi Grok: I made some comments in the linked thread, but I would like to repeat a few of them:

a) Your formula does a good job of addressing the relevant issues, including diversification.

b) In my opinion, your formula is very conservative. The example you posted showed individual for whom the options represented 6% of his net worth. That's less than the level of "play money" that many Bogleheads accept. However, your formula would have him exercise over 80% of his options....which I feel is not necessary.

c) I prefer this model when making the decision on company stock options:

http://www.parametricportfolio.com/down ... ptions.pdf


There is no "right" answer to this decision, and (changes in) income taxes are also a factor....but not one that can be modeled very well in such a formula. Bottom line is that both your formula and the attached link provide a framework for an employee to decide on when to exercise and how much to exercise.

Best wishes.

Thanks Andy,
THanks for posting the paper. I think perhaps you had posted it before- anyway it looked familiar but I enjoyed re-reading it. Couldn't quite find the previous thread though...

As far as my formula being conservative, I do understand where you are coming from. Part of my motivation in working out a formulaic approach is regret at having held onto options too long in the past. I wonder if other folks might feel the same after the crash of 2008. One could always apply a "factor" (say 2x) to my formula to increase it (or decrease it!) according to one's own risk tolerance. Obviously the important thing then would be not to change the factor over time, unless your risk tolerance changes for some clear reason (inherited wealth, spouse loss of job, etc.)

As we have discussed and the paper points out, the important thing is that you want to exercise more of your options when their intrinsic value (how much they are in the money) is high relative to their time value (value that comes from the potential for future stock price growth over time). So you want to exercise more options as:

1) the time to expiration shortens
2) the "stock price"/"strike price" increases
3) interest rates decrease

the paper mentions the first 2 of these (page 8-9) but not the third. I think the first is intuitive to most people (although some folks feel it is optimal to wait till the last day, which I obviously don't agree with). I'm not sure most people consider the 2nd and 3rd factors above. In this current low interest rate environment, for example, the "time value" of options is worth less and should make one want to exercise sooner, all things being equal.

On page 8 of the paper, it outlines an example where they find it optimal to exercise 15% of ones options (options intrinsic value=50% of wealth, T=5, S=125, X=100, 5 year interest rate in 2001=5%)

my formula would say to reduce the options to p% of wealth where

p=5%*5/(125/100-1) = 100% !

The interpretation would be not to sell any of the options! Its interesting that the paper is actually more conservative than my formula in this instance.

cheers,
grok, CFA
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Re: Got Employee Stock Options? Grok's rule for when to exer

Postby grok87 » Sun Feb 28, 2010 12:06 am

dtcrisp wrote:
Keep the value of your options to no more than p% of your portfolio- i.e. if they exceed this value, exercise enough options to reduce the value of the remaining options to p% of your portfolio


That's what I settled on working at m$ (the other m$) in the 90's. In this case the value of p held at 50% for years, until arbitrarily dropping to 0 in late 1999.

For a stock like msft over that time period, the difference between p=10% and p=90% was staggering. As well of course the choice of year to walk away. There's no right answer - it is an interesting, and quite personal, game.

dtcrisp,
Thanks for recounting your actual experience. Presumably you kept your p constant at 50% by exercising the most "in the money options" first?
cheers,
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Postby dtcrisp » Sun Feb 28, 2010 3:26 pm

Presumably you kept your p constant at 50% by exercising the most "in the money options" first?


Yes. Separately, I realize now this discussion, or at least my reply, glosses over the difference between exercise-and-sell vs. exercise-and-hold, and the subsequent tax consequences. I'm unable to add any helpful analysis to that, other than recognizing that a mathematical risk model would have been helpful at the time.
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Postby smackfu » Sun Feb 28, 2010 5:09 pm

Since my stock options are taxed as W-2 income, the taxes are really significant. I only get around 60% of the money, since it's all taxed at 25% federal plus all the other fed and state taxes.

Which factors should be adjusted for tax rate in this calculation.
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Postby grok87 » Mon Mar 01, 2010 12:54 am

smackfu wrote:Since my stock options are taxed as W-2 income, the taxes are really significant. I only get around 60% of the money, since it's all taxed at 25% federal plus all the other fed and state taxes.

Which factors should be adjusted for tax rate in this calculation.

I'm not sure...there are various ways to look at it.

1) if you do a cashless exercise and put the proceeds in Total Stock Market index, you will lose 40% of the money.
2) But then future growth will be taxed at lower long term capital gains rates. If you don't exercise, future growth will be taxed at higher ordinary income tax rates (plus FICA!)

While I'm all for being tax efficient, there are a couple of reasons why I don't think tax is the main story here:

1) the options will expire after 10 years anyway. So you can only delay the tax hit for a relatively short amount of time
2) you are dealing with your own employers stock. I think the diversification issue trumps the tax issue.

cheers,
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Re: Got Employee Stock Options? Grok's rule for when to exer

Postby Wagnerjb » Mon Mar 01, 2010 2:12 pm

grok87 wrote:As we have discussed and the paper points out, the important thing is that you want to exercise more of your options when their intrinsic value (how much they are in the money) is high relative to their time value (value that comes from the potential for future stock price growth over time). So you want to exercise more options as:

1) the time to expiration shortens
2) the "stock price"/"strike price" increases
3) interest rates decrease

the paper mentions the first 2 of these (page 8-9) but not the third. I think the first is intuitive to most people (although some folks feel it is optimal to wait till the last day, which I obviously don't agree with). I'm not sure most people consider the 2nd and 3rd factors above. In this current low interest rate environment, for example, the "time value" of options is worth less and should make one want to exercise sooner, all things being equal.



Hi Grok: I am struggling to understand why interest rates are part of this decision. I know they are part of the way stock options are priced, but I wonder if those aspects are relevant here. It has been a while since I was in grad business school studying this formula, so I did a bit of surfing to bone up.

It seems that interest rates affect the premium paid for an option. However, the employee doesn't pay a premium....so that isn't relevant. (Even if he paid a premium, that is irrelevant in the exercise decision anyway). I also saw an article stating that interest rates affect a put, but in this case we are only dealing with call options.

Maybe you could give me an example of how interest rates (and changes in rates) would affect the decision to exercise.

Thanks.
Andy
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Postby Wagnerjb » Mon Mar 01, 2010 2:19 pm

grok87 wrote:
smackfu wrote:Since my stock options are taxed as W-2 income, the taxes are really significant. I only get around 60% of the money, since it's all taxed at 25% federal plus all the other fed and state taxes.

Which factors should be adjusted for tax rate in this calculation.

I'm not sure...there are various ways to look at it.

1) if you do a cashless exercise and put the proceeds in Total Stock Market index, you will lose 40% of the money.
2) But then future growth will be taxed at lower long term capital gains rates. If you don't exercise, future growth will be taxed at higher ordinary income tax rates (plus FICA!)

While I'm all for being tax efficient, there are a couple of reasons why I don't think tax is the main story here:

1) the options will expire after 10 years anyway. So you can only delay the tax hit for a relatively short amount of time
2) you are dealing with your own employers stock. I think the diversification issue trumps the tax issue.

cheers,


My comments about taxes were aimed at situations where tax rates would be different between years. Say your option has a 10 year life and you are near the end of year 9. You got a great big bonus this year and are in an unusually high tax bracket, maybe paying AMT as well. This guy would wait a few months to exercise. Another guy might not have any unusual income issues, but he sees that Congress is raising tax rates for next year. He might exercise today.

A third guy might exercise some of his shares....just enough to stay in the lower tax bracket. This would be identical to the tactic used by many when they convert an IRA to a Roth.

That is the kind of decision that you simply cannot put into a formula.

Best wishes.
Andy
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Postby Random Poster » Mon Mar 01, 2010 2:47 pm

Respectfully, the "rule" or "formula" is much too complex for my liking.

Personally, I sell everything, immediately upon vesting.

I depend on my employer for my current income. I'm not going to depend on my employer for my future income.
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Postby indexfundfan » Mon Mar 01, 2010 2:59 pm

I have unexercised vested stock options. The after-tax value is currently approximately 30% (P) of my portfolio. At the peak about four years ago, P was closed to 45%, and it did fall to 0% around the end of 2008.

I regard these options mostly as a "special bonus" and I am fairly aggressive with them. Since I don't need the options for cashflow, I am in no hurry to exercise them. If it turns out well, it will be my ticket to FIRE (financial independence / early retirement).
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Postby Wagnerjb » Mon Mar 01, 2010 3:07 pm

Random Poster wrote:Respectfully, the "rule" or "formula" is much too complex for my liking.

Personally, I sell everything, immediately upon vesting.



It is a shame that our employers won't allow us to sell these options to others. In this case, I would be very happy to pay Random Poster the same value he got for exercising if I could buy the options from him. They may have 6 or 7 years left until expiration and we would both be happy about this exchange. He got his cash, and I gladly took the risk on the remaining life of his options. Sadly, this isn't allowed :evil:

Best wishes.
Andy
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Re: Got Employee Stock Options? Grok's rule for when to exer

Postby indexfundfan » Mon Mar 01, 2010 3:14 pm

Wagnerjb wrote:Hi Grok: I am struggling to understand why interest rates are part of this decision. I know they are part of the way stock options are priced, but I wonder if those aspects are relevant here. It has been a while since I was in grad business school studying this formula, so I did a bit of surfing to bone up.

It seems that interest rates affect the premium paid for an option. However, the employee doesn't pay a premium....so that isn't relevant. (Even if he paid a premium, that is irrelevant in the exercise decision anyway). I also saw an article stating that interest rates affect a put, but in this case we are only dealing with call options.

Maybe you could give me an example of how interest rates (and changes in rates) would affect the decision to exercise.

Thanks.

The Black-Scholes formula takes into account the interest rate in pricing a stock option. I guess the way to look at it is that if the bank interest rate is a sky high of 15%, strike price is relatively low and the stock could be expected to appreciate only 5% a year, it is more advantageous to simply exercise all now, take the gain and put the money into the bank.
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Postby dtcrisp » Mon Mar 01, 2010 5:11 pm

Personally, I sell everything, immediately upon vesting.


For some individuals, historically at least, that choice alone (of how long to wait) made the difference between a $1M vs. a $100M portfolio.

Invoking Black-Scholes for high-tech incentive stock option plans kinda misses the point, the point is that kind of model leads you astray. This situation has too many unknowns, too few data points.
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Re: Got Employee Stock Options? Grok's rule for when to exer

Postby Wagnerjb » Mon Mar 01, 2010 7:43 pm

indexfundfan wrote:The Black-Scholes formula takes into account the interest rate in pricing a stock option. I guess the way to look at it is that if the bank interest rate is a sky high of 15%, strike price is relatively low and the stock could be expected to appreciate only 5% a year, it is more advantageous to simply exercise all now, take the gain and put the money into the bank.


I am happy to evaluate an example like this, but I got stuck because I don't think the example holds together. If interest rates are 15%, a stock will be expected to appreciate at some rate higher than 15%. This is due to the equity risk premium that investors expect. I will be happy to assume either 1) a 3% interest rate and 5% expected stock appreciation, or 2) a 15% interest rate and a 17% expected stock appreciation, and take the example further from there. Agree?
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Re: Got Employee Stock Options? Grok's rule for when to exer

Postby indexfundfan » Mon Mar 01, 2010 8:22 pm

Wagnerjb wrote:
indexfundfan wrote:The Black-Scholes formula takes into account the interest rate in pricing a stock option. I guess the way to look at it is that if the bank interest rate is a sky high of 15%, strike price is relatively low and the stock could be expected to appreciate only 5% a year, it is more advantageous to simply exercise all now, take the gain and put the money into the bank.


I am happy to evaluate an example like this, but I got stuck because I don't think the example holds together. If interest rates are 15%, a stock will be expected to appreciate at some rate higher than 15%. This is due to the equity risk premium that investors expect. I will be happy to assume either 1) a 3% interest rate and 5% expected stock appreciation, or 2) a 15% interest rate and a 17% expected stock appreciation, and take the example further from there. Agree?

My extreme example was only intended to illustrate why interest rate is a part in the equation -- it does not provide an answer to at which point which path would be better.

A higher interest rate (think a fixed rate CD) would tend to induce people to exercise options early especially if the return from the CD is guaranteed / riskfree while that from the option is not.
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Re: Got Employee Stock Options? Grok's rule for when to exer

Postby Wagnerjb » Mon Mar 01, 2010 9:57 pm

indexfundfan wrote:A higher interest rate (think a fixed rate CD) would tend to induce people to exercise options early especially if the return from the CD is guaranteed / riskfree while that from the option is not.


When I run some numbers with a reasonable set of economic assumptions, I don't find any scenarios in which it makes sense to exercise early....from a strictly financial standpoint. Here is one example:

Strike price is $20. Current market price is $50. Interest rates are at 8%, so you would logically assume the stock would appreciate 10% in one year (I am assuming a zero dividend stock for simplicity).

You and I both have $30 sitting in the bank, and we both have the same stock options.

You exercise early, paying $20 in cash to buy the stock. You also have a $30 taxable gain and you pay $10 in cash income taxes. Now you hold the stock and have zero cash. After one year, the stock appreciates to $55 and you sell. You pay $0.75 on the capital gain and have $54.25 in the end.

I hold my options. I earn $2.40 in interest on my $30 in cash and I exercise my option after the year is up. The stock is worth $55 and my cashless exercise/sell yields me $35. I pay taxes on the interest of $2.40 and the $35 gain, amounting to $12.30. I have $32.40 in the bank and $35 from the exercise, less $12.30 in taxes, for a total of $55.10.

Note that my advantage amounts to roughly the after-tax interest on the $30 that you tied up in unproductive uses, while I got the same stock gains without putting up the $30 (the advantage was partially offset by your paying only 15% on your cap gain). I will always win because you and I are both taking the exact same equity risk but I am doing it with less capital.

What if the same scenario, but the stock price declines to $40? You end up with $41.50 assuming you can save taxes with the $10 tax loss. I end up with $45.

Bottom line for me is that academic theory tells us to hold until the last day, but diversification and taxes are two real life issues that may drive us to exercise early. I am still struggling to see how interest rates will drive an early exercise decision. Help me if I am missing something here.

Best wishes.
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Re: Got Employee Stock Options? Grok's rule for when to exer

Postby grok87 » Mon Mar 01, 2010 11:27 pm

Wagnerjb wrote:
grok87 wrote:As we have discussed and the paper points out, the important thing is that you want to exercise more of your options when their intrinsic value (how much they are in the money) is high relative to their time value (value that comes from the potential for future stock price growth over time). So you want to exercise more options as:

1) the time to expiration shortens
2) the "stock price"/"strike price" increases
3) interest rates decrease

the paper mentions the first 2 of these (page 8-9) but not the third. I think the first is intuitive to most people (although some folks feel it is optimal to wait till the last day, which I obviously don't agree with). I'm not sure most people consider the 2nd and 3rd factors above. In this current low interest rate environment, for example, the "time value" of options is worth less and should make one want to exercise sooner, all things being equal.



Hi Grok: I am struggling to understand why interest rates are part of this decision. I know they are part of the way stock options are priced, but I wonder if those aspects are relevant here. It has been a while since I was in grad business school studying this formula, so I did a bit of surfing to bone up.

It seems that interest rates affect the premium paid for an option. However, the employee doesn't pay a premium....so that isn't relevant. (Even if he paid a premium, that is irrelevant in the exercise decision anyway). I also saw an article stating that interest rates affect a put, but in this case we are only dealing with call options.

Maybe you could give me an example of how interest rates (and changes in rates) would affect the decision to exercise.

Thanks.

Andy,
Well "Put-call parity" says that

Call(X) = S – X/(1+i)^T + Put(X)

where
Call(X) is a call option with strike X and time T to expiration
Put(X) is a put option with strike X and time T to expiration
S= current stock price
i = risk free interest rate

Let's make things simpler by assuming the call option is deep in the money and only a few years from expiration. THen intuitively the put option is not worth much. Let's assume its worth 0.

Then

Call(X) ~= S – X/(1+i)^T

Now the value of a call option can be divided into its intrinsic value S-X, and time value:

Call(X) ~= [S-X] + [X - X/(1+i)^T]
=intrinsic value + time value

So the time value of the option is approximately

Time value = X*[1-1/(1+i)^T] ~= X*i*T

so for a deep in the money call option, as either i or T go to zero, the time value of the call option goes to zero and all that is left is the intrinsic value. A that point you may and well exercise your options and diversity since you are not losing any "time value" by doing so.

cheers,









For deep in the money call option a few years from expiration
put option approx =0
(1+i)^T approx = 1+i*T

call option = S – X/(1+i*T) approximately

Kelly criterion: bet your “edge” or in other words if you can buy an asset at a p% discount to it's value, then allocate p% of your portfolio to that asset.
http://home.williampoundstone.net/Kelly/Kelly.html

For employer stock options this “edge” or discount can be thought of as arising as follows:

1)At any time you can exercise 1 option and receive S – X in cash. (Unlike a standard exchange traded option you can not sell the option for fair value which is > S-X).
2)Then by choosing not to exercise the option, you are effectively purchasing it at S-X. In return you get the option. The estimate of fair value of the option is given above = S - X/(1+i*T).
3)So the fair value – purchase price = S – X/(1+i*T) -(S-X) = X – X/(1+i*T) = X*i*T/(1+i*T)
4)discount = (fair value – purchase price) / (fair value) = X*i*T / (1+i*T) / [S-X/(1+i*T)] = i*T / [S/X*(1+i*T) -1] = i*T / (S/X – 1) approximately


Sorry for all the math



cheers,
grok, CFA
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Re: Got Employee Stock Options? Grok's rule for when to exer

Postby Wagnerjb » Mon Mar 01, 2010 11:59 pm

grok87 wrote:[
so for a deep in the money call option, as either i or T go to zero, the time value of the call option goes to zero and all that is left is the intrinsic value. A that point you may and well exercise your options and diversity since you are not losing any "time value" by doing so.



Yeah...you kinda killed me with the math :D

But if you take your statement above, you will see that you are agreeing with me. If time goes to zero, your option is about to expire. That's a no-brainer. But if the interest rate goes to zero, what does that mean? It means that you cannot earn any interest on the $30 in capital that I referenced in my example. Thus, you are indifferent between exercising and not since you don't sacrifice anything by tying up capital. Obviously, this is exceedingly unrealistic, but is theoretically possible. At values anything but zero, the interest rate drives you to keep the options....with higher rates providing even stronger incentives to do so.

So in a practical sense, I don't see that the interest rate changes your decision at all. Unless it is 0%, it says hold on to your options. Thus, I honestly don't see why it is necessary in your formula....and why different values of the interest rate drive different amounts to be exercised. It seems to me that time to expiration, depth in the money and diversification would be the three valid variables to the decision.

I guess what you are saying is that higher interest rates provide a stronger incentive to hold options longer. Thus the higher the interest rate, the bigger the diversification problem must be in order to cause you to exercise early. Same for depth in the money....the higher the interest rate, the more depth required to force one to exercise. Do I have it?

Best wishes.
Andy
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Re: Got Employee Stock Options? Grok's rule for when to exer

Postby grok87 » Tue Mar 02, 2010 12:51 am

Wagnerjb wrote:
grok87 wrote:[
so for a deep in the money call option, as either i or T go to zero, the time value of the call option goes to zero and all that is left is the intrinsic value. A that point you may and well exercise your options and diversity since you are not losing any "time value" by doing so.



Yeah...you kinda killed me with the math :D

But if you take your statement above, you will see that you are agreeing with me. If time goes to zero, your option is about to expire. That's a no-brainer. But if the interest rate goes to zero, what does that mean? It means that you cannot earn any interest on the $30 in capital that I referenced in my example. Thus, you are indifferent between exercising and not since you don't sacrifice anything by tying up capital. Obviously, this is exceedingly unrealistic, but is theoretically possible. At values anything but zero, the interest rate drives you to keep the options....with higher rates providing even stronger incentives to do so.

So in a practical sense, I don't see that the interest rate changes your decision at all. Unless it is 0%, it says hold on to your options. Thus, I honestly don't see why it is necessary in your formula....and why different values of the interest rate drive different amounts to be exercised. It seems to me that time to expiration, depth in the money and diversification would be the three valid variables to the decision.

I guess what you are saying is that higher interest rates provide a stronger incentive to hold options longer. Thus the higher the interest rate, the bigger the diversification problem must be in order to cause you to exercise early. Same for depth in the money....the higher the interest rate, the more depth required to force one to exercise. Do I have it?

Best wishes.

Yes I think you have it- agree with your last paragraph.
:)
If you translate the put call parity formula for tradeable options into words it says:

Call Option + zero coupon bond (X) = stock position + put option

or

Call Option = stock position - zero coupon bond (X) + put option

Again assume a deep in the money call option so that the put option is worth little or nothing- assume 0.

Then effectively you are left with saying that a call option is the same as borrowing "X" amount of money to invest in a stock, where X is the strike price. THe value of the position is S- Present value (X). When interest rates are low Present Value (X) is close to X so the value of the position is close to S-X so there is little difference between the "intrinsic" or in-the-money value of the options (what you can get now for exercising them into cash) and the "true" value of the option (that since they are employer options you must hold onto the options to realize) inclusive of the time value. In other words the time value goes to zero not just when T goes to zero but when i goes to zero as well.
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Postby Random Poster » Tue Mar 02, 2010 9:30 am

Wagnerjb wrote:
Random Poster wrote:Respectfully, the "rule" or "formula" is much too complex for my liking.

Personally, I sell everything, immediately upon vesting.



It is a shame that our employers won't allow us to sell these options to others. In this case, I would be very happy to pay Random Poster the same value he got for exercising if I could buy the options from him. They may have 6 or 7 years left until expiration and we would both be happy about this exchange. He got his cash, and I gladly took the risk on the remaining life of his options. Sadly, this isn't allowed :evil:

Best wishes.


Curious that you are apparently willing to do such a thing without knowing the company for which I work.
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Postby Random Poster » Tue Mar 02, 2010 9:32 am

dtcrisp wrote:
Personally, I sell everything, immediately upon vesting.


For some individuals, historically at least, that choice alone (of how long to wait) made the difference between a $1M vs. a $100M portfolio.


And, for some individuals, historically at least, such a choice made the difference between a $1M vs. $0 portfolio.

Sometimes I wonder if anyone learned anything from the Enron et al scandals.
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Postby Wagnerjb » Tue Mar 02, 2010 11:10 am

Random Poster wrote:Curious that you are apparently willing to do such a thing without knowing the company for which I work.


It doesn't matter. My assumption is that you are not an insider trading with insider information (which would illegal anyway). Otherwise, I assume that the market knows - and has priced into the stock - the prospects for your firm.

For example, say you have a stock option to buy at $10 and today's stock price is $20. I will gladly give you $10 in cash today to buy the option from you. That means I am accepting the risk in the option. The stock price could drop below $10, wiping me out. Or it could stay at $20 and I break even. Or it could rise above $20 and I will profit.

The odds for this option are stacked in my favor. If I could do this for many people at many firms, I would be independently wealthy. Yes, some options would expire underwater (like Enron, Lehman, etc) but some would be handsomely profitable. With a diversified portfolio of these, I should be fine.

You may be assuming that you know your company is a dog and that its stock price will plummet in the near term. Your company may be a dog, but I would assert that others (and the market) know that already, so there is no reason to expect your stock to plummet as the expectations are realized.

Best wishes.
Andy
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Postby grok87 » Wed Mar 03, 2010 10:44 pm

Random Poster wrote:
dtcrisp wrote:
Personally, I sell everything, immediately upon vesting.


For some individuals, historically at least, that choice alone (of how long to wait) made the difference between a $1M vs. a $100M portfolio.


And, for some individuals, historically at least, such a choice made the difference between a $1M vs. $0 portfolio.

Sometimes I wonder if anyone learned anything from the Enron et al scandals.

This dilemma is what my formula is all about. I hate holding my company stock too. I sell it as soon as it vests. But options are different. You can't sell them for fair market value, only exercise them. If you exercise them too early you destroy the time value. So knowing when to exercise is all about balancing the intrinsic value (in the money value) and the time value. When the intrinsic in the money value is high and the time value is low, you want to exercise. In my formula the i*T part represents the time value. And the S/X-1 represents the intrinsic, in the money value.
So when the time value is low relative to the intrinsic value you want to hold a low amount of options (p should be low)- i.e. you should exercise most of them.
cheers,
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Managing Your Employee Stock Options

Postby Strikeout » Thu Mar 04, 2010 12:14 pm

The most celebrated executives from Steve Jobs, to James Dimon, to John Chambers to Larry Ellison waited to the final weeks to exercise their employee stock options. Why? because they did not want to forfeit any remaining "time premium" or pay an early tax.

If the holders of ESOs want to reduce the risk during the holding period, they can easily sell exchange traded calls or sometimes buy puts on the company stock. The taxes are friendly and it can be done with little transaction costs or margin. The result will be more value, less risk and less tax.

Those who claim otherwise have an agenda to benefit the company and others who benefit by premature exercises.

John Olagues
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Re: Managing Your Employee Stock Options

Postby grberry » Thu Mar 04, 2010 3:57 pm

Strikeout wrote:....

If the holders of ESOs want to reduce the risk during the holding period, they can easily sell exchange traded calls or sometimes buy puts on the company stock. ....

John Olagues


Unfortunately, the above is often forbidden by law and/or company policy. I know at least some classes of employee are required to forefit all profits from such activities to the company. And if there is an insider trading investigation - many of which don't make the press headlines - and an employee's name appears as having made money or changed positions in the right timeframe, that employee can be in for a world of legal trouble.
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Re: Managing Your Employee Stock Options

Postby Wagnerjb » Thu Mar 04, 2010 4:19 pm

Strikeout wrote:The most celebrated executives from Steve Jobs, to James Dimon, to John Chambers to Larry Ellison waited to the final weeks to exercise their employee stock options. Why? because they did not want to forfeit any remaining "time premium" or pay an early tax.



Hi John, and welcome to the forum. One of the reasons why these executives can - and do - wait until the final day is that diversification issues are not compelling for them. They may very well be undiversified, but with their salaries and immense wealth the options are not a "game changer" for them. I agree that the time premium is valuable, but at some point your diversification (for a regular individual investor) becomes more valuable than the time premium.

If the holders of ESOs want to reduce the risk during the holding period, they can easily sell exchange traded calls or sometimes buy puts on the company stock. The taxes are friendly and it can be done with little transaction costs or margin. The result will be more value, less risk and less tax.


That can be political suicide for a senior manager at a major company. And you will find that an 8-year option on your company stock.....if it exists at all, there isn't any volume traded (or the bid-asked spread is prohibitive).

Best wishes.
Andy
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There is no law that prohibits hedging

Postby Strikeout » Thu Mar 04, 2010 4:28 pm

Reply to GRberry.

I will send you a check for $1000.00 if you can cite one law that prohibits hedging against company stock or in the money vested ESOs.

It is true that some rare companies do prohibit the use of exchange traded calls and puts to reduce risks and enhance the options value by selling calls or buying puts. But the number is small. If they do, then the grantee/executive can merely do what J.P. Morgan and Goldman did ...that is short correlated stocks in their competitors.

There has never been a case when someone has been fired for hedging his positions. If there was no prohibition and the company took action action the employee who did, the company would be subject to large law suits.

Why would you claim something that is clearly false?
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The merits of a Diversified portfolio are overstated

Postby Strikeout » Thu Mar 04, 2010 4:39 pm

Reply to Wagner JB.

It can be shown that hedging ESOs before exercise is far better than forfeiting 'time premium" and selling and then holding a diversified portfolio.

The fact that "time premium" is forfeited and the early tax is paid upon early exercise reduces the investable amount to where the far better strategy is to hedge.

Strikeout
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Re: There is no law that prohibits hedging

Postby indexfundfan » Thu Mar 04, 2010 6:14 pm

Strikeout wrote:Reply to GRberry.

I will send you a check for $1000.00 if you can cite one law that prohibits hedging against company stock or in the money vested ESOs.

It is true that some rare companies do prohibit the use of exchange traded calls and puts to reduce risks and enhance the options value by selling calls or buying puts. But the number is small. If they do, then the grantee/executive can merely do what J.P. Morgan and Goldman did ...that is short correlated stocks in their competitors.

There has never been a case when someone has been fired for hedging his positions. If there was no prohibition and the company took action action the employee who did, the company would be subject to large law suits.

Why would you claim something that is clearly false?

Perhaps there is no such law. But my employer prohibits any employee from using any hedging strategy that profits from a fall in the company's stock price. I doubt this is only for "some rare companies".
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Re: The merits of a Diversified portfolio are overstated

Postby Wagnerjb » Thu Mar 04, 2010 7:49 pm

Strikeout wrote:Reply to Wagner JB.

It can be shown that hedging ESOs before exercise is far better than forfeiting 'time premium" and selling and then holding a diversified portfolio.

The fact that "time premium" is forfeited and the early tax is paid upon early exercise reduces the investable amount to where the far better strategy is to hedge.

Strikeout


I don't disagree with the theory of preserving the time premium. Please show me how to hedge an 8 year option in the real world. Maybe a CEO can use a structured product with his $5 million option value, but what about the guy making $150,000 per year as a manager who has an option worth $200,000?

So....you buy a put when volatility is high. Then the volatility shrinks dramatically. Then you lose your job and are forced to exercise your options and buy the put back. You get your lunch eaten. Your hedge didn't work. (Maybe I got the volatility example backwards....but you get the point - you are exposed to changes in volatility).

I just think you have too many real world frictions to make hedging a reasonable strategy.

Best wishes.
Andy
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No pledging does not mean no hedging

Postby Strikeout » Thu Mar 04, 2010 8:09 pm

To Index fund Fan.

Most employers do not prohibit hedging.

They prohibit transferring and pledging generally, although Google created a plan for transferring ESOs to some bankers.

They do not generally have language in the plans or agreements that prohibits hedging. If they do prohibit hedging , that makes the ESOs less valuable and gives the employee only one way to reduce risk and that is to make premature exercises which comes at a high cost.

I would be interested in seeing the language that prohibits hedging in your case.

The prohibition against pledging is not the same as a prohibition against hedging because an employee can hedge without pledging.

If hedging is prohibited, then you can always short the correlated competitors and reduce risk.



Cheers:

JO
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Re: There is no law that prohibits hedging

Postby m_j_paquette » Thu Mar 04, 2010 8:17 pm

indexfundfan wrote:Perhaps there is no such law. But my employer prohibits any employee from using any hedging strategy that profits from a fall in the company's stock price. I doubt this is only for "some rare companies".


Yup. This seemed pretty common in Silicon Valley. My last employer referred explicitly to this as part of their ethical standards internal web page, where such activity was considered grounds for termination.

Since I had acquired approximately a metric grunch of stock options in the late 1990s, I worried about crashes, hedging, and what I could do. It turned that the QQQs had a pretty tight correlation with movements in my employers stock, so I bought out of the money long term put options on the QQQs as a hedge. Through sheer dumb luck, that worked out really well.

I've since retired to a much less exciting portfolio.
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Great Replies, although my view is different than those repy

Postby Strikeout » Thu Mar 04, 2010 11:32 pm

I am pleasantly surprised that the persons replying have though things out as well as they have.

Reply to Wagner JB:

If you have ESOs which have an intrinsic value of $200,000 with two years life, they will still have some time premium. the amount depends on the relationship of the stock to the exercise price, the volatility and the risk free interest rate. If the volatility is low, interest rates are low and there is a good dividend and the stock is far above the exercise price, there may be little or no "time premium" remaining and the advantage of hedging is small.

However under other circumstances you can usually get a large advantage by selling calls that are slightly out of the money as a risk reducing, value enhancing strategy. There are also favorable tax treatments.
Tthere are consideration of SEC Rules and Securities Strategies that must be made if you are an officer or director. But all in all the constraints are modest and the benefits outweigh the concerns.

JO
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Re: Great Replies, although my view is different than those

Postby Wagnerjb » Fri Mar 05, 2010 12:13 am

Strikeout wrote:I am pleasantly surprised that the persons replying have though things out as well as they have.



I have been dealing with this for 20 years, with my first grant of stock options in 1991. Over that time, I have received maybe 10 different grants (each had a 10 year life). So....I have had a little time to "think things out" :D

However under other circumstances you can usually get a large advantage by selling calls that are slightly out of the money as a risk reducing, value enhancing strategy. There are also favorable tax treatments.


I take it that you agree with me that hedging an option with 8 years to expiration isn't feasible, so I assume you are talking about options with only one or two years left until expiration.

Maybe you can use a concrete example of the risk reducing value enhancing strategy to help us see your angle. If you sell a call that is slightly out of the money, haven't you basically locked in your gain? You would be limited on your upside to the strike price. If you are locking in your gain, why don't you just exercise? At least by exercising, you can diversify with the proceeds. By hedging, you are tying up the proceeds and preventing you from diversifying.

Best wishes.
Andy
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Re: Great Replies, although my view is different than those

Postby grok87 » Fri Mar 05, 2010 12:56 am

Strikeout wrote:I am pleasantly surprised that the persons replying have though things out as well as they have.

Reply to Wagner JB:

If you have ESOs which have an intrinsic value of $200,000 with two years life, they will still have some time premium. the amount depends on the relationship of the stock to the exercise price, the volatility and the risk free interest rate. If the volatility is low, interest rates are low and there is a good dividend and the stock is far above the exercise price, there may be little or no "time premium" remaining and the advantage of hedging is small.

agree- in this situation you want to exercise your options.

Strikeout wrote:However under other circumstances you can usually get a large advantage by selling calls that are slightly out of the money as a risk reducing, value enhancing strategy. There are also favorable tax treatments.

JO

Not sure about this. How does collecting a small option premium mitigate the risk of a large in-the-money option position vaporizing? As Wagner point out, selling a slightly out of the money option position caps your upside.
cheers,
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Any type hedging reduces the potential upside

Postby Strikeout » Fri Mar 05, 2010 2:06 am

You should sell the LEAP calls (sell the longest term as you can) and pick the slightly out-of the- moneys.

For Example Apple is trading at 209 and the Jan 2012 , 250s are trading
at 25.0 That's about 12% of the stock.

If you want to protect against extreme moves in the stock buy a few at-the -money puts in place of some call sales.

Always hold a substantial summed long delta position. Hedge gradually, starting soon after the grants are made . Start hedging 10 to 15% in the early years. You can make adjustments as time passes and the stock moves around.

JO
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Re: Any type hedging reduces the potential upside

Postby Wagnerjb » Fri Mar 05, 2010 9:56 am

Strikeout wrote:You should sell the LEAP calls (sell the longest term as you can) and pick the slightly out-of the- moneys.



Sounds like you are describing a covered call strategy. I don't see how that makes sense as a risk mitigation factor for options. I can see the appeal for those long the stock itself, although I am not convinced that is a compelling strategy anyway.

Hedge gradually, starting soon after the grants are made .


For the third time, this is impossible. The apple LEAPs only go out to January 2012. That is less than 2 years. ESO's are (to my knowledge) mostly 10 year options. Hedging "soon after the grants are made" simply isn't possible.


By the way - you previously suggested that the tax treatment of your covered call strategy was favorable. Would you mind walking us through an example of this too? Thanks.

Best wishes.
Andy
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Comparison of hedging with exercise and diversify

Postby Strikeout » Fri Mar 05, 2010 10:27 am

Assume that a stock has advanced 100% from the time ESOs were granted 8 years ago. The 100% increase would have had a probability of less than .25 with assumptions of .35 volatility, a 8% expected return , no dividend and a log normal distribution of stock prices.

So the Stock is trading at 200 but the 1000 ESOs have an exercise price of 100, which was the price on grant day. The time premium remaining with 2 years to expiration is perhaps 5 dollars.

So if there is an early exercise with 2 years to expiration. the following results are had .

The intrinsic value is $100,000 and it is compensation income requiring perhaps a 40% tax leaving $60,000 (or less) for the employee to diversify.

Now lets compare that to the employee who sell 10 calls with a strike price of $250 with two years remaining. The calls would be trading at $25.22, so the seller received $25,220 .

If the stock and the diversified portfolio were unchanged after the two years and there are no further trades, the results are as below when every thing is liquidated.

$60,000 minus commissions and management fees

The result of hedging by selling calls is

$60,000 plus 63% of $25,220.

If we assume other scenarios of the stock movements, the results are

generally superior to the premature exercise , sell and diversify strategy.

If we assume scenarios with the exercise price of $130 and the present

stock price of $200, the comparison looks even better with hedging

getting the better results.

The only time premature exercise, sale and diversifying gets the better

results is if the individual stock performs far worse than the index.


JO
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Re: There is no law that prohibits hedging

Postby Frank Rizzo » Fri Mar 05, 2010 11:18 am

Strikeout wrote:I will send you a check for $1000.00 if you can cite one law that prohibits hedging against company stock or in the money vested ESOs.


My company has strict trading windows, with trading being closed for all employees at four times in the year. I do believe that any hedged positions must be closed as a part of that as well. Therefore this strategy unfortunately wouldn't work for me.

Thanks to all for the interesting (and complicated) discussion on stock options! Unfortunately my paltry number of options is only 4% of my portfolio, so for now they'll remain unexercised.


Frank
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Re: Comparison of hedging with exercise and diversify

Postby indexfundfan » Fri Mar 05, 2010 11:45 am

Strikeout wrote:Assume that a stock has advanced 100% from the time ESOs were granted 8 years ago. The 100% increase would have had a probability of less than .25 with assumptions of .35 volatility, a 8% expected return , no dividend and a log normal distribution of stock prices.

So the Stock is trading at 200 but the 1000 ESOs have an exercise price of 100, which was the price on grant day. The time premium remaining with 2 years to expiration is perhaps 5 dollars.

So if there is an early exercise with 2 years to expiration. the following results are had .

The intrinsic value is $100,000 and it is compensation income requiring perhaps a 40% tax leaving $60,000 (or less) for the employee to diversify.

Now lets compare that to the employee who sell 10 calls with a strike price of $250 with two years remaining. The calls would be trading at $25.22, so the seller received $25,220 .

If the stock and the diversified portfolio were unchanged after the two years and there are no further trades, the results are as below when every thing is liquidated.

$60,000 minus commissions and management fees

The result of hedging by selling calls is

$60,000 plus 63% of $25,220.

If we assume other scenarios of the stock movements, the results are

generally superior to the premature exercise , sell and diversify strategy.

If we assume scenarios with the exercise price of $130 and the present

stock price of $200, the comparison looks even better with hedging

getting the better results.

The only time premature exercise, sale and diversifying gets the better

results is if the individual stock performs far worse than the index.


JO
Am I correct to say that with this strategy, the upside will be capped to a stock price of $250?

I might consider hedging for the options that are down to the last 2 year stretch before expiration. Problem for me, as I stated before, is that my employer prohibits this. Hedging with a related stock is less accurate and could backfire if the selected stock moves in opposite direction to the company stock.
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Re: Comparison of hedging with exercise and diversify

Postby Wagnerjb » Fri Mar 05, 2010 12:40 pm

Strikeout wrote:The only time premature exercise, sale and diversifying gets the better

results is if the individual stock performs far worse than the index.

JO


JO: but that's exactly what we are trying to hedge against. If the stock price plunges to $95, the stock options expire worthless. Sure, you got small gains but you didn't hedge very effectively.

If we assume other scenarios of the stock movements, the results are generally superior to the premature exercise , sell and diversify strategy.


I disagree. The framework that I prefer (not the more conservative rule that Grok prefers) would have the individual sell some - but not all - of these options. If the price surges another $100 to $300, you might find that the partial exercise scenario is superior to your covered call strategy.

The bottom line is that you are proposing a covered call strategy, which is not necessarily suited for an options diversification problem. The covered call strategy sells a little upside, while leaving the downside unprotected. That isn't what we need here.

Best wishes.
Andy
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Sorry about your company policy

Postby Strikeout » Fri Mar 05, 2010 12:57 pm

Indexfundfan:

Sorry to hear that your company has chosen to diminish the value of your options grants by prohibiting hedging. Perhaps you should consider selling an ETF which correlated with your company stock. But that may be prohibited also.

JO
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Extreme moves of Stock After hedging

Postby Strikeout » Fri Mar 05, 2010 2:06 pm

Dear Andy and Index Fun:

It is true that if hedging is done by selling call alone, the best results will not be had when there are extreme moves in either direction. That can be mitigated somewhat by making adjustments to modify the summed deltas if the stock moves a good bit in either direction.

On the other hand if he were substantially concerned about extreme moves, he could buy a few puts and reduce the number of calls sold from the begining, understanding that buying puts causes erosion (i.e. negative theta).

With the implied vols being low at present, it may pay to buy a few puts plus the calls selling.

My view is that the best way to go is avoid premature exercises and hedge if you wish to reduce risk and taxes.

Cheers:

john
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Re: Any type hedging reduces the potential upside

Postby Wagnerjb » Fri Mar 05, 2010 2:57 pm

Strikeout wrote:You should sell the LEAP calls (sell the longest term as you can) and pick the slightly out-of the- moneys.

For Example Apple is trading at 209 and the Jan 2012 , 250s are trading
at 25.0 That's about 12% of the stock.



What if you work for a more typical company?

For example Chevron is trading at $74 and the Jan 2012 90's are trading at $2.33. That's about 3% of the stock.

For example DuPont is trading at $35 and the Jan 2012 40's are trading at $2.10. That's about 6% of the stock.

For example, IBM is trading at $127 and the Jan 2012 150's are trading at $5.80. That's about 5% of the stock.

For example, Coke is trading at $55 and the Jan 2012 65's are trading at $1.59. That's about 3% of the stock.


Best wishes.
Andy
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Re: Extreme moves of Stock After hedging

Postby grok87 » Fri Mar 05, 2010 9:53 pm

Strikeout wrote:
With the implied vols being low at present, it may pay to buy a few puts plus the calls selling.

john,
I think perhaps you are meaning to say that impled vols are lowER than they have been recently. From an historical perspective volatility seems to be about average right now at 17.4

http://finance.yahoo.com/echarts?s=^vix



cheers,
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Postby Strikeout » Sat Mar 06, 2010 11:40 am

To: Wagner and Grok.

The vast majority of employee stock options have no intrinsic value (i.e. exercise prices that are either greater than the present market prices) or have an intrinsic value less than 65% of the exercise price.

The great majority of employee stock options are on stocks that are reasonably volatile and have little or no dividend.

The great majority of existing employee stock options are less than 8 years old, especially if you exclude those held by CEOs to near expiration.

Given the above, why do you guys focus on employee stock options that are in the vast minority.

The vast majority of existing ESOs are candidates for hedging strategies if the holders are interested in reducing risk and enhancing their value with lower taxes (I do exclude those that are held by officers and directors that are at or out of the money, where the executive holds no stock).

The strategy of premature exercise , sell stock, and diversify has merit in only very few cases and is far inferior to efficient hedging strategies in most cases. And those are where the stocks have little or no time premium remaining. But all of the ESOs which now have little or no time premium, once did have substantial time premium which was entirely at substantial risk.

So what is the purpose of focusing on a small majority of cases when the great majority gets ignored?

JO
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Re: Comparison of hedging with exercise and diversify

Postby grok87 » Sat Mar 06, 2010 1:00 pm

Wagnerjb wrote:
Strikeout wrote:The only time premature exercise, sale and diversifying gets the better

results is if the individual stock performs far worse than the index.

JO


JO: but that's exactly what we are trying to hedge against. If the stock price plunges to $95, the stock options expire worthless. Sure, you got small gains but you didn't hedge very effectively.

If we assume other scenarios of the stock movements, the results are generally superior to the premature exercise , sell and diversify strategy.


I disagree. The framework that I prefer (not the more conservative rule that Grok prefers) would have the individual sell some - but not all - of these options. If the price surges another $100 to $300, you might find that the partial exercise scenario is superior to your covered call strategy.

The bottom line is that you are proposing a covered call strategy, which is not necessarily suited for an options diversification problem. The covered call strategy sells a little upside, while leaving the downside unprotected. That isn't what we need here.

Best wishes.

Agree
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