This article is about something that seems to be completely ignored in the
employee stock options arena. This article is about the risks associated with holding "naked" (i.e. un-hedged)
ESOs.
Rather than dividing the risks into
delta risks (i.e. change in value as a result of price movements of the underlying stock), theta risks (i.e.
erosion of
time premium) and risks of changing
volatility and interest rates, we simply set out what the probability is of the
ESOs being worthless at expiration.
This probability is the same as the probability of the stock trading below the exercise price at expiration.
We then give some values of the options at grant day to illustrate the fair value of what is at risk.
Risks of holding "naked" (un-hedged) ESOs:The following matrix illustrates the risk of holding un-hedged
employee stock options. It is important to note that when the stock is trading at the
ESOs'
exercise price, the probability of the stock being below the exercise
price at expiration is nearly 50% on reasonably volatile stocks.
This makes the holding of un-hedged
ESOs
highly risky, because there is a 50% chance that stock will be
out-of-the money at expiration and the grantee will get absolutely
nothing as the
ESOs would be worthless on expiration day.
These illustrated risks should influence the grantee and his advisers to find ways to reduce those risks, especially when the
ESOs constitute a large percentage of the grantee's assets.
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Risk Matrix of Holding Stock Options to Expiration
The matrix below gives an idea of the specific risks associated with holding un-hedged ESOs, if we assume the accuracy of theoretical options pricing models. These models make the assumption that stock prices are log-normally distributed.
Expected time......Expected Volatilities.......Probabilities of ESOs
to Expiration.........of the Underlying.............being Worthless
..................................Stock..........................at Expiration
7 yrs................................30.................................41
5 yrs...............................30.................................40
3 yrs................................30.................................44
1 yr..................................30.................................47
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7 yrs................................50.................................62
5 yrs................................50.................................60
3 yrs................................50.................................57
1 yr.................................50.................................54
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7 yrs...............................70.................................72
5 yrs...............................70.................................69
3 yrs...............................70.................................65
1 yr.................................70.................................59
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The ESOs with 5 years of expected time to expiration and an assumed expected volatility of .30 have a 40% probability of being worthless at expiration because 40% is the probability of the stock being below the exercise price on expiration day.
The ESOs with 1 year expected life with a .50 volatility have a 54% chance of being worthless at expiration of the options.
As can be seen, the higher volatility stocks have a greater probability of being out-of-the-money at expiration.
All
calculations are made when the stock is trading at the same price as
the exercise price. The expected rate of return is 8%. if we assumed a
higher rate of return, the probability of the ESOs being worthless at expiration would be slightly less.
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Below is a matrix of theoretical (fair) values of employee stock options
when granted. The employee/executive, therefore, subjects himself to
the above probabilities of losing all of the amounts in the below
matrix, if he does not hedge his ESOs.
We use the Black Scholes theoretical pricing model with appropriate assumptions.
We assume that the contractual life of the options is 10 years and the expected life is 6.1 years
when granted, in order to discount the options value in consideration
of expected early employment termination, premature exercises, and lack
of transferability.
We assume the market value of the stock is 40 and the granted options are to to buy 1000 shares. We assume that the exercise price is 40.
# of ESOs.......Assumed.........Assumed.........Theoretical Value of
Granted........Interest rate......Volatility..........1000 ESOs at grant
1000.....................3..................25..................$12,600
1000.....................3..................40..................$17,400
1000.....................3..................50..................$20,470
1000.....................3..................60..................$23,300
1000....................3..................70..................$25,890
1000.....................3..................90..................$30,290
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So the true value of 1000 ESOs granted with an exercise price of 40, and with 10 years of contractual (i.e. 6.1 years of expected life) life with expected volatility of 70 and an assumed interest rate of 3% is approximately $25,890 on the day granted.
There is, at that point, a 69% probability that the grantee will lose the $25,890 if he holds the ESOs un-hedged until expiration day.
If the expected rate of return were assumed to be greater, then the probability of being worthless at expiration would be less.
By selling exchange traded calls or buying puts, the holder of ESOs can preserve a large part of the options value regardless of what the stock does.
Making
premature exercises then selling the stock together with the immediate
investment in a diversified portfolio is far inferior to hedging or
just holding the ESOs un-hedged. On average the hedger nets after tax about 50% more than the systematic premature exercises.
John Olagues
Glossary
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