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# When is the right time to sell an option to minimize risk and maximize return?

Posted on 2011-03-22
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I thought perhaps the math/science experts would have an engineered opinion.

I have an application where I can put in how many stock options were awarded to an employee (let's say 1000) at a given price (let's say \$50/share).  The employee can sell the option at any time (assuming the going price during the time of sell is greater than the granted price).

Let's also assume the employee will pay 30% in income taxes as a result of the sale, and (because the company is so great) he/she invests the proceeds in the same company's stock.

Is there an event horizon or graph that can be displayed as a function of this, to show the employee the tradeoffs of hanging on versus selling the options?  what's the ideal price to sell at (where the % gain/loss on the stock option versus the actual stock purchased is minimized) - or where the yield from selling the options is such that there's low regret if the stock gets higher in value?

I hope I've articulated this well enough.  Guy gets options, is watching the market, when does he start to become indifferent, such that he cashes out to minimize downside risk - as the options have an expiry date, but he's bullish in the longer term for the company stock altogether.
Cheers,

Dave
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Question by:dlmille

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Expert Comment

It makes very little difference whether the stork is obtained by purchase or is received as an option. Sell when your best guess is that the stock will increase less than an alternative.
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"what's the ideal price to sell at"   As high as possible

"as the options have an expiry date". You say the owner is bullish on the company therefore Sell just before the expiry date

"there's low regret if the stock gets higher in value? "  There will always be regret if the stock goes higher after a sale..
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Assisted Solution

phoffric earned 100 total points
If you can find a correlation between the stock of the option you purchase with other artifacts (e.g., other option, stock prices, and recently, one article reported that certain words in articles about a stock were predictors of the stocks direction). So all you have to do is find a leading indicator of the stocks direction in order to know when to take the profit.

This is a question on finding correlations:
http://rdsrc.us/crWXtN

One University Of Pennsylvania Wharton graduate student told me that for options, when the price goes down away from the strike price, you can sell, but that studies have shown that statistically, once you reach the strike price, it is better to hold on as it tends to go higher. (He didn't tell me the exact time to cash in though.)
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Expert Comment

The short answer to your question is that you can't do it.  There is no way to predict future prices of stocks so there is no way to know when to get out.  There are risk mitigation strategies though to help you sleep better at night.

A strategy that you can use to maximize your gain but limit the downside is to place trailing stop-loss orders.  The difference between the exercise price and the stop-loss price is governed by your appetite for risk and the volatility of the stock.

If the option has a value of \$50 then you may want to place a stop-loss order at \$45.  If the price drops below \$45 they will be exercised, you take you profits.  As the stock climbs to \$55 you change your stop-loss to \$50.  The idea is to protect yourself on the downside but at the same time leave room for volatility in the price.

What you describe sounds like a non-qualified stock option plan (options granted to employee by the company) and not publicly traded options (buy puts or calls on an open exchange.)  I don't know what the mechanics are of implementing this strategy if the options aren't publicly traded.

If the stock is publicly traded you could always just buy out of the money put options to protect yourself on the downside.  You give up some gains by buying the "insurance" but you are protected in a down market.  Witha big drop you take the profits from the put options and continue to hold the original options on teh stock for the next rebound.
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>> There is no way to predict future prices of stocks so there is no way to know when to get out.

There are companies who do predict future prices of stocks using sophisticated algorithms and daily research to constantly modify the weighting factors.
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Author Comment

The options aren't publicly traded, they are grants at a specified grant price.  if the stock price goes below that, they have no value.  However, their value is the stock price less the grant price at any given time when the stock price is higher than the grant price.

It would seem that as the stock price goes higher, one might become more and more indifferent to converting to actual stock, as the percent change on the upside narrows between a held stock at some point and an open option.

This is not about predicting price.  This is about looking at a point in time and saying, if I cash out, I don't get the downside if stock goes down, and if stock price goes up, I've gotten a % yield benefit from the option so the tradeoff wasn't bad.

E.g., the stock price is now \$500.  If I cashed out versus held at this point and the price goes to \$575, I'm presuming there's less given up on the upside than say the stock price were \$200 and goes to \$275.

At least that's what I'm trying to determine how to visualize.

Dave
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Expert Comment

http://en.wikipedia.org/wiki/Black–Scholes
But be warned that billions of dollars have been lost because real life fluctuations have a fatter tail than the normal distribution assumed by the formula
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Expert Comment

Since he's an employee he should sell immediately after he makes a major mistake that is likely to cripple the company - or is that insider trading ;)
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Accepted Solution

thehagman earned 400 total points
Thus the employee starts with 1000 options of 50\$ each and if he trades them at a stock price of x \$, he'll
- optain 1000 shares at a price of 1000 * 50 \$
- sell these for 1000 * x \$
- pay 30% of 1000*(x-50) \$ as income tax (that's 300*(x-50) \$)
- lay aside the 50000 \$ used for trading the option
- buy shares from the remaining 700 * x -35000 \$
Thus the employee ends up with 700 - 35000/x shares and the state ends up with 300*(x-50) \$ of income tax.

As one might have immediately guessed: Do this when x is as high as possible. It makes you (and the state) happiest
(I've neglected the effect  the selling of 1000 shares might have on the price for buying in the final step)
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Author Comment

http://money.cnn.com/magazines/moneymag/money101/lesson10/index4.htm provided some useful insights as well.

I was able to take that and the logic thehagman provided to model purchase, tax impact (NQ option, though ISO's I think are taxed as income now as well), and compare to the option value alternative (after tax) through a spectrum of prices - from strike price to triple strike price.

I made a conditional format on the delta (sell and hold, versus option value) on a percentage basis, coloring green where the delta was within +/- 20% of twice the strike price (e.g., if you made the decision this is a good company and no other worries wrt % in portfolio, one rule of thumb mentioned was to sell at twice the strike price), so one could sell "early" not willing to risk the 2X for 80% potential value.

Selling high is good, yes.  But then after that if the stock reverted to the strike price or lower, there's still money (the stock, anyway) in the bank.

Alternatively, if one sold at twice the strike price, and the stock went as high as 3x the strike price, one would see the "opportunity loss" of about 33% of the value they held, having held the stock (before or after tax, the % delta is the same - if at the same tax rate and capital gains kicks in after 2 years of holding the stock, if I read correctly).

The overriding assumption is the company the employees are vested in is solid, expected to continue to grow, etc., (not skyrocket, but grow) where doubling has happened about ever 7 years, and the options are good for say 5 or 10 years before expiry.  While the employee may not be willing to "hold out" until just before expiry, he/she would want to understand what potential upside was being given up, while also understanding if a downside came, what benefit from earlier conversion could be derived.

I think I've created that horizon, based on this analysis.  Of course, employees expecting to continue to receive options throughout their career would need some type of methodology to manage turnover.  Those that receive on a one-off basis might be a bit more nervous about this - especially with the recent recovery, so having something to look at to understand "what-if" at least gives them something to chew on versus "knee-jerk" reactions or unintended consequences.

The tax impact is something I've only started thinking about - as timing their conversion also should consider if they move to a different bracket and by how much, as opposed to a disciplined approach - average cost out so many options/year might be a "best" solution (not counting for market volatility as with the folks who may have cashed out just before the IPO bust).

Thanks for your thoughts, both serious and humourus!

Dave
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Author Comment

I appreciate any follow-up comments on what I posted, before I close out...

So - has anyone considered converting options to options?  Does anyone EXTEND their options to ride out a downcycle (est every 7-10 years, theoretically?)

If one was early in his career, is there a benefit to maintaining leverage with options as opposed to conversion???

Dave
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