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Author: jimgillies Big gold star, 5000 posts Top Recommended Fools Feste Award Winner! Old School Fool CAPS All Star Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: of 1205  
Subject: Re: Price movements of options at different stri Date: 6/7/2005 9:45 AM
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Good morning,

Actually, I have to adjust IlanBigfoot's explanation, as I think there might be some misunderstandings of option value.

Yes, an option is the combination of intrinsic and time values.
Option Value = Intrinsic Value + Time Value

Intrinsic value is what an option would be worth if it expired today, and is nothing more than the difference between the underlying stock price (S), and the option strike price (X). However, this difference can be negative, so intrinsic value is actually a MAX function.
Intrinsic Value of a Call:  MAX[0, S - X]
Intrinsic Value of a Put: MAX[0, X - S]

Time value is simply what an investor is willing to pay for the potential further payoff of the option over time. It is, by it's definition, a wasting asset, that decreases as the option expiry date approaches until, at expiry, the option is simply worth it's Intrinsic Value (which might be zero).

Looking at your DECK options, and considering DECK's latest closing price of $21.93, the option prices are all time value:

25 call @ $3.00 30 call @ $1.50
+---------------------+---------------------+
S = | $21.93 | $21.93 |
X = | $25.00 | $30.00 |
S - X = | - 3.07 | - 8.07 |
Intrinsic Value = | Max[0, -$3.07] = 0 | Max[0, -$3.07] = 0 |
Time Value = | $3.00 | $ 1.50 |
+---------------------+---------------------+

Comparing time premiums, even though it may not appear so, the 30 calls are 76% more expensive. Why? Because you get 2x leverage. In other words, if you are confident DECK will go over $30 in 6 months (demanding a 65% annualized increase) you can buy twice the options.

While somewhat correct, in that you can control twice the number of shares with the the $30 calls versus the $25 calls, the rest of this passage is a bit dangerous. Simply hinging your decision on your 'confidence' of DECK going over $30 in six months is a recipe for losing 100% of your investment. What do you base confidence on? How do you measure it?

For example, if you have $3,000 to invest (and I'm going to ignore transaction costs and potential capital gains taxes) you could buy 136 shares, 1000 $25 calls, or 2000 $30 calls. Let's look at the potential results. The table below shows your investment value and profit for various expiry date share prices.
          
Shares $25 Calls $30 Calls
Investment Value @ $21.93 @ $3.00 @ $1.50
----------------------------------------------------------------------
At Start $2,982 $3,000 $3,000
----------------------------------------------------------------------
At Expiry
S = $18 $2,448 0 0
Profit -17.9% -100% -100%
----------------------------------------------------------------------
S = $20 $2,720 0 0
Profit - 8.8% -100% -100%
----------------------------------------------------------------------
S = $25 $3,400 0 0
Profit +14.0% -100% -100%
----------------------------------------------------------------------
S = $27.50 $3,740 $2,500 0
Profit +25.4% -16.7% -100%
----------------------------------------------------------------------
S = $30 $4,080 $5,000 0
Profit +36.8% +66.7% -100%
----------------------------------------------------------------------
S = $32.50 $4,420 $7,500 $5,000
Profit +48.2% +150.0% +66.7%
----------------------------------------------------------------------
S = $35 $4,760 $10,000 $10,000
Profit +59.6% +233.3% +233.3%
----------------------------------------------------------------------
S = $40 $5,440 $15,000 $20,000
Profit +82.4% +400.0% +566.7%
----------------------------------------------------------------------

So what can we take away from this table?

First - observe the power of leverage as the underlying stock price increases. At S = $35, the two option payoffs are identical, while at S = $40, the $30 call pays-off a full third higher than the $25 call. This 'power' is the siren song that attracts many people to options that perhaps should not be dabbling in this area.

Second - realize that, even if the options finish in-the-money (ITM), it does not necessarily mean you'll come out ahead. Look at the $25 call. Because you pay $3 for the option, you actually don't make a profit unless the stock finishes above $28 ($25 strike price + $3 option price). Look at the case where the stock finishes at $27.50 on the date of option expiry. In such a case, you would still be facing a loss on your investment of 16.7%, whereas, if you had simply bought DECK stock, you'd be sitting on more than a 25% gain in six months (most assuredly, a market-beating return).

Third - Time is not your friend when dealing with options. At expiry, even if DECK continues to lag, if you own the stock, it is almost impossible (>99.999999%) that you will lose 100% of your investment on this no-debt, cash flow positive company. It's a very real possibility when using options, and that possibility increases with the level of the option's strike price. In other words, to score big, you have to bet big.

Fourth - Assume options finish out-of-the-money (OTM). If you own the shares and believe in the company, you can simply wait out the market - you still own the shares (or you can sell them and receive some value for them). No so for the expired options.


Finally, I asked earlier how you measure confidence when it comes to assessing an option purchase. It's my view that, if you cannot answer that question, you should not be risking option purchase. Fortunately, there is a tool to give us an assessment. It's a component of the Black-Scholes option-pricing model, and tells us the probability of an option finishing ITM. Note, this does not mean the probability of making money on your option position. Rather it's the probability that the $25 call will finish with a stock price >$25, and the probability that the $30 call will finish with a stock price >$30. Remember, you actually only make money when the stock price is greater than the combination of strike price and option premium, so $28 in the case of the $25 call, and $31.50 in the case of the $30 call. Fortunately, we can 'goose' the model to spit out the probability of ending in profit too.

Inputs to the model include:


25 call @ $3.00 30 call @ $1.50
+---------------------+---------------------+
S = | $21.93 | $21.93 |
X = | $25.00 | $30.00 |
Time to Expiry (T) = | 0.5288 yrs | 0.5288 yrs |
Underlying Volatility = | 58.43% | 58.43% |
Risk-free Rate (Rf) = | 2.98% | 2.98% |
+---------------------+---------------------+
Probability Finish ITM = | 47.65% | 31.29% |
+---------------------+---------------------+
Probability Profit = | 37.24% | 27.33% |
+---------------------+---------------------+

In short, I use options to bolster my returns. However, without substantially more study into the the underlying asset (DECK), this particular option strategy (buying a 6-mth naked call) is not a bet I would be making with such a poor probability of profitability.

I wrote a little bit on how to be warily respectful of options in the following post: http://boards.fool.com/Message.asp?mid=22569136.

Cheers,

Jim
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