Understanding Time Premium - Part Two

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...continued from Part One

ARE OPTIONS EXPENSIVE?
Many people claim that options are prohibitively expensive, and sometimes they are right. However, often they are fairly priced (or even underpriced) compared to reasonable expectations of how the stock is likely to perform. Therefore, they can offer surprisingly good value as insurance.

Let's use an example of hedging Reuters at $45, by buying the at-the-money put for $2.25. (Again, look at Figure 1.) Let’s say that you hold the stock and are worried about where the stock might go. Based on past behavior, you think that a big move is possible. (The stock has traded as high as $50 and as low as $32 over the past 12 months.)

With the at-the-money put, you are buying the maximum insurance. This is because you are buying insurance, with no deductible, against a big move in either direction.
It may surprise you to know that if an at-the-money option is fairly priced (i.e. the premium is in line with future volatility), there will be a 69% likelihood that the stock will end up outside the range of this premium paid. In the case of Reuters, it could move more than $2.25 to above $47.25, or down more than $2.25 to below $42.75. Either way, after the fact, you are likely to be glad you bought the option.

SEEING IS BELIEVING
This GRAPH provides a visual example of how this particular hedged position performs. The heavy bent line (and the left-hand scale) shows the gains (or losses) of the stock plus the hedge, while the curve with the drop lines (and the right-hand scale) shows the probability distribution. The area above $47.25 represents 35% of the possible outcomes, while the area below $42.75 represents 34%.

If the stock makes a big move in either direction, you will be happy you bought insurance. If Reuters goes to $60.00, you will have made a $12.75 profit ($15 less than the premium you paid). Alternatively, if the stock falls to $30, the put will offset the loss on the stock, so that all you will lose will be your $2.25 premium.

THE CHEAPER "DEDUCTIBLE"
But what if you are bullish on Reuters, but still feel that you need to insure against a really big loss? Or, what if you have turned extremely cautious on the stock, but do not want to miss out if the stock were to rise significantly? In either case, you may be willing to take a “deductible” on your time premium insurance.

For instance, if you are bullish and are willing to forgo some of your insurance on the downside (against cash losses), then you can take the “deductible” by buying the out-of-the-money $40 strike put for $0.75. The $5.00 difference between the stock and the strike price represents your deductible. That is how much you are willing to give up before your insurance kicks in. On the upside, your profits will be greater, because you have bought less insurance.

Alternatively, if you are very cautious about holding the stock, but don’t want to fully discount the possibility of a large rise, you can take a deductible by hedging with the in-the-money put. By buying the in-the-money $50 put for $5.65, you have effectively taken a $5.00 deductible on possible gains. Remember that your time premium is only $0.65. At expiration, for all outcomes below $50, gains and losses in the stock and the option offset each other, so that all you will lose is the $0.65 time premium. If the stock goes from $45 to $60, you will have made $9.35, ($15 less your $5.65 premium).


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