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# How Do You Define Risk?

###### Key Points
• Trading always involves some level of risk, but “risk” can be defined in many different ways.

• Is it the probability of profit compared to the probability of loss? Or is it the amount you could earn compared to the amount you could lose?

• Plus, how do you quantify risk? Is it the number of shares or the dollar amount?

Is options trading risky? This is a harder question to answer than you might think, because it depends upon how you define “risk.”

Most traders define risk in one of two ways. The first method is the probability of earning a profit versus the probability of incurring a loss. The second way is the amount of money you could lose compared to the amount of money you could earn. Let’s look at both.

#### Probability of profit vs. probability of loss

For traders who define risk as the probability of profit vs. probability of loss, the amount at risk is generally a lesser consideration, because a loss is not anticipated. This type of trader will typically focus on strategies in which the probability of profit is much higher than the probability of loss. Assuming the trader’s forecast on the underlying security is ultimately correct, a single use of any of the following strategies would generally be considered low risk:

#### Amount you could lose vs. amount you could earn

This is also sometimes called the risk-to-reward ratio. For traders who define risk this way, the fact that a profit of any kind is unlikely, is generally a lesser consideration, because the amount at risk is considered very small. This type of trader will typically only consider trades in which the potential gain is much higher than the potential loss. Assuming the trader’s forecast on the underlying security is ultimately correct, a single use of any of the following strategies would generally be considered low risk:

• An out-of-the-money long call
• An out-of-the-money long put
• An out-of-the-money long strangle
• A lottery ticket
• A long position in a penny stock

Let’s look at an example and see whether it’s a “risky” trade. Our hypothetical example is a buy/write of XYZ, a highly rated, “blue-chip” stock:

Buy 100 shares XYZ                  @   108.70
Sell 1 XYZ 05/17/2014 105 call @       7.45
Net debit =  101.25 (\$10,125)

This option is initially more than \$3 in-the-money, and it has a Delta of .61. This theoretically implies that (at the moment the trade is placed) there’s a 61% chance that the option will expire in the money, resulting in assignment and a profit of \$375 (105 strike price – 101.25 initial cost x 100 shares) before commissions. This is the maximum profit that can be earned.

Additionally, because the breakeven price is \$101.25, the stock has to drop 7.45 points by expiration for the trade to result in a loss (before commissions). Further, the Trade and Probability Calculator in StreetSmart Edge® shows that with a \$101.25 breakeven price (at the moment the trade is placed), there’s a 75.38% probability that the strategy will earn at least some profit at expiration.

Note: For the purposes of all following examples, assume that the probability of expiration and the breakeven point are at the moment the trade is placed. Similarly, profits and losses are before commissions.

Source: StreetSmart Edge.

If you define risk as the probability of profit vs. probability of loss, you might consider a 61% chance of earning the maximum profit on a highly rated stock (that has to drop more than 7 points to lose money), a relatively low-risk trade. However, if you define risk as the amount you could lose vs. the amount you could earn, you might be concerned that you are risking \$10,125 (max loss) to earn only \$375 (max gain). While this means you could earn about 3.7% in six months, you may find the risk-to-reward ratio of about 27:1 way too high.

#### Long call example

Many traders would consider the following long call trade a relatively low-risk strategy if XYZ was a highly rated, “blue-chip” stock with a current price of 108.70:

Buy 1 XYZ 05/17/2014 120 call @      1.37
Net debit =  1.37 (\$137)

If you define risk as the amount you could lose vs. the amount you could earn, you may not think this trade is overly risky. XYZ is a highly rated stock and this option has about six months until expiration, which may be plenty of time for it to increase in price. Besides, the option doesn’t have to go in the money, it just has to increase in price quickly enough to offset time decay for you to sell it at a profit. Additionally, the maximum loss on this trade is only \$137. Plus, this trade theoretically has unlimited upside potential so you may consider it a relatively low-risk trade, as the risk-to-reward ratio is extremely small.

However, this option is initially more than \$11 out of the money and has a Delta of only .19, or a 19% probability that the option will expire in the money. This option also has a Theta of about -0.015, which implies that it will initially lose about \$1.50 per day in value, even if the stock price does not change at all. Finally, the breakeven price is \$121.37 (120 strike price + 1.37 option premium), meaning that the stock has to increase by more than 12 points for this trade to result in any profit if held until expiration.

Using the Trade and Probability Calculator, we can determine that with a \$121.37 breakeven price, there’s an 11.84% chance that the strategy will be profitable at expiration. In other words, while \$137 may be a relatively small amount to risk, the odds are about 88% that you will lose money—and about 81% that you will lose all of your money—on this trade if you hold it until expiration.

#### Long call example

Source: StreetSmart Edge.

#### How do you quantify risk?

Another question that sometimes troubles traders is: How do you quantify risk? Is it the number of shares or the dollar amount? Traders who substitute a stock strategy with an option strategy that controls the same number of shares vs. an option strategy that risks the same amount of money, are likely taking on significantly different amounts of risk.

Consider these hypothetical scenarios for XYZ—a highly rated, blue-chip stock with a current price of 105.80:

• Stock trade: Buy 100 shares of XYZ at \$105.80 for a total cost of \$10,580
• Alternative option trade 1 (controls the same number of shares): Buy 1 XYZ 05/17/2014 105 calls @ 5.90 for a total cost of \$590
• Alternative option trade 2 (risks the same amount of money): Buy 18 XYZ 05/17/2014 105 calls @ 5.90 for a total cost of \$10,620

Note that strategies involving no stock position (options only) do not entitle the trader to certain benefits often associated with stock ownership, such as dividends (if any), voting rights, and no expiration date.

This option is initially almost at the money and it has a Delta of about .50, or a 50% probability that the option will expire in the money. It also implies that initially the call options will increase (decrease) about \$0.50 if XYZ increases (decreases) by \$1.00.

In alternative option trade 1 (which controls 100 shares of stock):

• The option position purchased would initially be expected to increase or decrease by only about half of the dollar value of the stock.
• However, due to its lower overall cost, this trade would move significantly more on a percentage basis, making the risk-to-reward ratio significantly lower than the purchase of 100 shares of stock.
• Additionally, the maximum loss in alternative 1 is only about 5% of the maximum loss of the stock trade, some traders may consider this trade less risky, even though the characteristics will change over time and the option could eventually expire worthless.
• Further, the likelihood of sustaining maximum loss on the option trade is significantly higher than with the stock.
• The option will sustain maximum loss if the stock is below 105 at expiration; the stock has to drop to zero to sustain maximum loss.

In alternative option trade 2 (which has about the same dollar amount at risk as the stock trade):

• Eighteen call options are purchased in lieu of the actual stock.
• Initially a \$1.00 increase (decrease) in the price of XYZ would be expected to result in about \$900 profit (loss) before commissions, compared to only \$100 profit (loss) for the stock trade.
• While the initial cost of both trades is very similar, alternative 2 would be considered far more risky by most traders because the options are initially about right at the money, with a Delta of about .50.
• This theoretically implies a 50% probability that the options will expire in the money.
• This also means there is about a 50% chance they could expire worthless, resulting in a 100% loss.

Using the Trade and Probability Calculator in the same manner as in the previous examples, we can determine that with a \$110.90 breakeven price, if you hold the options until expiration there’s a 29% chance this strategy will be profitable.  In other words, the odds are about 71% that you will lose money on this trade. A comparable loss on the stock trade would require XYZ to go to 0, whereas the options would expire worthless if XYZ is below 105.

So are long calls riskier than long stock? If you trade in units of capital (dollars), they can be.  However, if you trade in units of stock, long calls are less risky than a long stock position.

#### Bottom line

Trading always involves some level of risk, but “risk” can be a very ambiguous term and it can be defined in many different ways. When products, strategies, markets, and account features are described as high risk, low risk, or moderate risk, make sure you understand how the risk is being defined, before you risk your own money.

I hope this enhanced your understanding of options. I welcome your feedback—clicking on the thumbs up or thumbs down icons at the bottom of the page will allow you to contribute your thoughts.

#### Important Disclosures

Options carry a high level of risk and are not suitable for all investors. Certain requirements must be met to trade options through Schwab. With long options, investors may lose 100% of funds invested. Covered calls provide downside protection only to the extent of the premium received and limit upside potential to the strike price plus premium received. Please read the options disclosure document titled Characteristics and Risks of Standardized Options before considering any option transaction. Supporting documentation for any claims or statistical information is available upon request.

For the sake of simplicity, the examples in this presentation do not take into consideration commissions and other transaction fees, tax considerations, or margin requirements, which are factors that may significantly affect the economic consequences of strategies displayed. Please contact a tax advisor for the tax implications involved in these strategies.

Past performance is no indication (or "guarantee") of future results. The information provided here is for general informational purposes only and should not be considered an individualized recommendation or personalized investment advice.

The information presented does not consider your particular investment objectives or financial situation, and does not make personalized recommendations. Any opinions expressed herein are subject to change without notice. Supporting documentation for any claims or statistical information is available upon request.

The investment strategies mentioned here may not be suitable for everyone. Each investor needs to review an investment strategy for his or her own particular situation before making any investment decision. Examples are not intended to be reflective of results you can expect to achieve.

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