## 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:

- Any buy/write strategy
- A deep in-the-money long call
- A deep in-the-money long put
- A far out-of-the-money naked call
- A far out-of-the-money naked (or cash secured) put

**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

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*. All profits and losses are *before commissions.*

**Buy/write example **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 05/17/2017 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). With a $101.25 breakeven price (at the moment the trade is placed), the probability is about 75% that the strategy will earn at least *some* profit at expiration.

If you define risk as the probability of profit vs. probability of loss, you might consider a 75% chance of earning at least some 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 05/17/2017 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 for you to sell it at a profit; it just has to increase in price quickly enough to offset time decay. Additionally, the maximum loss on this trade is only $137. 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 time 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.

With a $121.37 breakeven price, the probability that the strategy will be profitable at expiration is only about 12%. 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.

**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 05/17/2017 105 calls @ 5.90 for a total cost of $590

- Alternative option trade 2 (risks the amount of money): Buy 18 XYZ 05/17/2017 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 used in both alternative option trades is initially almost right at the money so 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.