# The Greeks: Analyzing Risk for a Spread Position

Analyze position risk, using the Greeks.
Do you need an introduction to the Greeks?
Table
The Greeks: Sold 5 put spreads
The numbers are per option

GreekJul 75 PJul 80 P5-lot SpreadTheta 1.9 cents per day    2.6 cents per day      + 3.5 cents per day Delta -18 cents per point -33 short 75Gamma  2.3 cents per point       3.2 short 4.5Vega 10 cents per point 14 short 20Rho 0.13 cents per point 0.06 long 0.35

Last column = per spread value * 5.

The Greeks for the whole position equals the sum of the individual Greeks.

When you own an option, add its Greeks.
When you are short an option, subtract its Greeks.

Theta. Options have negative Theta. When you own an option, the passage of time reduces the value of your option, i.e., you lose money. Because we own Jul 75 puts, we have 1.9 negative theta for each put owned.

When short an option, the passage of time is good for the position (it earns money). Why? Because you are subtracting a negative — and that is a positive number. You are short 2.6 Theta for each of the Jul 80 puts.

Combining the long and short positions, each spread has a positive theta of + 2.6 -1.9 = + 0.7

You sold five spreads, so Theta/spread is multiplied by 5. Net theta position is +3.5 cents per day. Reminder; each option represents 100 shares, so 100 * 3.5 = \$3.50.

Bottom line risk/reward: You can expect to earn \$3.50 per day. Your position has zero Theta risk.

NOTE: Theta accelerates as time passes and tomorrow’s Theta should be a little bit greater than today’s Theta.

Delta. Delta can be considered as the “share equivalent. In other words, when you own a position that is +75 delta, the position performs very nearly the same as a position that is long 75 shares of stock. This is true over a narrow price range.

Delta for puts is negative, and ranges from 0 to -100. Call options have positive Delta between 0 and +100.

Be careful with decimals when making calculations. For example, when an option has +20 Delta, you know that a one point change in the stock prices results in a gain or loss of ~ 20 cents, and never \$20. The option price does not change by more than the stock price.

You own the Jul 75 puts an that adds 18 NEGATIVE DELTA per option to your position. You sold the Jul 80 puts, gaining 33 positive Delta for each. The Jul 80 puts contribute positive Delta because you sold negative Deltas. Subtracting -33 gives you +33.  Adding -18 and + 33, each spread comes with +15 Delta.

Bottom line risk/reward: You are at risk to the tune of \$75 per point when ABCD declines. If ABCD quickly moves to \$85, expect to show a profit of \$75 due to Delta. If the stock price quickly declines to \$83, expect the position to lose \$75, again due to Delta.

However, Delta is not constant and changes value as the stock price changes.
Gamma. Gamma requires further explanation.

Short interlude for readers who care about the math:  Gamma is a “2nd order” Greek –that means it is a 2nd derivative. Specifically, it is the second derivative of the option’s value with respect to the underlying price.

Delta is the first derivative of the option value with respect to the underlying price. The Greeks covered in this post are all first order Greeks, with the exception of Gamma.

Gamma is a second-order Greek and describes how one of the Greeks (specifically Delta) changes when the underlying price changes by one point. Gamma is always positive, so owning any option adds positive Gamma. Selling any option, adds negative Gamma to your position.

Each put spread has 0.9 negative gamma. The 5-lot position comes with +75 delta and -4.5 gamma. Thus if ABCD’s price changes:

• From \$84 to \$85, Delta loses 4.5 cents/share. At 85, position Delta is ~70.
• From \$84 to \$83, Delta gains 4.5 cents/share. At \$83, position Delta is ~80.

Bottom line risk/reward: If the stock price moves lower, the rate at which money is lost increases. With the stock at \$84, that rate is an extra \$4.50 per contract per point. Note that gamma is not constant and changes as the stock price changes.
Vega. Vega measures the sensitivity of the option price to a change in the implied volatility of the options. If your studies have not yet included “volatility” take a few moments to get some background information.

Vega is positive for all options. Each long Jul 75 put contributes +10 Vega to the portfolio and the Jul 80 puts each contribute -14 (negative because you sold these options). Total position Vega is -4 per spread, or -20 total.

Most of the time implied volatility changes are gradual, and there is not much day-to-day Vega risk. However — and this is a very significant however — on occasion implied volatility undergoes large changes very quickly.  It may occur all at once after a major (usually negative) event (the 9/11 attack), or stock market decline (Oct 19, 1987). It can occur over a period of a few days or weeks as the market trends steadily higher or lower. The point is that exposure to Vega risk is not something to ignore because that risk can add or remove a substantial sum from your account value.

Bottom line risk/reward: The position gains or loses \$20 for each one-point change in implied volatility. This position is short Vega, so any IV increase results in a loss (the spread value increases). Any decrease in IV results in a gain. Your Vega risk (-20) is not a large number and almost all trades should be comfortable with that risk.

However, there is a potential problem. If there is an “event” IV could increase by enough (10 to 20 points) that the resulting loss is significant (\$200 to \$400 for the 5-lot put spread). But worse than that, if the market were to tumble, Delta risk, combined with Gamma and Vega risk would result is a good-sized loss (but never more than the maximum possible loss). It is unlikely that you will see this happen with any frequency, but it is not smart to believe that you will never see it.
Rho. Rho measures the sensitivity of an option’s price to a change in interest rates. When interest rates are low, the chance of a 1% increase is essentially zero. Rates do not jump form 1% to 2% too quickly. In addition the interest rate is a minor factor in the price of an option — when rates are low.

However, rates will not remain low forever and one day Rho may be worth considering. As the table indicates, this position has hardly any exposure to Rho.

One additional point: When trading long-term options (LEAPS) with expiration dated two plus years into the future, Rho is more significant.
Analysis

There are no set rules when analyzing a position for risk. Decide how much you are willing (and can afford) to lose under normal circumstances and be certain that this limit is not exceeded. Write (in the trade plan) the action you expect to take if and when losing that sum becomes more likely.

Use position size to prevent a disaster. Sometimes you lose the ability to manage risk (because the stock price gaps well beyond the price at which you planned to cut losses ad exit the trade).

Do not become a pessimist who is afraid to trade. The whole idea behind mentioning risk is to make you aware of what can go wrong so that you are not caught off guard. If you trade with an appropriate position size, you will never incur an unacceptable loss. That is the key to long-term survival.

Example, if your risk tolerance dictates that you lose no more than \$200 per trade, be aware that a 3-point decline will cost at least 3 x \$51 from Delta. Add to that the expected additional loss from Gamma, and you would be near that \$200 limit. Theta will not help too much unless many days have passed, but pay attention to the implied volatility because the negative Vega is likely to make things worse (IV rallies when stocks decline — most of the time).

If you have access to risk graphs, use them every day to let you know where danger lurks.