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Front Spread w/Puts
AKA Ratio Vertical Spread
NOTE: This graph assumes the strategy was established for a net credit.
The Strategy
Buying the put gives you the right to sell stock at strike price B. Selling the two puts gives you the obligation to buy stock at strike price A if the options are assigned.
This strategy enables you to purchase a put that is atthemoney or slightly outofthemoney without paying full price. The goal is to obtain the put with strike B for a credit or a very small debit by selling the two puts with strike A.
Ideally, you want a slight dip in stock price to strike A. But watch out. Although one of the puts you sold is “coveredвЂќ by the put you buy with strike B, the second put you sold is “uncovered,вЂќ exposing you to significant downside risk.
If the stock goes too low, you’ll be in for a world of hurt. So beware of any abnormal moves in stock price and have a stoploss plan in place.
Options Guy’s Tips
Some investors may wish to run this strategy using index options rather than options on individual stocks. That’s because historically, indexes have not been as volatile as individual stocks. Fluctuations in an index’s component stock prices tend to cancel one another out, lessening the volatility of the index as a whole.
The maximum value of a front spread is usually achieved when it’s close to expiration. You may wish to consider running this strategy shorterterm; e.g., 3045 days from expiration.
The Setup
 Sell two puts, strike price A
 Buy a put, strike price B
 Generally, the stock will be at or above strike B.
NOTE: All options have the same expiration month.
Who Should Run It
NOTE: Due to the significant risk if the stock moves sharply downward, this strategy is suited only to the most advanced option traders. If you are not an AllStar trader, consider running a skip strike butterfly with puts.
When to Run It
You’re slightly bearish. You want the stock to go down to strike A and then stop.
Breakeven at Expiration
If established for a net debit, there are two breakeven points:

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 Strike B minus the net debit paid to establish the position.
 Strike A minus the maximum profit potential.
If established for a net credit, there is only one breakeven point:
 Strike A minus the maximum profit potential.
The Sweet Spot
You want the stock price exactly at strike A at expiration.
Maximum Potential Profit
If established for a net debit, potential profit is limited to the difference between strike A and strike B, minus the net debit paid.
If established for a net credit, potential profit is limited to the difference between strike A and strike B, plus the net credit.
Maximum Potential Loss
If established for a net debit:
 Risk is limited to the net debit paid if the stock price goes up.
 Risk is substantial but limited to strike A plus the net debit paid if the stock goes to zero.
If established for a net credit:
 Risk is substantial but limited to strike A minus the net credit if the stock goes to zero.
Ally Invest Margin Requirement
Margin requirement is the requirement for the uncovered short put portion of the front spread.
NOTE: If established for a net credit, the proceeds may be applied to the initial margin requirement.
After this position is established, an ongoing maintenance margin requirement may apply. That means depending on how the underlying performs, an increase (or decrease) in the required margin is possible. Keep in mind this requirement is subject to change and is on a perunit basis. So don’t forget to multiply by the total number of units when you’re doing the math.
As Time Goes By
For this strategy, time decay is your friend. It’s eroding the value of the option you purchased (bad). However, that will be outweighed by the decrease in value of the two options you sold (good).
Implied Volatility
After the strategy is established, in general you want implied volatility to go down. That’s because it will decrease the value of the two options you sold more than the single option you bought.
The closer the stock price is to strike A, the more you want implied volatility to decrease for two reasons. First, it will decrease the value of the nearthemoney options you sold at strike A more than the inthemoney option you bought at strike B. Second, it suggests a decreased probability of a wide price swing, whereas you want the stock price to remain stable at or around strike A.
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PCA and proportion of variance explained
In general, what is meant by saying that the fraction $x$ of the variance in an analysis like PCA is explained by the first principal component? Can someone explain this intuitively but also give a precise mathematical definition of what “variance explained” means in terms of principal component analysis (PCA)?
For simple linear regression, the rsquared of best fit line is always described as the proportion of the variance explained, but I am not sure what to make of that either. Is proportion of variance here just the extend of deviation of points from the best fit line?
4 Answers 4
In case of PCA, “variance” means summative variance or multivariate variability or overall variability or total variability. Below is the covariance matrix of some 3 variables. Their variances are on the diagonal, and the sum of the 3 values (3.448) is the overall variability.
Now, PCA replaces original variables with new variables, called principal components, which are orthogonal (i.e. they have zero covariations) and have variances (called eigenvalues) in decreasing order. So, the covariance matrix between the principal components extracted from the above data is this:
Note that the diagonal sum is still 3.448, which says that all 3 components account for all the multivariate variability. The 1st principal component accounts for or “explains” 1.651/3.448 = 47.9% of the overall variability; the 2nd one explains 1.220/3.448 = 35.4% of it; the 3rd one explains .577/3.448 = 16.7% of it.
So, what do they mean when they say that “PCA maximizes variance” or “PCA explains maximal variance“? That is not, of course, that it finds the largest variance among three values 1.343730519 .619205620 1.485549631 , no. PCA finds, in the data space, the dimension (direction) with the largest variance out of the overall variance 1.343730519+.619205620+1.485549631 = 3.448 . That largest variance would be 1.651354285 . Then it finds the dimension of the second largest variance, orthogonal to the first one, out of the remaining 3.4481.651354285 overall variance. That 2nd dimension would be 1.220288343 variance. And so on. The last remaining dimension is .576843142 variance. See also “Pt3” here and the great answer here explaining how it done in more detail.
Mathematically, PCA is performed via linear algebra functions called eigendecomposition or svddecomposition. These functions will return you all the eigenvalues 1.651354285 1.220288343 .576843142 (and corresponding eigenvectors) at once (see, see).
@ttnphns has provided a good answer, perhaps I can add a few points. First, I want to point out that there was a relevant question on CV, with a really strong answer—you definitely want to check it out. In what follows, I will refer to the plots shown in that answer.
All three plots display the same data. Notice that there is variability in the data both vertically and horizontally, but we can think of most of the variability as actually being diagonal. In the third plot, that long black diagonal line is the first eigenvector (or the first principle component), and the length of that principle component (the spread of the data along that line–not actually the length of the line itself, which is just drawn on the plot) is the first eigenvalue–it’s the amount of variance accounted for by the first principle component. If you were to sum that length with the length of the second principle component (which is the width of the spread of the data orthogonally out from that diagonal line), and then divided either of the eigenvalues by that total, you would get the percent of the variance accounted for by the corresponding principle component.
On the other hand, to understand the percent of the variance accounted for in regression, you can look at the top plot. In that case, the red line is the regression line, or the set of the predicted values from the model. The variance explained can be understood as the ratio of the vertical spread of the regression line (i.e., from the lowest point on the line to the highest point on the line) to the vertical spread of the data (i.e., from the lowest data point to the highest data point). Of course, that’s only a loose idea, because literally those are ranges, not variances, but that should help you get the point.
Be sure to read the question. And, although I referred to the top answer, several of the answers given are excellent. It’s worth your time to read them all.
1×2 ratio vertical spread with calls
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Potential goals
To profit from a stock price move to the strike price of the short calls with limited downside risk.
Explanation
Example of 1×2 ratio vertical spread with calls
Buy 1 XYZ 100 call at 3.30 
Sell 2 XYZ 105 calls at 1.50 each 
A 1×2 ratio vertical spread with calls is created by buying one lowerstrike call and selling two higherstrike calls. The second short call is uncovered (naked) and has unlimited risk. This strategy can be established for either a net debit (as seen in the example) or for a net credit, depending on the time to expiration, the percentage distance between the strike prices and the level of volatility. Profit potential is limited, and the maximum profit is realized if the stock price is at the strike price of the short calls at expiration. Above the breakeven point risk is unlimited, because the stock price can rise indefinitely.
Maximum profit
If the position is created for a net debit (cost), profit potential is limited to the difference between the strike prices minus the net debit including commissions. In the example above, the maximum profit is 4.70, because the higher strike price minus the lower strike price is 5.00 (105.00 – 100.00) and the net debit is 0.30. Therefore, 5.00 – 0.30 = 4.70.
If the position is created for a net credit (amount received), profit potential is limited to the difference between the strike prices plus the net credit less commissions. If the position had been established for net credit of 50 cents (0.50), the maximum profit would be 5.50, because the higher strike price minus the lower strike price is 5.00 (105.00 – 100.00) and the net credit would have been 0.50. Therefore, 5.00 + 0.50 = 5.50.
Maximum risk
On the upside, risk is unlimited, because the position has an uncovered short call (naked call), and the stock price can rise indefinitely.
On the downside, potential risk depends on whether the position is established for a net debit or a net credit. If established for a net debit, the maximum risk is equal to the net debit including commissions. If established for a net credit including commissions, there is no downside risk. If the stock price is below the lower strike price at expiration, then all calls expire worthless and the net credit is kept as a profit.
Breakeven stock price at expiration
If the position is established for a net debit, there are two breakeven points:
Lower breakeven point: Lower strike price plus the net debit
In this example: 100.00 + 0.30 = 100.30
Higher breakeven point: Higher strike price plus the maximum profit
In this example: 105.00 + 4.70 = 109.70
If the position is established for a net credit, there is one breakeven point:
Assuming the position is established for a net credit of 50 cents (0.50):
Breakeven point: Higher strike price plus the maximum profit
In this example: 105.00 + 5.50 = 110.50
Note: If this position is established for a net credit, there is no “lower breakeven point.” If the stock price is below the lower strike price at expiration, then all calls expire worthless, and the net credit is kept as profit.
Profit/Loss diagram and table: 1×2 ratio vertical spread with calls
Buy 1 XYZ 100 call at 3.30 
Sell 2 XYZ 105 calls at 1.50 each 
Stock Price at Expiration  Long 1 100 Call Profit/(Loss) at Expiration  Short 2 105 Calls Profit/(Loss) at Expiration  Net Profit/(Loss) at Expiration 

113  +9.70  (13.00)  (3.30) 
112  +8.70  (11.00)  (2.30) 
111  +7.70  (9.00)  (1.30) 
110  +6.70  (7.00)  (0.30) 
109  +5.70  (5.00)  +0.70 
108  +4.70  (3.00)  +1.70 
107  +3.70  (1.00)  +2.70 
106  +2.70  +1.00  +3.70 
105  +1.70  +3.00  +4.70 
104  +0.70  +3.00  +3.70 
103  (0.30)  +3.00  +2.70 
102  (1.30)  +3.00  +1.70 
101  (2.30)  +3.00  +0.70 
100  (3.30)  +3.00  (0.30) 
99  (3.30)  +3.00  (0.30) 
98  (3.30)  +3.00  (0.30) 
97  (3.30)  +3.00  (0.30) 
Appropriate market forecast
A 1×2 ratio vertical spread with calls realizes its maximum profit if the stock price is at the strike price of the short calls at expiration. The forecast, therefore, can either be “neutral” or “modestly bullish,” depending on the relationship of the stock price to the strike prices of the calls when the position is established.
If the stock price is at or near the strike price of the short calls when the position is established, then the forecast must be for continued stock price action near the strike price of the short calls (neutral).
If the stock price is below the strike price of the short calls, and possibly below the strike price of the long call, when the position is established, then the forecast must be for the stock price to rise to the strike price of the short calls at expiration (modestly bullish).
While one can imagine a scenario in which the stock price is above the strike price of the short calls and in which a 1×2 ratio vertical spread with calls would profit from bearish price action, it is most likely that another strategy would be a more profitable choice for a bearish forecast.
Strategy discussion
A 1×2 ratio vertical spread with calls is the same as buying a bull call spread and simultaneously selling an uncovered (naked) call. The premium from the uncovered call is used to at least partially pay for the bull call spread. The position profits from time decay as the underlying stock trades near the strike price of the short calls. While the “low” net cost to establish the strategy – or possible net credit – is viewed as an attractive feature by some traders, the strategy has unlimited risk from the uncovered call. There is also a margin requirement for the uncovered call in additional to the upfront cash requirement for the bull call spread. This strategy, therefore, is suitable only for experienced traders who are suited to accept the unlimited risk.
Choosing a 1×2 ratio vertical spread with calls requires both a high tolerance for risk and trading discipline. A high tolerance for risk is required, because potential risk is unlimited on the upside. Trading discipline is required because the ability to “cut losses short” is an attribute of trading discipline. Many traders who use this strategy have strict guidelines – which they adhere to – about closing positions when the market goes against the forecast.
Impact of stock price change
“Delta” estimates how much a position will change in price as the stock price changes. Long calls have positive deltas, and short calls have negative deltas. The net delta of a 1×2 ratio vertical spread with calls varies from +1.00 to −1.00, depending on the relationship of the stock price to the strike prices of the options.
The position delta approaches +1.00 if the long call is in the money and the short calls are out of the money as expiration approaches. In this case, the delta of the long call approaches +1.00, and the deltas of the short calls approach zero.
When the stock price is above the strike price of the short calls as expiration approaches, the position delta approaches −1.00, because the delta of the long call approaches +1.00 and the deltas of the two short calls approach −1.00 each.
The position delta approaches zero as the stock price falls below the strike price of the long call, because the deltas of all the calls approach zero.
Impact of change in volatility
Volatility is a measure of how much a stock price fluctuates in percentage terms, and volatility is a factor in option prices. As volatility rises, option prices tend to rise if other factors such as stock price and time to expiration remain constant. Long options, therefore, rise in price and make money when volatility rises, and short options rise in price and lose money when volatility rises. When volatility falls, the opposite happens; long options lose money and short options make money. “Vega” is a measure of how much changing volatility affects the net price of a position.
Since a 1×2 ratio vertical spread with calls has one long call and two short calls, rising volatility generally hurts the position and falling volatility generally helps. In the language of options, this is “net negative vega.” As expiration approaches, however, the impact of changing volatility depends on the relationship of the stock price to the strike prices of the options. If the stock price is close to the strike price of the long call, then the net vega tends to be positive. If the stock price is close to the strike price of the short calls, then the net vega tends to be negative. The net vega approaches zero if the stock price falls below the lower strike or rises sharply above the higher strike.
Impact of time
The time value portion of an option’s total price decreases as expiration approaches. This is known as time erosion. “Theta” is a measure of how much time erosion affects the net price of a position. Long option positions have negative theta, which means they lose money from time erosion, if other factors remain constant; and short options have positive theta, which means they make money from time erosion.
Since a 1×2 ratio vertical spread with calls has one long call and two short calls, the impact of time erosion is generally positive. In the language of options, this is a “net positive theta.” As expiration approaches, however, the impact of time erosion depends on the relationship of the stock price to the strike prices of the options. If the stock price is close to the strike price of the long call, then the net theta tends to be negative and time erosion hurts the position. If the stock price is close to the strike price of the short calls, then the net theta tends to be positive and time erosion benefits the position.
Risk of early assignment
Stock options in the United States can be exercised on any business day, and holders of short stock option positions have no control over when they will be required to fulfill the obligation. Therefore, the risk of early assignment is a real risk that must be considered when entering into positions involving short options.
While the long call in 1×2 ratio vertical spread with calls has no risk of early assignment, the short calls do have such risk. Early assignment of stock options is generally related to dividends, and short calls that are assigned early are generally assigned on the day before the exdividend date. Inthemoney calls whose time value is less than the dividend have a high likelihood of being assigned.
If assignment is deemed likely, there are three possibilities. First, one of the two short calls is assigned. In this case, 100 shares of stock are sold short and the long call and the second short call remain open. Second, both of the short calls are assigned. In this case, 200 shares are sold short and the long call remains open. Third, neither call is assigned. No matter how likely assignment may seem, there is no assurance that it will occur. In this case the 1×2 ratio vertical spread with calls remains intact.
If early assignment of one or both calls does occur, stock is sold, and a short stock position of 100 shares or 200 shares is created. If a short stock position is not wanted, 100 shares can be closed by exercising the long call, but the second 100 shares must be purchased in the marketplace. Note, however, that whichever method is used, the date of the stock purchase will be one day later than the date of the short sale. This difference will result in additional fees, including interest charges and commissions. Assignment of a short call might also trigger a margin call if there is not sufficient account equity to support the short stock position.
Potential position created at expiration
The position at expiration depends on the relationship of the stock price to the strike prices. If the stock price is at or below the strike price of the long call (lower strike), then all calls expire worthless and there is no stock position.
If the stock price is above the lower strike but not above the higher strike, then the long call is exercised and the short calls expire. Exercising a long call causes stock to be purchased at the strike price, so the result is a long stock position. Since long options are exercised at expiration if they are one cent (0.01) in the money, if long shares are not wanted, the long call must be sold prior to expiration.
If the stock price is above the higher strike price then the long call is exercised and both short calls are assigned. In the example above, this means that 100 shares are purchased and 200 shares are sold. The result is a position of short 100 shares. If the stock price is above the higher strike immediately prior to expiration, and if a position of short 100 shares is not wanted, then one of the short calls must be closed.
Other considerations
In a “ratio spread” there is a difference between the number of options purchased and the number of options sold. The term “vertical” in the name of this strategy implies that more options are sold than purchased. In contrast, in the “1×2 ratio volatility spread with calls,” the term “volatility” implies that more options are purchased than sold.
This strategy – the 1×2 ratio vertical spread with calls – is also known as a “front spread,” because it is generally used with shortterm, or “frontmonth,” options as opposed to longerterm, or “backmonth,” options. Shorterterm options are more suitable for this strategy, because this strategy profits mostly from time decay when the short calls are at the money and close to expiration. Atthemoney shortterm options experience a greater rate of time decay than longerterm options.
Related Strategies
A 1×2 ratio vertical spread with puts is created by buying one higherstrike put and selling two lowerstrike puts.
A long stock plus ratio call spread position is created by buying (or owning) stock and simultaneously buying one atthemoney call and selling two outofthemoney calls.
Article copyright 2020 by Chicago Board Options Exchange, Inc (CBOE). Reprinted with permission from CBOE. The statements and opinions expressed in this article are those of the author. Fidelity Investments cannot guarantee the accuracy or completeness of any statements or data.
Options trading entails significant risk and is not appropriate for all investors. Certain complex options strategies carry additional risk. Before trading options, please read Characteristics and Risks of Standardized Options. Supporting documentation for any claims, if applicable, will be furnished upon request.
Greeks are mathematical calculations used to determine the effect of various factors on options.
Charts, screenshots, company stock symbols and examples contained in this module are for illustrative purposes only.

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