Covered Combination Explained

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So what is a combination bet? Well this is a getting together multiple bets on a series of selections. The idea behind a combination bet is to reduce the risk while maximising the potential gain that you could get back. There is a big advantage because of the coverage as opposed to a regular bet on a single, double or accumulator. That is because it doesn’t require all of the selections in the wager to win in order to return something.

Let’s look at this like this. You fancy Manchester City to win their game on Saturday and you have a 12 stake to play. But instead of placing that entire steak on City, you could split it up, and have a 4 stake on Man City, Liverpool and Chelsea all to win their matches on the day. Why would you do that? It is because if you had staked the entire lot on Man City and they failed to win their match then you would have been out of pocket. However if they lost and both Liverpool and Chelsea won, then you would get something coming back.

How does a combination bet work?

So from your initial stake, you would have cut down the risk on your capital outlay. There are many different types of combustion bets, and they all have names that you will probably come across. There is the Yankee, the Super Yankee, the Lucky 15, the Patent and the Canadian for example which are all combination bets because they offer a variety of bets that could happen from the number of selections in them. Let’s break them down to paint a clearer picture of a combination bet.

One important difference to understand in types of combination bets is the one between a Full Cover Bet and a Full Cover Bet with Singles. The former only builds doubles, trebles and accumulators from selections (examples are Trixie, Yankee, Canadian, Heinz) and don’t cover the single selections. Betting options like the Patent and the Lucky 15 do the same job but they expand the coverage by also having the single wagers on the selections as well. This obviously requires a larger outlay of stake because of more bets being combined from the selections.

This is the most popular of combination bets because it needs just three selections. From those three selection you have four wagers (one treble and three doubles). So if at least two of the selections win, then you will have returns.

Like the Trixie this combination bet has just the three selections, but it covers seven bets as opposed to four because it has the three singles, one treble and three doubles. You would only need the one win to return something.

Four selections will be turned into 11 separate bets (6 doubles, 4 trebles and fourfold accumulator). You would need to have two selections at minimum to win to get something back.

Lucky 15
Like the Trixie, this is one of the most popular types of combination bets around and you will see it heavily used on horse racing. You have four selections but with 15 separate bets in it. Basically it is a Yankee with the four selected singles bets thrown in.

Combination Bet Calculator

The quickest way to figure out what returns you could be getting is just by using our combination bet calculator. That cuts down a lot of the leg work and helps you assess the value of your wager. Always remember that you have to go Stake x Bet Selections as an outlay. So if you wanted a £1 stake on a Yankee then that would be an £11 stake (as a Yankee is a combination of eleven bets).

So there you have the combination bet. They have big value over an accumulator for example because of the fantastic extra coverage that you get by having combinations of bets. The downside is that because of all potential of landing big wins, because you are spreading the bets then you will be looking at a reduced payout.

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Just to highlight this, a 15 x £1 stake on a Lucky 15 (15 bets) with selections at 8/11, 3/1, 10/11 and 2/1 would return £158.45 profit if all four selections won. If you had put that £15 stake on a straight fourfold accumulator which won at the same odds, then you would have returned a massive £578.55 profit. So weigh up your risk and reward and consider those combination bets.

We only recommend bookmakers for combination bets that live up to the highest standards of quality. Our list of best online bookmakers is compiled with expert knowledge.

Covered Combinations: Merging Covered Call Writing and Put-Selling into One Strategy

A Covered combination (“combo trade”) trade is the simultaneous sale of an out-of-the-money (OTM) call and an out-of-the-money put with the same expiration date on 100 shares of a stock or ETF (exchange-traded fund). It consists of a combination of a covered call and a short put position on a share-for-share basis. The investor generates two premiums from the sale of the call and the put, in exchange for taking on the risk of doubling his stock position should the price decline below the strike price of the put by the expiration date.

Recently, we have had several BCI members inquire about this strategy and that is the motivation for this blog. This strategy is appropriate only for investors willing to hold long stock positions in 200 share increments as this article will explain. The motivation for using this strategy is to increase premium returns and to double a stock position half of which can be at a discount (if put is exercised).

Hypothetical covered combination trade

  • Buy 100 shares of BCI at $52 per share for $5200
  • Sell 1x OTM $55 call at $1.75 (1-month expiration)
  • Sell 1 x OTM $50 put at $1.50 (1-month expiration)
  • Secure the $50 put sale with a deposit of $5000 into brokerage cash account (broker may allow you to deduct put premium)

Outcome if share price closes above $55 at expiration

This is the outcome that will maximize the returns:

  • The put expires out-of-the-money and worthless
  • The call is exercised and shares are sold at the $55 strike price
  • No shares are owned after expiration
  • Total option profit = $325 ($175 + $150)
  • Stock profit = $300 (100 x $3) after buying at $52 and selling at $55
  • Total profit = $625
  • Cost basis is $5200 (buy 100 shares) + $5000 (to secure the put) = $10,200
  • 1-month percentage return = $625/$10,200 = 6.1%

Outcome if share price closes below $50 at expiration

This is the worst case scenario and may necessitate the implementation of exit strategy maneuvers.

  • Net cost of 100 shares of BCI assigned from put = $50 – $3.25 (two premiums) = $46.75
  • Still long 100 shares at a cost basis of $52
  • Average cost basis of 200 shares = $49.38

Outcome if share price closes between $50 and $55 at expiration

Both options expire out-of-the-money and worthless

  • No option assignment
  • Retain 100 shares originally purchased at $52
  • Option 1-month return = $325/$10,200 = 3.2%
  • Cost basis of the 100 shares is reduced to $48.75 ($52 – $3.25)

Possible outcomes that are part of this strategy

  • Obligation to sell 100 shares at $55
  • Obligation to buy 100 shares at $50
  • Double stock position on the downside
  • Early assignment of the call is possible prior to an ex-dividend date
  • Early assignment of deep in-the-money puts is possible if the time value approaches zero

Position management

BCI books, DVDs and blog articles have detailed exit strategy opportunities for both strategies and these should be utilized whenever indicated. The fact that covered combinations employ both strategies simultaneously does not eliminate the critical importance of position management to mitigate losses and enhance gains.


I wrote this article in response to member inquiries. I am not necessarily encouraging the implementation of covered combinations but rather presenting an overview for those who are considering its use. There are many ways to make money in the stock and option markets and education is the tool that will maximize those returns.

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Beware of the VIX

Despite the market increases this week, I am inclined to take a more conservative stance in my portfolio for the January contracts because of the sharp movement of the VIX (CBOE Volatility Index also called the investor fear gauge). Generally, the VIX and the S&P 500 are inversely related so an increase in market volatility may enhance our option profits, but it also represents more risk incurred. For most of us, this is not a positive. The chart below reflects this inverse relationship and shows the 3 large spikes in the VIX during the past 6 months. I am still encouraged by our markets, just taking a short-term defensive stance:

The inverse relationship between the VIX and the S&P 500

Market tone

The market seemed to forget all its global concerns when the Fed announced its intention for no interest rate hike for a “considerable time” It appears that short-term interest rates will continue to be held to near zero at least through mid-2020.Here are this week’s reports:

  • Industrial production in November rose by 1.3%, nearly double the 0.7% expected by analysts
  • According to the Labor Department, the Consumer Price Index (CPI) declined by 0.3% in November, the largest decrease in the past 6 years. This had everything to do with the dramatic drop in oil prices
  • In the past year, the CPI rose by 1.3%, below the 2% target rate set by the Fed
  • New residential construction dropped by 1.6% in November from October stats. However, November figures reflected the first time in 6 years that new housing starts exceeded 1 million for 3 consecutive months
  • The Conference Board’s index of leading economic indicators in November increased by 0.6%, better than the 0.5% projected by economists. This was the 6th increase in the last 7 months. In addition, the board reported signs of wage growth

For the week, the S&P 500 increased by 3.4%, for a year-to-date return of 14%, including dividends.


IBD: Market in correction

GMI: 5/6- Sell signal since market close of December 15, 2020

BCI: Cautiously bullish due to the severe swings in the VIX, selling equal numbers of in-the-money and out-of-the-money strikes. Selling out-of-the-money puts is another way to navigate unusually volatile markets

What is a Covered Call? Learn the Pros and Cons

Before diving into the complexities of what a covered call trade is and how it can be used to generate portfolio income lets first define what an option contract is and what it means to each party involved. There are two main types of options, call options and put options. A call option is a contract that gives the holder (buyer) the right, but not the obligation, to buy a security at a specified price for a certain period of time.

Buying one call stock option gives the purchaser the right to buy 100 shares of a stock. If the stock price is greater than the options exercise (strike) price the option can be exercised and the option buyer will make a profit based on the difference between the current price and the strike price. When this happens the option is considered to be ‘in the money’. If the price of the stock is below the strike price on expiration the option becomes worthless or ‘out of the money’.

It is possible for an investor to either buy or sell options; selling naked calls means an investor sold a call option without owning any underlying stock to offset option. Selling naked calls is a very risky endeavor. If an investor sells a naked call and the stock dramatically rises above the options strike price the investor will owe 100 times the difference between the stock price and the options strike price.

Both buying call options and selling naked call options are speculative strategies where the investor stands to only make a profit if they correctly guessed the direction of the stock’s price.

Between the date the option contract is initiated and the date it expires the price of the stock will constantly fluctuate. The more a stocks price is expected to fluctuate over this time frame the harder it is to predict whether or not the option will be in the money at expiration. To account for this, options are priced at a premium, and that premium declines as the expiration date nears. All else held the same, an option expiring in one month will be worth more today than tomorrow if the stock price remains the same. For more detailed information on how options are priced read The Greeks: From Past to Present.

Covered Calls Explained

What is a covered call? Let’s now look at an example. XYZ stock is trading at $52 today; a call option to purchase XYZ at $55 one month from now is priced at $3. To initiate a covered call on XYZ stock an investor would purchase 100 shares of XYZ and sell a call option which obligates him to sell XYZ at $55 one month from now if exercised by the option buyer. For simplicity we will ignore commissions.

Pros of Selling Covered Calls for Income

– The seller receives the premium from writing the covered call immediately on the date of the transaction, in this case $300. If the price remains below $55 at option expiration the seller will keep the 100 shares of stock and the $300 he received for the option.

– If the price of the stock is over $55 at option expiration the call option will be exercised. At this point the 100 shares of stock are sold, the investors profit is equal to the $300 received for selling the option plus the $300 in capital appreciation (100 shares * ($55 sell price – $52 purchase price)) for a total profit of $600.

– The premium received can help offset a downward move in the stock price. In this example the investor purchased the shares at $52, if the stock were trading at $49 on expiration and the investor decided to sell his shares the total profit would be $0. The $3 loss on the shares of stock is offset by the $3 received in option premium.

Cons of Selling Covered Calls for Income

– If the stock rises well above the strike price, the seller does not enjoy the full appreciation. The seller’s profit is limited to the premium received plus the difference between the stocks purchase price and the options strike price.

The option seller cannot sell the underlying stock without first buying back the call option. A significant drop in the price of the stock (greater than the premium) will result in a loss on the entire transaction.

– Premium amounts are based on the historical volatility of the underlying stock. Stocks with higher option premiums will have a greater risk of price fluctuation.

– Losses due to downward moves in the underlying stocks price are only limited by the amount of premium received.

Is Selling Covered Calls “Worth It”?

As you can see, selling covered calls for income offers both advantages and disadvantages to outright stock ownership. They can be a great tool to generate additional income from an equity portfolio; however using only a simple covered call strategy can get you into trouble due to its limited upside potential and limited downside protection.

Strategies using options to generate income can be as simple as selling covered calls, while others add strict rules and processes to manage income, emotion and risk. If you are looking to add an income producing strategy using options, compare the risk/reward profiles of every strategy and pick one that matches your objectives, risk tolerance, time horizon and temperament. For more information on using options in your portfolio read our free special report: Myths & Misconceptions About Exchange Traded Options.

Combinations and Permutations

What’s the Difference?

In English we use the word “combination” loosely, without thinking if the order of things is important. In other words:

“My fruit salad is a combination of apples, grapes and bananas” We don’t care what order the fruits are in, they could also be “bananas, grapes and apples” or “grapes, apples and bananas”, its the same fruit salad.

“The combination to the safe is 472”. Now we do care about the order. “724” won’t work, nor will “247”. It has to be exactly 4-7-2.

So, in Mathematics we use more precise language:

  • When the order doesn’t matter, it is a Combination.
  • When the order does matter it is a Permutation.

So, we should really call this a “Permutation Lock”!

A Permutation is an ordered Combination.

To help you to remember, think “Permutation . Position”


There are basically two types of permutation:

  1. Repetition is Allowed: such as the lock above. It could be “333”.
  2. No Repetition: for example the first three people in a running race. You can’t be first and second.

1. Permutations with Repetition

These are the easiest to calculate.

When a thing has n different types . we have n choices each time!

For example: choosing 3 of those things, the permutations are:

n × n × n
(n multiplied 3 times)

More generally: choosing r of something that has n different types, the permutations are:

(In other words, there are n possibilities for the first choice, THEN there are n possibilites for the second choice, and so on, multplying each time.)

Which is easier to write down using an exponent of r:

n × n × . (r times) = n r

Example: in the lock above, there are 10 numbers to choose from (0,1,2,3,4,5,6,7,8,9) and we choose 3 of them:

10 × 10 × . (3 times) = 10 3 = 1,000 permutations

So, the formula is simply:

n r
where n is the number of things to choose from,
and we choose r of them,
repetition is allowed,
and order matters.

2. Permutations without Repetition

In this case, we have to reduce the number of available choices each time.

Example: what order could 16 pool balls be in?

After choosing, say, number “14” we can’t choose it again.

So, our first choice has 16 possibilites, and our next choice has 15 possibilities, then 14, 13, 12, 11, . etc. And the total permutations are:

16 × 15 × 14 × 13 × . = 20,922,789,888,000

But maybe we don’t want to choose them all, just 3 of them, and that is then:

16 × 15 × 14 = 3,360

In other words, there are 3,360 different ways that 3 pool balls could be arranged out of 16 balls.

Without repetition our choices get reduced each time.

But how do we write that mathematically? Answer: we use the “factorial function”

The factorial function (symbol: ! ) just means to multiply a series of descending natural numbers. Examples:

  • 4! = 4 × 3 × 2 × 1 = 24
  • 7! = 7 × 6 × 5 × 4 × 3 × 2 × 1 = 5,040
  • 1! = 1
Note: it is generally agreed that 0! = 1. It may seem funny that multiplying no numbers together gets us 1, but it helps simplify a lot of equations.

So, when we want to select all of the billiard balls the permutations are:

But when we want to select just 3 we don’t want to multiply after 14. How do we do that? There is a neat trick: we divide by 13!

16 × 15 × 14 × 13 × 12 . 13 × 12 . = 16 × 15 × 14

That was neat. The 13 × 12 × . etc gets “cancelled out”, leaving only 16 × 15 × 14.

The formula is written:

where n is the number of things to choose from,
and we choose r of them,
no repetitions,
order matters.

Example Our “order of 3 out of 16 pool balls example” is:

16! = 16! = 20,922,789,888,000 = 3,360
(16-3)! 13! 6,227,020,800

(which is just the same as: 16 × 15 × 14 = 3,360)

Example: How many ways can first and second place be awarded to 10 people?

10! = 10! = 3,628,800 = 90
(10-2)! 8! 40,320

(which is just the same as: 10 × 9 = 90)


Instead of writing the whole formula, people use different notations such as these:

Example: P(10,2) = 90


There are also two types of combinations (remember the order does not matter now):

  1. Repetition is Allowed: such as coins in your pocket (5,5,5,10,10)
  2. No Repetition: such as lottery numbers (2,14,15,27,30,33)

1. Combinations with Repetition

Actually, these are the hardest to explain, so we will come back to this later.

2. Combinations without Repetition

This is how lotteries work. The numbers are drawn one at a time, and if we have the lucky numbers (no matter what order) we win!

The easiest way to explain it is to:

  • assume that the order does matter (ie permutations),
  • then alter it so the order does not matter.

Going back to our pool ball example, let’s say we just want to know which 3 pool balls are chosen, not the order.

We already know that 3 out of 16 gave us 3,360 permutations.

But many of those are the same to us now, because we don’t care what order!

For example, let us say balls 1, 2 and 3 are chosen. These are the possibilites:

Order does matter Order doesn’t matter
1 2 3
1 3 2
2 1 3
2 3 1
3 1 2
3 2 1
1 2 3

So, the permutations have 6 times as many possibilites.

In fact there is an easy way to work out how many ways “1 2 3” could be placed in order, and we have already talked about it. The answer is:

(Another example: 4 things can be placed in 4! = 4 × 3 × 2 × 1 = 24 different ways, try it for yourself!)

So we adjust our permutations formula to reduce it by how many ways the objects could be in order (because we aren’t interested in their order any more):

That formula is so important it is often just written in big parentheses like this:

where n is the number of things to choose from,
and we choose r of them,
no repetition,
order doesn’t matter.

It is often called “n choose r” (such as “16 choose 3”)

And is also known as the Binomial Coefficient.


As well as the “big parentheses”, people also use these notations:

Just remember the formula:

Example: Pool Balls (without order)

So, our pool ball example (now without order) is:

16!3!(16−3)! = 16!3! × 13!

= 20,922,789,888,0006 × 6,227,020,800

Or we could do it this way:

16×15×143×2×1 = 33606 = 560

It is interesting to also note how this formula is nice and symmetrical:

In other words choosing 3 balls out of 16, or choosing 13 balls out of 16 have the same number of combinations.

16!3!(16−3)! = 16!13!(16−13)! = 16!3! × 13! = 560

Pascal’s Triangle

We can also use Pascal’s Triangle to find the values. Go down to row “n” (the top row is 0), and then along “r” places and the value there is our answer. Here is an extract showing row 16:

1. Combinations with Repetition

OK, now we can tackle this one .

Let us say there are five flavors of icecream: banana, chocolate, lemon, strawberry and vanilla.

We can have three scoops. How many variations will there be?

Let’s use letters for the flavors: . Example selections include

  • (3 scoops of chocolate)
  • (one each of banana, lemon and vanilla)
  • (one of banana, two of vanilla)

(And just to be clear: There are n=5 things to choose from, and we choose r=3 of them.
Order does not matter, and we can repeat!)

Now, I can’t describe directly to you how to calculate this, but I can show you a special technique that lets you work it out.

Think about the ice cream being in boxes, we could say “move past the first box, then take 3 scoops, then move along 3 more boxes to the end” and we will have 3 scoops of chocolate!

So it is like we are ordering a robot to get our ice cream, but it doesn’t change anything, we still get what we want.

We can write this down as (arrow means move, circle means scoop).

In fact the three examples above can be written like this:

(3 scoops of chocolate):
(one each of banana, lemon and vanilla):
(one of banana, two of vanilla):

OK, so instead of worrying about different flavors, we have a simpler question: “how many different ways can we arrange arrows and circles?”

Notice that there are always 3 circles (3 scoops of ice cream) and 4 arrows (we need to move 4 times to go from the 1st to 5th container).

So (being general here) there are r + (n−1) positions, and we want to choose r of them to have circles.

This is like saying “we have r + (n−1) pool balls and want to choose r of them”. In other words it is now like the pool balls question, but with slightly changed numbers. And we can write it like this:

where n is the number of things to choose from,
and we choose r of them
repetition allowed,
order doesn’t matter.

Interestingly, we can look at the arrows instead of the circles, and say “we have r + (n−1) positions and want to choose (n−1) of them to have arrows”, and the answer is the same:

So, what about our example, what is the answer?

(3+5−1)! = 7! = 5040 = 35
3!(5−1)! 3!×4! 6×24

There are 35 ways of having 3 scoops from five flavors of icecream.

In Conclusion

Phew, that was a lot to absorb, so maybe you could read it again to be sure!

But knowing how these formulas work is only half the battle. Figuring out how to interpret a real world situation can be quite hard.

But at least now you know how to calculate all 4 variations of “Order does/does not matter” and “Repeats are/are not allowed”.

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