Options – A complete and Straightforward Explanation


Options still have a kind of nimbus:

Very complicated and only to be understood by a few illustrious financial freaks.

Total nonsense.

There are many misunderstandings about options, even among many financially educated people, simply because the common explanations are unnecessarily complicated.

Therefore, I would like to try today to illustrate the matter a little more vividly.

I am convinced that even if you already have options, you will have a little aha moment after this article.


  • What is an option?
  • How does the rating of options work?
  • Does that also apply to Covered Calls, Spreads and Iron Condors?
  • How people fall for options with options
  • Are the option models perfect?
  • Is it possible to earn money with options trading?
  • Should I hedge my portfolio with put options?
  • Are options an alternative to ETF and stocks?
  • For the sake of completeness: What an option is not
  • Conclusion
  • You think this post is good? Then support Homemade Finance!

What is an option?

There is so much technical gibberish in this area I want to omit as far as possible. However, we first have to agree on a few terms.

A common definition is as follows:

An option gives the owner the right but not the obligation to buy (call) or sell (Put) a certain commodity within a certain time (American) / at a certain time (European).

American: option may be exercised at any time during the term

European: Option may only be exercised at maturity.

If you represent the above definition strictly graphically, then you can illustrate the two types of options as follows:

Long-call option


Long-put option

If the price of the underlying (ie what the option relates to, eg a stock) is below or above the strike at the time of exercise, it may make sense not to exercise the option.

Simply put, if, for example, a stock is currently traded for € 90 on the market, I will not exercise the right and buy it for $ 100, even if a call would allow me to. Would not be advantageous.

How does the rating of options work?

Here’s the sticking point:

Many know a few models by name, such as Black-Scholes or the binomial model.

You enter a few data in front (such as maturity, risk-free interest, etc.) and at the end you get a number spit out. The fair value of an option.

But what does that mean anyway?

Fair means in mathematics that the expected value is zero.

The classic example is a coin toss. Imagine we both throw a coin and the odds of winning or losing is 50% each. If you win I pay you 10 € and if you lose you pay me 10 €.

Our expected value is 0, because: 0,5 * 10 € -0,5 * 10 € = 0 €

Now let’s take a look at the graphic for the definition of a long call from above:

Long-call option

What is the expected value?

In other words, what’s the worst thing that can happen to you here? Right, that you do not make profit or loss.

What is the best that can happen to you? That the Underlying / Underlying goes off like a rocket and you bring back fat booty.

We may not know the exact probabilities, but we can say that the expectation value is definitely positive, because x * (+ y) – (1-x) * 0 = + xy

So what would you do if someone offered you something with a positive expectation? Right, you would bet as much as possible.

Would that be a fair game? Of course not, because your positive expected value corresponds to the negative expected value of your contract partner.

Trivially speaking, nobody will offer you an option for free. Eh clear.

What now makes an option pricing model, it tries to calculate what the expected value of the above game is. You have to make some assumptions about that, especially how the returns on the underlying are distributed.

Let me illustrate this graphically:

Option Probability distribution

Ok, step by step.

The red curve is the assumed probability distribution for the underlying. Now you go and divide the whole thing into intervals.

In the example above, I picked out an interval at random. It can be seen from the probability distribution that the probability that the underlying is somewhere in between when exercised here is 10% .

On average, for example, you will also have made 5 € profit if you finish in this interval. For our expected value is thus 0.1 * 5 € = 0.50 €

This interval thus contributes 50 cents to the expected value. Of course there are more such intervals.

option probability distribution-2

If you start to make the intervals infinitesimally small and add up the expectation values ​​of all these intervals, you get the expectation value for this option.

option probability distribution-3

All these small intervals with their expected values ​​add up.

Let’s just assume that the expected value for the above option is $ 10.

What would you ask for a bonus so that the game is fair for both sides?

Quite simply, 10 € or better said, exactly the expected value!

We remember, at the beginning of our train of thought, the situation looked like this:

A good deal for the buyer of an option (long), a bad thing for the seller of an option (short).

While the buyer has nothing to lose but can win everything, the seller can lose everything but win nothing.

To try the numbers from our example, the buyer has a positive expected value of 10 € and the seller has a negative expectation of 10 €.

To make the whole thing fair, the buyer of an option now has to prepay the seller for the expected value as a premium.

Finished. Now we have a fair game or a fair valued option.

That’s the basic idea when evaluating options. By the way, this also applies to puts.

Does that also apply to Covered Calls, Spreads and Iron Condors?

Yes. No matter how you combine options and stocks, when Black-Scholes applies, you do not change the expectation.

covered call

The point is, you can use options to create really creative payoffs, but at the end of the day they all have the same expectation from the point of view of Black-Scholes or Cox-Ross-Rubinstein (binomial model) .

iron condor

You can turn yourself upside down, in the end it does not matter what you do or how complex your position is. You do not influence your expected value.

bull spread

If you want a nice overview of a variety of option strategies, then I can recommend you the page “The Options Guide” .

Do not forget: the expected value remains the same!

How people fall for options with options

What appeals to many people are strategies that generate regular revenue from premiums by selling options.

A good example is the Iron Condor. This is usually built up in such a way that the current price is somewhere in the middle and you therefore take the premium even if it does not move.

So you act on the short side and take, for example, the premium regularly every month. Let’s just say, 5% a month is sold as a seller (for the time being).

It sounds great too: Plannable revenue! Well the height is limited but they come regularly.

I love that, every human being does that!

Often people dare to hesitate, realize that it seems to be doing well and after a few months in the firm belief that they have found the Holy Grail for financial freedom.

This goes on for about 20 months (100% / 5% = 20) and then comes the big bang. A big market movement, a crisis or something else consumes all premiums previously received.

Absolute mourning on the part of investors.

All that has happened here is that many small premiums earned regularly have been exchanged for a rare big loss.

Of course, the big bang can happen sooner or later. When exactly, you do not know that. From a mathematical point of view, however, in our example it will appear on average every 20 months.

From the perspective of an option valuation model, nothing changes in your expected value!

Do not forget that.

Short Warning: There are also many self-proclaimed stock market gurus who sell this type of options as a trading system to unsuspecting investors. Absolutely foolproof and extremely profitable.

For only € 49.99 a month.

This is bullshit, of course. As always with such surefire boxes one should ask oneself why these scammers (it must be said so) have to sell their stock market letters and not simply their own system to act for themselves.

Quite simply, after a while, they implode and consume all the previous small gains.

Until then, the milked investor has paid but a few months his contributions to a worthless system.

Are the option models perfect?


It has been proven that certain assumptions of the individual models are not entirely true to reality.

This can be proven by two phenomena in reality:

1. The Volatilitymile

The volatility mlile shows that a closer examination of the impact of volatility on the option price is in disagreement with Black-Scholes.

implied volatility

Without going too deep now, this simply means that volatility in reality does not behave as Black-Scholes assumed.

Higher volatility leads to a higher option price. You can imagine that, the more uncertain the world around you, the more grateful you are for a hedge / insurance.

From the point of view of Black Scholes, the Volatility Mile means that options that are far away from the current price are more expensive than provided in the option valuation model.

Important: From the perspective of the option model, the inconsistency exists! But that does not automatically mean that the market is wrong. Rather, it should be worded that Black-Scholes does not behave as it should in reality!

Therefore, seemingly too expensive options in reality may not be too expensive, but priced just right.

2. Volatility premium

Again, without going too deep, this phenomenon implies that from the model viewpoint (!) Options in the past were systematically too expensive. Because the volatility used in valuing options was slightly overestimated on average.

If something seems to be too expensive, then it is obvious to sell this. So, if options were systematically too expensive, it should have been sold systematically.

There is a so-called PUT-Write Index by the CBOE simulating a constant short sale of puts on the S & P 500.

put index

Source: CBOE

In terms of return this was very similar to the S & P 500 but he was less volatile.

So there is evidence that options in the past (like nobody knows in the future) were actually a bit too expensive as the models suggest.

Is it possible to earn money with options trading?

I have to say that because I can hear a few people in front of the screen and maybe believe in their luck in options trading:

Despite all the criticism, the models are not bad in practice and still prevalent today. The prices are certainly not perfect but especially if we take into account transaction costs and taxes, most of the time is extremely adequate.

If there are occasions when an option is obviously priced dramatically wrong, then the big ones (banks, hedge funds) with their gigantic infrastructure are so fast on the spot, because you have as a small individual investor as good as no chance.

I would not spend too much time building up my own trading system.

Even with the anomalies, these are not normal only from the perspective of the option pricing model . In reality, for example, the smile may be the norm and Black-Scholes the extraordinary.

Also, with regard to the volatility premium, the differences have not been so great that one can say that this would have paid off especially for tax implications.

Should I hedge my portfolio with put options?

In my opinion no and here’s why:

A hedge (“I believe the market collapses soon, I buy a put as an insurance”) is nothing but a kind of market timing associated with costs. Of Markettiming even I hold nothing at all.

Another reason is that as we have seen, the expectation value does not change with an option. This would be a secured position.

put protection

Attentive readers recognize that paying out the hedged portfolio is the exact equivalent of paying out a long call. With the corresponding expected value.

In addition, I still have transaction costs and tax bickering. All in all, my expectation value is no longer zero, but very likely even negative.

I have only a few principles in life but this is definitely one of them:

Stay away from negative expectations!

So I do not secure my depot. It does not do anything, so I do not do it.

As simple as that.

Are options an alternative to ETF and stocks?

Options, as we have just seen, are more of a type of insurance and not an investment.

We want to invest and not open insurance, so despite my love of options, I consider a broader ETF portfolio , which I routinely recommend during my life for more meaningful.

In options itself, I only have some play money to try out a few things in practice and to satisfy my curiosity. Everything of a purely academic nature is understood


Learning to Read Your Personal Record – It’s Exciting!

Today it’s about a topic where I can well imagine that some will roll with the eyes:

Read your personal record.

Granted, this does not sound particularly sexy, but I guarantee you, at the end of this post not only has your perspective on your financial situation changed, but also on yourself.

What you read here is, in my opinion, essential to truly understand your path to financial independence.


  • (D) Reading a balance sheet: not just business fuzziness
  • Pictorial explanation of the basics
  • How a stock portfolio behaves in your balance sheet
  • How a self-bought car behaves in your balance sheet
  • You too are worth something!
  • Conclusion and what you can take with you
  • You think this post is good? Then support Homemade Finance!

(D) Reading a balance sheet: not just business fuzziness

When it comes to balance, one inevitably thinks of accounting, boring Excelklopferei and thickly bespectacled paragraph rider.


That’s how I felt for a long time, until I realized at some point that you can draw a balance for yourself (Wortwitz intends).

And here it will be interesting in my opinion, because a balance is so clearly the investment of a company but also persons dar.

What could be more useful in building assets than showing it clearly from time to time?

Pictorial explanation of the basics

I do not want to bore you with unnecessary details for reading a review, I limit myself to the bare minimum.

Here is just a simple graphical representation:

Links (one says for this side also assets) stands your fortune.

Right (liabilities) is how this property was paid. Either from your own pocket (called equity) or borrowed money (called debt).

In addition, there is one more but very important rule:

The sums on both sides must always be the same size. Always.

If not, then the maw of hell will open and erase everything that is dear and dear to you.

So be sure to take care of that.

That’s basically it, that’s a balance sheet.

Here is a small example of how a simple balance sheet might look like:

read balance example


As we can easily see, a condominium, a custody account as well as bank balances can be found on the side of the property.

On the right side there is now only equity and no debt. The one who owns this balance is currently debt free, so much we can say before.

Last but not least the Hellmouth Rule is also fulfilled, on both sides the sums are the same, so all right.

How a stock portfolio behaves in your balance sheet

What makes a statement so valuable to us is the pretty graphic representation of how consumer debt differs from investment debt. However, one by one.

Let’s take the stock portfolio from the example above:

Imagine, the market value of this portfolio remains unchanged but over the next year, it will give you dividends of € 1000 which your broker will transfer to your bank account.

Then we can observe the following change in the balance:

read the dividend balance sheet

As we can see, the sums do not match. Only at the sight I am already completely afraid and anxious. I can almost feel like it starts to get warm behind me.

So that the balance rises again, there is now a new special sub-item on the right:

The annual surplus. This also belongs to equity.

dividend balance sheet (1)


Phew, better.

Because what happened here? Our wealth has grown by € 1000, while on the right side has done nothing, in the sense of there was no debt or the like.

So we are 1000 € better than before. Profit. Hot.

How a self-bought car behaves in your balance sheet

You may hate me for this statement, but most of what we possess is simply becoming worthless stuff.

Day by day, month by month and year by year, it is losing value all the time. That applies to almost all things of consumption.

Take, for example, a privately used car. Make fun, be smart but it loses value.

Let’s go over this in a nutshell:

Step 1: You have before to buy a car, so your financial position looks like for the time being:

car in the balance

2nd step: You bought your car. Price was 10.000 € and in the beginning we assume for the sake of simplicity you could resell it immediately at the price. So it’s worth 10.000 €.

car in the balance sheet (2)

So far so good, but after a year, your car will already be worth less than at the beginning. If it loses 1000 € in value in a year, then the situation looks like this:

car in the balance sheet (3)

So that the hell rule is fulfilled on both sides, it needs a negative net income, also called annual deficit.

You too are worth something!

No, I do not mean your organs, I would not necessarily include in my balance sheet now. Especially since most of us would be hard to estimate a price for it.

Rather, I mean your worker and education. Because these produce similar to ETF or real estate cash for you and improve so ultimately your personal balance sheet.

personal balance

Here are many unknowns, because the exact value of your work or training can not be quantified exactly. But you can try to increase the value by various measures.

Conclusion and what you can take with you

What I do not want with this article is to urge you to meticulously update your balance sheet every day.

That makes no sense, is boring and brings nothing.

Rather, you should at longer intervals (from me once a year) times to check briefly how your financial situation has changed and whether that was good or bad.

Even before larger purchases, it can help to present the effects so briefly.

In addition, I would like to recommend again my article on ” You yourself are your best investment ” to the heart, because in my opinion, your personal balance just does not end with the miserable enumeration of money and material things.

On the contrary, there are also intangible assets, such as education / training, your workforce or simply certain skills.

Consider whether this is an investment and whether it generates cash or money for you in any way.

Consumer or capital goods, that’s the question.

In my opinion, reading a personal balance sheet is even something very exciting.

Because it helps you to better understand yourself and your path to financial independence.



Calculate Your Return: You May Do It Wrong


Today it’s about something very fundamental when it comes to investing money:

How to calculate the average return of your investment correctly. There is a small stumbling block here that you better jump over.


  • Arithmetic vs. geometric mean
  • The arithmetic mean is a blender when it comes to returns
  • Calculate the return using the geometric mean
  • Summary
  • You think this post is good? Then support Homemade Finance!

Arithmetic vs. geometric mean

You certainly know the simple (arithmetic) average. You simply add all the values ​​in a sample and divide by the number of values. That’s pretty trivial:

Sample: 10, 15, 20, 5

Total: 50

Number of values: 4

simple average: 12.5

So far, all right, and you may be thinking, “What is he up to?” Well, let’s look at another example. This time, the annual, percentage gains of the DAX. So simply, what percentage has lost or won the German leading index in a year.

year DAX change % Change
2005 5,408.26
2006 6,596.92 1,188.66 21.98
2007 8,067.32 1,470.40 22.29
2008 4,810.20 -3,257.12 -40.37
2009 5,957.43 1,147.23 23.85
2010 6,914.19 956.76 16,06
2011 5,898.35 -1,015.84 -14.69
2012 7,612.39 1,714.04 29.06
2013 9,552.16 1,939.77 25.48
2014 9,805.55 253.39 2.65
2015 10743.01 937.46 9.56
total 95.87
Number of values 10

So, if we calculate the simple average, we get:

95.87 / 10 = 9.587 or 9.587%

Okay, on average the DAX has risen by 9.587% pa in the last 10 years. If you do that maybe for the last 20 years, then we have an average that allows us to estimate what the stock market is like.

Not correct!

Why is that wrong? Well, calculate it, what does an annual average rate of return with the above average over 10 years mean?

This corresponds to 1.09587 * 1.09587 * 1.09587 * 1.09587 * 1.09587 * 1.09587 * 1.09587 * 1.09587 * 1.09587 * 1.09587 = 1.09587 ^ 10 = 2, 5

Starting from the starting value 2015 (= final value 2014), which is at 5408.26, the DAX would now have to be 2.5 * 5408.26 = 13,520 .

At the time of this article, the DAX has never been at this value, so somewhere must be a mistake in logic.

One of the reasons lies with an old acquaintance: the compound interest. Because of this effect, it is only possible to generate considerable assets in a lifetime. It leads to a non-linear, exponential development. In other words, a euro you deposit is worth more than a euro. Sounds funny, but it is.

However, in most cases this non-linear behavior can not be correctly represented with a simple average.

The arithmetic mean is a blender when it comes to returns

Here is an example to illustrate why the arithmetic mean is not suitable for you as an investor. Look at the following sequences:

Year 1: + 16%

Year 2: -16%

Year 3: 0%

In simple terms, nothing would have happened here, because this is 0 . What would an investor have experienced in these three years? Let’s assume it is the gains of a stock, which at the beginning (year 0 of if you will) would have been worth € 100. So the development would look like:

Year 1: € 116 (+ 16%)

Year 2: € 97.44 (-16%)

Year 3: € 97.44 (0%)

Right here lies the stumbling block at the arithmetic mean. It just does not work when it comes to returns.

Because actually you would have made loss here and not 0%.

Here’s another example with other numbers:

Year 1: 8%

Year 2: 5%

Year 3: 8%

If we calculate the simple average return, then we come to 7%. Let’s compare, for example, how would a stock with an initial value of € 100 hit the arithmetic averaged rate of return and the actual returns achieved.

year actual development arithmetic mean
1 € 108 € 107
2 € 113,40 € 114.49
3 € 121.34 € 122,50

As you can easily see, if you estimate with the simple average how the return would develop, then you systematically overestimate.

So how could you do it better?

Calculate the return using the geometric mean

In simple terms, the geometric mean takes into account compound interest. Take the previous example: From € 100 at the beginning € 121.31 have become after three years. Overall, this equates to a return of (121.31 / 100) = 1.2134 therefore 0.2134 or even 21.34%. We are now distributing this return over three years so that, taking interest on interest rates into account, we will reach € 121.34. This is done with the following formula:

∛ (1.2134) = 1.0666 therefore 6.66%

Believe it or not, the representation of root signs in the web is quite limited and not quite correct at the top, so I’ll formulate the formula briefly in words: The third root of 1.2134.

Short check whether this is true: 1.0666 ^ 3 = 1.2134. So it’s true

Generally speaking, you simply pull the nth root out of your total return . N stands for the number of years that have passed from beginning to end. In our example, as I said, it took three years to get from € 100 to € 121.34.

Earlier we had the small table with the values ​​of the DAX over 10 years where we had found that the arithmetic mean was too optimistic or simply wrong.

The initial value of the series was 5,408.26 at the end of 2005 and the final value was 10,743.01 in 2015. The average geometric return is calculated as follows:

10 root out of 10743.01 / 5408.26 = 10 root out of 1.9864 = 1.071 ⇔ 7.1% pa on average

Short check calculation: 1,071 ^ 10 = 1,9856 fits. Attention, the values ​​are rounded to the fourth decimal place.

Here you will find the whole thing shown again in a graphic:

We note: the arithmetic mean was 9.587% pa , thus mercilessly overestimating the DAX. That was unavoidable, as we have seen, because that is the nature of the arithmetic return. The geometric mean, however, was 7.1% pa and correctly considered the compound interest effect.

On the topic average / geometric return, I have also picked out an interesting video.

Here is another general explanation of the geometric return:


For us as an investor, it is of course interesting to calculate the average return over several years. We want to know how our investments have developed over the long term, year after year. It is important to use the correct mean and that is the so-called geometric mean . Because this takes into account the non-linear development of returns.

The formula for this is: nth root of end assets / initial assets where n stands for the number of years.

With this tool and a twofold try it is easy for you to easily turn around this cliff of investing.