Thursday, April 17, 2014

Trading: Call Options - introduction

Investment oportunity

Imagine that you would meet somebody who is from the future.

And that somebody would tell you that each gold bar which
now costs 100$
will cost 115$ in a years time.

And imagine that for some reason you would believe him (as for example he looks exactly like you just 10 years older).

Now stop for a moment and think: What would you do regarding this gold situation?

Possible solution

It seems that a wise choice would be to invest all your money into gold and then sell it in a year.

You have 5,000$ in savings and the bank is willing to lend you maximum amount of 250,000$ with a generous interest rate of 5% per year.

So, let's do some calculations.

How much money do we actually have? This is a simple formula:
   our savings + borrowed money = 5,000 + 250,000 = 255,000 $

So, now the question is how many gold bars can we buy for this amount. To get this value we just divide our total amount by today's price of one gold bar:
   amount we have / today's price of gold bar = 255,000 / 100 = 2,550 gold bars

2,550 gold bars seems like a quite nice amount. But it would be good to actually know how much money we'll get for it in a year. To find it out just use this formula:
   amount of gold bars * price of gold bar in a year = 2,550 * 115 = 293,250 $
It seems that we have earned something. But how much actually is it?

First find out how much we have gained above our invested amount:
   earned amount - invested amount = 293,250 - 255,000 = 38,250 $

This seems like a quite nice sum but this is still not our net/clear income as we still need to pay the interest for the borrowed money which is:
   borrowed amount * interest rate percentage / 100 = 250,000 * 5 / 100 = 12,500 $

Once we pay this amount as well we'll get the clear income:
   investment return - interest for borrowed money = 38,250 - 12,500 = 25,750 $

So with our savings (5,000$) and borrowed money (250,000$) we've been able to earn 25,750$. As we return the borrowed money but keep the savings we now have:
   clear income + savings = 25,750 + 5,000 = 30,750$

This seems to be quite a nice year, don't you think?

Return percentage

Lets do some deeper analysis of how good we actually did.

At first we'll look what was the best/maximum percentage of return we could have achieved using this method.

To get this we'll find the difference of future gold price and its current price value:
   price in a year - price today = 115 - 100 = 15 $

And from this we find how big increase it actually is:
   (price difference / price today) * 100 = (15 / 100) * 100 = 15%

So 15% is the maximum we could have gained if we would use only our savings (and there would be no need to pay interest for borrowed money).
Which means that for each 100 $ we would earn 15% which is 15 $.

So if we would use just our savings we would gain: 5,000 * 15 / 100 = 750 $.

But as we were borrowing some money and we paid some interest rate, lets find out how good we actually did. For this purposes we use this calculation:
   (net income / invested amount) * 100 = (25,750 / 255,000) * 100 = 10.098 %

So lets summarize:
With using just our savings (5,000 $), we would have the highest return percentage (15%) but as only small amount would be invested, we would gained lower total income as well = 750 $.

With the borrowed money our total investment has increased rapidly (255,000 $) and although the return percentage was lower (10.098% - which is still regarded as good investment) our total income was much higher = 25,750 $.

It seems that it was a good decision to use not just our own savings but to borrow some money from bank as well.


Other options - Call option

Now the question is: Can we do better than this?

Imagine that during our application for the bank loan, we would state that: I would like to buy gold bars because I expect their value to rise in a years time.

Our friendly banker would for some reason stop for a while. After a moment of deep thoughts he would tell us:
"I would have a proposal for you. Of course we will lend you the money. You're a good client as you already have 5,000 $ of your own, so I'm sure you'll be able to handle additional 250,000 $.
But why would you buy all of this gold right now, when instead I would offer you something better.

I can offer you the possibility to buy gold bars from us in a year for the same price as they costs today. So if the price of gold will be higher then today you'll earn some money. And the best thing is that if the price is lower there is no obligation for you to buy the gold bars from us, so you'll lose no more money at all. This seems really promising doesn't it? And to do so, all you have to do is sign this contract and pay the initial fee of 8 $ for each gold bar you'll be able to buy.""

Ok, so our friendly banker has offered us the possibility (but not the obligation) to buy something in the future for an agreed price. This is a contract which is normally known as 'Call Option'. The fee you have to pay for signing/entering this contract is known as 'Option Premium'.

So we have a new possibility now. But is it worth using this possibility? Let's do some math again to find it out.

First we'll find out how many 'Call options' can we actually buy:
   amount we have / option premium = 255,000 / 8 = 31,875 pieces

Now we have some amount of 'Options'. Lets imagine, that instead of buying the gold in years time for 100 $ and selling it back for 115 $ there are people who would buy our contracts for the price difference 15 $. So how much would we gain in the end:
   count of option calls * difference in gold price = 31,875 * 15 = 478,125 $

OMG, this is a horrendous sum. But remember we still need to subtract our invested amount and interest we need to pay for borrowed money to get the net/real income:
   investment return - invested amount - interest for borrowed money = 478,125 - 255,000 - 12,500 = 210,625 $

Holy macarony. This is way better than the previous 25,750 $. Lets see the actual percentage of return:
   (net income / invested amount) * 100 = (210,625 / 255,000) * 100 = 82.598 %

This seems like the best possible approach. We received much more money (210,625 $ instead of 25,750 $) as well as higher return percentage (82.598 % instead of 10.098 %).

The funny thing is that we could never achieve something like this with just buying gold on its own. Instead we were buying something that was derived from buying the gold. An option to buy the gold. Because of that we say that 'Call Option' is a 'Derivative'. There are many more 'Derivatives' that are being used, but for now just remember that 'Call Option' is one of them.

Negative scenario - possible losses explained

You might ask yourself. Why would the friendly banker ever provide us such an excellent opportunity? Aren't they only smiling on the outside but are rotten inside?

Well actually our friendly banker is nor good nor bad. All what he did is provided us the possibility to "multiply" the possible gain, but also (and this is important) the possible loss.

Let's imagine that all of the future traveling would be just a prank and the price of gold bar in years time would instead of rising by 15 $ to 115 $ actually fell by (only) 5 $ to 95 $.

How much would we actually loose?

We've already discussed few scenarios and each of them would have different losses:

a) if we would use only our savings

For 5,000 $ we could buy only 50 gold bars. In one years time the price of those gold bars would be:
   amount of gold bars * price of gold bar in a year = 50 * 95 = 4,750 $

So we would loose:
   earned amount - invested amount = 4,750 - 5,000 = -250 $

Which in percentages is a loss of:
   (clear loss / invested amount) * 100 = (250 / 5,000) * 100 = 5 %

b) if we would use savings and borrowed money

The actual price we would receive once selling the gold bars would be:
   amount of gold bars * price of gold bar in a year = 2,550 * 95 = 242,250 $

So the loss would be:
   earned amount - invested amount = 242,250 - 255,000 = -12,750 $

As we still need to pay the interest for borrowed money, our clear loss would be:
   investment difference + interest = 12,750 + 12,500 = 25,250 $

Which in percentages is a loss of:
   (clear loss / invested amount) * 100 = (25,250 / 255,000) * 100 = 9.902 %

This means that we would not even loose all of our savings, but beside this we would still need to pay back the dept of 20,250 $.

c) if we would call options with our savings and borrowed money

in this case we would actually loose everything. And by losing everything I mean we would loose our savings, borrowed money and would still need to return it plus the interest. The problem is that we used all the money to buy a promise which is now worthless. In situations before we at least had gold which was cheaper but still had SOME value and people would be willing to pay this smaller value for it. But now we only hold many papers which allow us to buy gold for higher value than we would get on the market. And nobody (with properly functioning mind) would pay us for this disadvantageous option. So in the end we would be in debt of:
   borrowed money + interest = 250,000 + 12,500 = 262,500 $

But remember, to get the net/real loss we still need to add our lost savings:
   262,500 + 5,000 = 267,500 $
Which in percentages is a loss of:
   (clear loss / invested amount) * 100 = (267,500 / 255,000) * 100 = 104.902 %

So as you can see, if this would be "only" a prank, it could be a very costly prank indeed.

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