Why mathematics will always be against option buyers?

As investors tend to be loss averse they inherently are willing to pay more for than the fair value for risk protection products like options. Thus, when law of large numbers catches up, option buyers are most likely to lose. Transaction costs just makes it worse.

If there is one major misconception that exists in the financial world that is the belief that buying options can help you become rich. Not that it cannot. But if it does, it is purely a matter of luck as the mathematics is firmly against it.

Call and put options are one of the most well know financial derivative products that on the face of it seems to enable the buyers to earn potentially huge amounts of profits while limiting the downside. These products allow you to earn $10 or even more for every dollar invested and that too within a short span of time, if things move in your favor. If price moves against you, then all your loss is the $1 investment. Sounds too good. isn’t it?

But as they say, if something sounds too good to be true, it probably is. Before I explain this further, you need to know these products better. If you do not have prior knowledge, you can learn about them from wikipedia or any other sources.

Now, let me explain this to you with a simple bet based on rolling of a dice. Let us say, you are offered the bet with the following payoff:

Value on the dice 1 2 3 4 5 6
Earnings/(payout) (in $) -50 -30 -10 10 30 50

Thus, under this bet you would be losing money if the value on the roll is 3 or below and you  would be earning money if the value is 4 or above. So, while you can get a profit as high as $50 you also have an equally likely chance of losing $50.

How likely are you to accept this bet?

And as you make up your mind, let us say you are offered another interesting choice. They promise to bear all the loss for you but will let you keep the profit. But you need to pay a flat $16 per bet as service fees. So, once you pay the flat fees you do not have worry about the losses at all but all the profit is yours.

How attractive is the second bet?

If you thought it is way better than the first bet, you could not be more wrong. Wondering why? That is where probability, law of large numbers and loss aversion comes into picture.

A trader never trades in just one bet. They enter into many transactions. That way, let us assume that you are going to enter into as many as 6,000 bets (just for convenience of calculation). In a fair dice, every value has exactly 1/6th of a probability to occur. So, this is how the payoff of the two bets are likely to occur.

Value on the dice 1 2 3 4 5 6 Total
No. of times the value likely to occur 1000 1000 1000 1000 1000 1000 6,000
Payout on bet 1
Total payout on bet 1 -50,000 -30,000 -10,000 10,000 30,000 50,000 0
Payout on bet 2
Payout excluding fees 0 0 0 10,000 30,000 50,000 90,000
Fees (16*6000) -16,000 -16,000 -16,000 -16,000 -16,000 -16,000 -96,000
Total Payout on bet 2 -16,000 -16,000 -16,000 -6,000 14,000 34,000 -06,000

As you can see, while the first bet is likely to give you neither any profit nor any loss, the second bet is destined to give us loss.

The first bet is like buying the shares or entering into a forward contract. You make profit when the value goes and make loss when value goes (assuming long position). While the second bet is like an option, where for a fixed premium you seem to be able to avoid loss while being able to earn profit. But, invariably the premiums would be so high that it more than negates any profit you may earn from it.

You may now be wondering as to what if the premiums are not high or why would the premiums be always high. The answer to that lies in our loss aversion. If for a moment you thought option 2 was better, you are also a victim of the same loss aversion as do most part of the world. In simple terms, most of would feel more bad for losing $1 than we would feel bad for forgoing an opportunity to earn $1. That is why most of us would be unknowingly be willing to pay a higher premium for the illusion of risk safety. Still not convinced? Then ponder why insurance companies earn profit when it is in fact you who is getting all the benefits of risk management.

Coming to our discussion on option, if mathematically buying option is not a profitable proposition then should we all start selling the option to make money. I would say yes, but only if you can take an extremely diversified set of positions. Remember, the math would work only we have large number of bets. And the large number should not be on same event but it should be on different events.

So, if you have enough money to deposit as margin for a diversified set of positions, you are most likely to make more money. But unfortunately, most retail investors never have that kind of money. On the other hand, large financial houses do have and there are a lot of them who report huge profits every year just by writing options.

But before I conclude, then aren’t there people who make a lot of money by buying options? Perhaps, yes. But for every one such winner you would have at least two losers. So, again, unless the trader is an expert or access to superior information, there is more probability that the option buyer is likely to be on the losing side than on the winning side.

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