Many times the investors switch stocks with fallacious reasoning created by a flawed argument. I would show an example of one simple puzzle which leads into complex error of judgment.

*Let's say you are given two indistinguishable envelopes, each of which contains a positive sum of money. One envelope contains twice as much as the other. You may pick one envelope and keep whatever amount it contains. You pick one envelope at random but before you open it you're offered the possibility to take the other envelope instead.*

*Now, suppose you reason as follows:*

*I denote by A the amount in my selected envelope**The probability that A is the smaller amount is 1/2, and that it's the larger also 1/2**The other envelope may contain either 2A or A/2**If A is the smaller amount the other envelope contains 2A**If A is the larger amount the other envelope contains A/2**Thus, the other envelope contains 2A with probability 1/2 and A/2 with probability 1/2**So the expected value of the money in the other envelope is*

*V = ½ * 2A + ½ * A/2 = 5/4 *A*

*This is greater than A, so I gain on average by swapping*

* Source- wikipedia*

* *Your intuition would most probably realize that there is something wrong but you may find it difficult to spot flaw in the reasoning given above.

- Let the amount in the envelope you chose be
*A*. Then by swapping, if you gain you gain*A*but if you lose you lose*A*/2. So the amount you might gain is strictly greater than the amount you might lose. - Let the amounts in the envelopes be
*Y*and 2*Y*. Now by swapping, if you gain you gain*Y*but if you lose you also lose*Y*. So the amount you might gain is equal to the amount you might lose.

**Solution:**

Argument 2 has already been explained above so let us focus on argument one. When I lose I’m holding a sum twice as large as the sum I’m holding when I gain by swapping. So the A/2 in losing swap transaction is equal to A in the gaining swap transaction because A in both are not same.

## 2 comments:

Hi,

I read your solution to the two envelope problem but I think it does not solve the paradox. What you have done is to assimilate the argument of 2) into 1). You have not shown at what point the argument of 1) actually goes wrong, as the argument of 1) the value A is the same in the two cases being examined ie A, A/2 vs A, 2A.

I have spent a lot of time on solving the paradox and if you are interested my solution appears here:

http://soler7.com/IFAQ/two_envelope_paradox_solution.htm

Its hard to tell a bottom on a stock.

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