Question

Q-During the course I talked about Thaler’s encounter with 23 executives. He asked them whether they would be willing to take a deal that gives them a 50% chance of making $2 Million and a 50% chance of losing $1 Million. Only three of the 23 executives were willing to take this deal. However, the CEO of the company was shocked by this because he didn’t look at these 23 deals in isolation but as a portfolio of 23 deals.

1. What is the expected profit/loss of the 23 deals taken together?
2. What is the probability of a loss taken the 23 deals together?

Answer 1

a) The expected profit per deal is computed here as:

= 0.5*Profit of 2 million + 0.5*Loss of 1 million

= 0.5*2 - 0.5*1

= 0.5

Expected Profit for 23 deals is computed here as:
= 23*Expected profit per deal

= 23*0.5

= 11.5

Therefore $11.5 million is the expected profit for the 23 deals taken together.

b) There will be a net loss on the 23 deals, if k deals are in loss and rest (23 - k) are in profit. Then, we have here:

2*(23 - k) < k

46 < 3k

k > 15.33, that is 16 deals at least out of the 23 deals.

The distribution of the number of deals with loss is modelled here as:

Now the required probability here is computed as:

Therefore 0.0466 is the required probability here.