The following questions apply to the following simplified bank balance sheet

-Shareholders in the bank above are offered the following deal.The bank will gamble the whole loan book on a double or nothing coin toss (i.e.50% chance loan book doubles in value,50% chance it has zero value).From the shareholders point of view,this deal
A) gives them a 50% chance of losing 10 and a 50% chance of gaining 10
B) gives them a 50% chance of losing 10 and a 50% chance of gaining 20
C) gives them a 50% chance of losing 10 and a 50% chance of gaining 100
D) gives them a 50% chance of losing 100 and a 50% chance of gaining 100
E) gives them a 50% chance of losing 100 and a 50% chance of gaining 200

Question

The following questions apply to the following simplified bank balance sheet
 
-Shareholders in the bank above are offered the following deal.The bank will gamble the whole loan book on a double or nothing coin toss (i.e.50% chance loan book doubles in value,50% chance it has zero value).From the shareholders point of view,this deal
A) gives them a 50% chance of losing 10 and a 50% chance of gaining 10 
B) gives them a 50% chance of losing 10 and a 50% chance of gaining 20 
C) gives them a 50% chance of losing 10 and a 50% chance of gaining 100 
D) gives them a 50% chance of losing 100 and a 50% chance of gaining 100 
E) gives them a 50% chance of losing 100 and a 50% chance of gaining 200

Quizplus · Accepted Answer

If the loan book doubles in value, the assets for the bank will be worth 200, and the liabilities will still be 100. Therefore, the shareholders will have a gain of 100, which is the difference between assets and liabilities. If the loan book has zero value, the assets will be worth only 10, and the liabilities will still be 100. Therefore, the shareholders will have a loss of 90, which is the difference between assets and liabilities. Since the coin toss is fair, the probability of gaining 100 or losing 90 is both 50%. Therefore, the expected return for this gamble is (50% x 100) + (50% x -90) = 5, which means on average, the shareholders will gain 5 from this deal.

The Following Questions Apply to the Following Simplified Bank Balance