Question

Consider a stock market with two stocks A and B. Stock A always sells for $5 or
$10; stock B always sells for $6 or $12. If stock A is selling for $5 today, there is a 75%
chance it will sell for $5 tomorrow. If stock A is selling for $10 today, there is a 90% chance
it will sell for $10 tomorrow. If stock B is selling for $6 today, there is a 90% chance it will
sell for $6 tomorrow. If stock B is selling for $12 today, there is 70% chance it will sell for
$12 tomorrow.

Required: Compute the costs of stock A and stock B.

Answer 1

Stock A = sells for 5 or 10,

so if stock A sells for 5 today, tommorow = 75% sell for 5, and 25% sell for 10

If stock A sells for 10 day, tommorow = 90% sell for 10, and 10% sell for 5.

Similarly, Stock B sells for 6 or 12,

so if stock sells for 6 today, tommorw = 90% sell for 6, 10% sell for 12

IF stock B sells for 12 today, tommorow = 70% sell for 12, 30% sell for 6.

Expected value/payoffs is the multiplication of the payoffs with their respective probabilities of occurence.

So, expected value for tommorow if Stock A sells for $5 today:

A(5) = 0.75 * 5 + 0.25 * 10 = 6.25

Expected value for tommorow if Stock A sells for $10 today:

A(10) = 0.9 * 10 + 0.1 * 5 = 9.5

Expected value for tommorow if Stock B sells for $6 today:

B(6) = 0.9 * 6 + 0.1 * 12 = 6.6

Expected value for tommorow if Stock B sells for $12 today:

B(12) = 0.7 * 12 + 0.3 * 6 = 10.2

So, we see the expected value for stock A is greater when it sells for $10 today and the expected value of stock B is greater when it sells for $12 today.

So, as the value provided is greater, the cost/price is greater, so the cost of A = $10, and cost of B = $12.