Question

4. Diversification can eliminate risk if two events are perfectly negatively correlated. Suppose that two firms are competing for a government contract and have an equal chance of winning. Because only one firm can win, the other must lose, so the two events are perfectly negatively correlated. You can buy a share of stock in either firm for $20. The stock of the firm that wins the contract will worth $40, while the stock of the loser will worth $10. • If you buy two shares of one firm, calculate the expected value and variance of two shares. • If you buy one share on each firm, calculate the expected value and variance of two shares.

Answer 1

Answer:-

Let the two company's be A and B.

Given:-

Price of stock A or B= $20
The sock of the company that wins the contract = $ 40
The stock of the company that looses the contract= $ 10
The probability of winning ii equal for both companies ie P(A) = P(B) = 0.5

1) If we buy two share of one firm the expected return is:-

In this scenario
we purchased two shares of one firm and it won the contract or it lose the contract

Therefore the profit in case of winning the contract = $ 40 ($40+$40-$20-$20)
The loss in case of loosing the contract = -$ 20 ($10+$10-$20-$20)

The expected return (E)= 0.5( $40) + 0.5(-$20)
= $ 20 - $ 10
  E = $ 10

	X	P(X)	X* P(X)	(X-E)^2 *P(X)
Win Contract	40	0.5	20	(40-10)^2 * (0.5) = 450
Loose Contract	-20	0.5	-10	(-20-10)^2 * (0.5)= 450

Therefore variance = 450 +450= 900

2) If we buy one share of each company then
If we win the contract = $40+$10-$20-$20= $10
If we lose the contract= $40 +$10-$20-$20= $ 10

Expected return= $10(0.5) + $10(0.5)= $10

	X	P(X)	X*P(X)	(X-E)^2 * P(X)
Win Contract	10	0.5	5	(10-10)^2 * (0.5) = 0
Loose Contract	10	0.5	5	(10-10)^2 * (0.5) = 0

Therefore Variance = 0