Question

Suppose you are deciding how to invest $2,000. There are two
options: shares in an airline company and shares in a petroleum company. There is a 0.25
probability that oil prices will go up, a 0.25 probability that prices will go down, and a 0.50
percent probability they will remain the same. The value of each $100 invested after prices
adjust is as follows:

Event	Probability	Airline	Oil Company
prices fall	0.25	$120	$70
prices same	0.50	$105	$110
prices rise	0.25	$80	$130

a. Calculate the expected value and standard deviation of the value of the total investment if
you invest the entire $2,000 in the airline company.
b. Calculate the expected value and standard deviation of the total investment if you invest
the entire $2,000 in the oil company.
c. Calculate the expected value and standard deviation of the total investment if you invest
$1,000 in the airline and $1,000 in the oil company.
d. Which investment (‘a’, ‘b’, or ‘c’) has the highest risk? Which has the lowest risk?

Answer 1

(a) Expected value and standard deviation of $100 of investment in airline company is calculated below:

Thus, the values for 20 times the investment, or $2000 of investment is:

Expected Value = 20(102.5) = $2050

Standard Deviation = 20(14.361) = $287.22

(b) Similarly, the expected value and standard deviation of $100 worth of investment in oil company is calculated below:

Thus, the values for 20 times the investment, or $2000 of investment is:

Expected Value = 20(105) = $2100

Standard Deviation = 20(14.361) = $435.88

(c) If we invest $1000 in the Airline and $1000 in the Oil company, we must find the values of 10 times the portfolios of $100 and also the correlation between the two companies, i.e., we have to find the value of

We know that,

We calculate the values of our portfolio C as follows:

We know that if Z = aX+bY, then variance of z is given by A²Var(X)+b²Var(Y)+2abcov(X,Y) . Thus, we have:

(d) The standard deviation represents the risk of each portfolio. Comparing the values, we see that:

Investment C has the lowest risk ($106.815), while Investment B has the highest risk ($435.88) despite investing the same amount of $2000 in both.