Question

1. The returns on shares of Valley Transporter are predicted under the following various economic conditions:
Recession -0.13
Normal +0.08
Boom +0.25
If each economy state has the same probability of occurring (33.33%), what is the variance of the stock?


Place your answer in decimal form using four decimal places.

2. The return on shares of the Orange Company are predicted under the following states of nature. The states of nature are all equally likely, and because there are a total of three states, each state has a 33.333% chance of occurring.

Recession -0.11
Normal +0.07
Boom +0.25

What is the standard deviation of Orange?

* Place your answer in decimal form, for example as say .0675 and not 6.75.

Answer 1

1. Valley Transporter

We have been provided with returns on investing in the shares of Valley Transporter predicted under three different economic scenarios, viz.,

Recession R₁: -0.13
Normal R₂: 0.08
Boom R₃: 0.25

Since all the three scenarios are equally likely, we can calculate the mean return or the expected return E(R) on the stock as

E(R) = (0.33 x (-0.13)) + (0.33 x 0.08) + (0.33 x 0.25) = 0.0667

Now, we calculate the variance using the below formula:

where,
R_i represents the returin in scenario i,
E(R) is the expected return, and
N is the number of scenarios

The table below shows the steps involved:

Scenario	Return Ri	Expected Return E(R)	Deviation Ri - E(R)	Squared Deviation (Ri - E(R))2
Recession	-0.1300	0.0667	-0.1967	0.0387
Normal	0.0800	0.0667	0.0133	0.0002
Boom	0.2500	0.0667	0.1833	0.0336
Sum	0.0725

Using the sum 0.0725 in the above formula, we get Var of 0.0725 / 3 = 0.0242

Hence, the variance of the stock of Valley Transporter is 0.0242

2. Orange Company

Here again, we are provided with the returns on investing in the shares of Orange Company predicted under three different economic scenarios, i.e.,

Recession R₁: -0.11
Normal R₂: 0.07
Boom R₃: 0.25

Since all the three scenarios are equally likely, we can calculate the expected return E(R) on the stock as

E(R) = (0.33 x (-0.11)) + (0.33 x 0.07) + (0.33 x 0.25) = 0.07

The table below shows the steps involved:

Scenario	Return Ri	Expected Return E(R)	Deviation Ri - E(R)	Squared Deviation (Ri - E(R))2
Recession	-0.1100	0.0700	-0.1800	0.0324
Normal	0.0700	0.0700	0.0000	0.0000
Boom	0.2500	0.0700	0.1800	0.0324
Sum	0.0648

Using the sum 0.0648 in the above formula for variance, we get Var of 0.0648 / 3 = 0.0216

Standard deviation being the square-root of Var, we get the standard deviation of the stock of Orange Company of 0.1470