Question

1. An asset is forecast to have a return of 30% with a probability of .5 (50%) and a return of 10% with a probability of .5 (50%). The expected return is 20%. What is the variance of the returns?

a) 0

b) none of these

c) 0.1

d) 0.01

2. An asset has a variance of .0009. The standard deviation of the asset is:

a) 0

b) 0.3

c) 0.003

d) 0.03

3. Which of the following would typically be considered as an unsystematic risk factor?

a) a major product of the firm, accounting for 80% of its sales, is found to be unsafe and may no longer be sold

b) gross domestic product is forecast to grow more slowly than expected

c) the cost of petroleum is expected to increase significantly

d) the federal government increase corporate tax rates by 20 percentage points

4. An asset with only one possible outcome would

a) have a zero standard deviation

b) have no risk

c) have a zero variance

d) all of these

Answer 1

1.

Probability	Expected Return
0.5	30%
0.5	10%

Expected Return = E[R] = p₁*R₁+p₂*R₂ = 0.5*30%+0.5*10% = 20%

Variance can be calculated using the formula:

σ² = p₁*(R₁ - E[R])² + p₂*(R₂ - E[R])² = 0.5*(30%-20%)² + 0.5*(10%-20%)² = (0.5*0.01)+(0.5*0.01 = 0.01

Answer -> 0.01

2. Variance = 0.0009

We know that the standard deviation of an assets is the square root of its variance.

Standard Deviation = (0.0009)^1/2 = 0.03

Answer -> 0.03

3. Unsystematic risk is the firm-specific risk or the risk that can be diversified.

We see that in option a, the product of the firm which accounts for 80% of its sale is found to be unsafe. Hence this is the firm-specific risk.

Change in GDP, Cost of petroleum and corporate tax are the risk associated with the economy or market and is not a firm-specific risk

Answer -> a major product of the firm, accounting for 80% of its sales, is found to be unsafe and may no longer be sold

4. An asset with one possible outcome will definitely have zero variance and standard deviation.

Suppose R is one possible outcome. Hence, the Expected return will be equal to R itself i.e., R = E[R] and below is the formula for calculating the variance. Substituting R = E[R] is the following equation, we can see that the variance is zero.

σ² = (R₁ - E[R])²

Since standard deviation is the square root of the variance, hence it is also zero. Standard Deviation is zero.

We know that the standard deviation of the return of an asset is the measure of its risk. So, the asset will not have any risk.

Therefore, the asset has no risk.

Answer -> all of these