Investment risk and project analysis

Question 1

Determine which of the following statements regarding investment risk measures is TRUE.

A
The downside standard deviation is the square root of the variance.

B
Since the semi-variance only cares about the downside risk rather than the upside variability, the semi-variance can be negative.

C
If X is a random variable that represents the investment gain in a security over one period and the Value-at-Risk of X at α=5% is 1%, then there is a 95% probability that the investment gain over one period will be no more than 1%.

D
If X is a random variable that represents the investment gain in a security over one period and the Value-at-Risk of X at α=5% is 1%, then there is a 95% probability that the investment gain over one period will be more than 1%.

E
Value-at-Risk is more conservative than Tail-Value-at-Risk.

Answer 1

D
If X is a random variable that represents the investment gain in a security over one period and the Value-at-Risk of X at α=5% is 1%, then there is a 95% probability that the investment gain over one period will be more than 1%.

Statement A is false:

The downside standard deviation is the square root of the semi-variance.

Statement B is false:

Semi-variance must be non-negative. Even though all of the terms in min(0,R−E[R]) are non-positive, the terms are then squared, resulting in a value that is non-negative.

Statement E is false:

Tail-Value-at-Risk is more conservative than Value-at-Risk as it provides a greater buffer against adverse outcomes.

Question 2

Determine which of the following statements regarding project risk analysis is TRUE.

A
When break-even analysis is used, we calculate the value of each parameter so that the project has an IRR of zero.

B
The IRR is the rate at which NPV is zero.

C
Scenario analysis involves changing the input variables one at a time to see how NPV changes.

D
Sensitivity analysis explores how IRR changes when various desired subsets of the complete set of model variables are changed simultaneously

E
In a Monte Carlo simulation, input variables are assumed to be independent with each other.

Answer 2

B

The IRR is the rate at which NPV is zero.