1. Although there is some truth in the following statements, which best describes accepting risk as part of a decision-making process, given the definition of risk we have used in this class?
   1. Taking a course of action when you are not sure about what will happen in the future.
   2. Taking a course of action even though you know that only bad things could possibly happen.
   3. Taking a course of action when you are uncertain about the future, but only good outcomes can occur.
   4. Taking a course of action when you are uncertain about the future, and there are some outcomes in which bad things can occur as well as some good things.
   5. Taking a course of action when you are uncertain about the future, there is a possibility of loss, and the expected return is zero.

2. The concept of risk management is best described by which of the following statements?
   1. Take a course of action that contains risk, even though there are some bad things that can happen.
   2. Eliminate as much risk as possible before taking a course of action.
   3. Identify and measure the risk before taking a course of action.
   4. Identify and measure the risk so that all the risk can be eliminated before taking a course of action.
   5. Identify and measure the risk, try to mitigate or avoid the worst outcomes, and then determine if the expected benefits outweigh the potential losses enough to justify a course of action.

3. A probability distribution with fat tails means that there are more occurrences with very large values and very small values compared to a Normal distribution.
   1. True
   2. False

4. A probability distribution which is more peaked at the center of the distribution than a Normal distribution means that
   1. the values near the mean are larger than the values in a Normal distribution.
   2. there are more values near the mean than in a Normal distribution.

5. To show a typical bell-shaped distribution in Excel,
   1. sort the data and plot in a scatter diagram.
   2. sort the data and plot in a histogram.
   3. plot the data as they occurred, with the values on the y-axis and the date on the x-axis.

6. Continuous discounting involves
   1. natural logs and raising e to various powers.
   2. APRs and APYs.
   3. trigonometric functions.
   4. power function distributions

7. The advantage of continuous discounting in analyzing historical data is that
   1. the calculation of returns is more accurate and easy to explain.
   2. compounded returns are calculated by the addition of short-term returns, and the same up and down returns arrive at the same starting investment value.

8. Extreme Value Theory (EVT) includes estimating a mathematical model to fit the large values in the middle of a distribution that is more peaked than a Normal distribution.
   1. True
   2. False

9. Value at Risk (VaR) identifies an average loss that might occur, given that a loss takes place for an event that occurs in the tails of a distribution.
   1. True
   2. False

10. Expected Shortfall (ES) identifies a single value for an estimate of a loss that might occur or worse, in a given time period at a stated probability for an undesirable event.
    1. True
    2. False