Final answer:
To measure the risk of an investment using the Monte Carlo method, construct a PDF for each investment and calculate the expected value. The investment with the highest expected value is considered the safest. Risk can also be assessed by examining the range of possible outcomes and their probabilities.
Step-by-step explanation:
To measure the risk of an investment using the Monte Carlo method, you first need to construct a Probability Density Function (PDF) for each investment option. This PDF represents the likelihood of different outcomes or returns for each investment. Once you have the PDFs, you can calculate the expected value for each investment, which is the weighted average of the possible outcomes. The investment with the highest expected value is considered the safest. To measure the risk of an investment, you can also analyze the range of possible outcomes, such as the best-case and worst-case scenarios, and consider the probability of each outcome occurring.
For example, let's consider the three investments mentioned in the question. To measure the risk, we need to calculate the PDF for each investment option. For the first investment, the PDF could be: 10% chance of a $5,000,000 profit, 30% chance of a $1,000,000 profit, and 60% chance of losing the million dollars. Similar PDFs can be constructed for the other investments.
Next, we calculate the expected value for each investment by multiplying each possible outcome by its probability and summing them up. The investment with the highest expected value is considered the safest, as it has the highest average return. To measure the risk, you can also assess the range of possible outcomes and the probability of each outcome occurring. The investment with a higher probability of negative outcomes and a wider range of possible outcomes would be considered riskier.