Final answer:
To solve numerically for the proportions of each asset and for the expected return and standard deviation of the optimal risky portfolio, we need to calculate the expected value for each investment and then determine which investment is the safest and riskiest. Finally, we can identify the investment with the highest expected return.
Step-by-step explanation:
To solve numerically for the proportions of each asset and for the expected return and standard deviation of the optimal risky portfolio, we need to calculate the expected value for each investment and then determine which investment is the safest and riskiest. Finally, we can identify the investment with the highest expected return.
a. To construct a Probability Density Function (PDF) for each investment, we multiply the probability of each outcome by the corresponding profit/loss and sum them up.
b. The expected value for each investment is obtained by multiplying each possible outcome by its probability and summing them up.
c. The safest investment can be determined by comparing the probabilities of losses for each investment.
d. The riskiest investment can be determined by comparing the probabilities of the highest potential losses for each investment.
e. The investment with the highest expected return can be determined by comparing the expected values of each investment.