Final answer:
The safest investment is the third one (biotech firm) with the lowest probability of loss. The riskiest is the first one (software company) with the highest probability of loss. The investment with the highest expected return is the second one (hardware company) with an expected value of $600,000.
Step-by-step explanation:
According to the mean-variance criterion, when comparing investments, one investment dominates others if it has a higher expected return for the same level of risk or if it has a lower level of risk for the same expected return. When looking at the given investments:
- The expected value for Investment 1 (software company) is: (0.1 * $5,000,000) + (0.3 * $1,000,000) - (0.6 * $1,000,000) = $500,000 + $300,000 - $600,000 = $200,000.
- The expected value for Investment 2 (hardware company) is: (0.2 * $3,000,000) + (0.4 * $1,000,000) - (0.4 * $1,000,000) = $600,000 + $400,000 - $400,000 = $600,000.
- The expected value for Investment 3 (biotech firm) is: (0.1 * $6,000,000) - (0.2 * $1,000,000) = $600,000 - $200,000 = $400,000.
The safest investment is the third investment (biotech firm), as it has the lowest probability of loss. Conversely, the riskiest investment is the first investment (software company), due to its highest probability of loss. The investment with the highest expected return, on average, is the second investment (hardware company), as it balances the probability of gains and losses better than the others and results in the highest expected value