To evaluate the investment options for Cora's client, we can analyze both options based on their potential returns, risks, and net outcomes.
Investment Option A:
- Initial Cost: $500
- Potential Value in 2 Years: $1,000
- Risk of Loss: 60%
- Probability of Gain (40% chance): If the investment is successful, the outcome is $1,000.
- Probability of Loss (60%): The investment would result in a total loss of $500.
Expected Value Calculation for Option A:
- Expected Gain: \[ (0.4 \times 1000) + (0.6 \times 0) = 400 \]
- Expected Loss: \[ (0.6 \times 500) = 300 \]
- Net Expected Outcome (after investment): \[ 400 - 300 = 100 \] (which means Cora can expect a return of $100 on this option)
Investment Option B:
- Initial Cost: $750
- Potential Value in 2 Years: $900
- Risk of Loss: 30%
- Probability of Gain (70% chance): If the investment is successful, the outcome is $900.
- Probability of Loss (30%): The investment would result in a total loss of $750.
Expected Value Calculation for Option B:
- Expected Gain: \[ (0.7 \times 900) + (0.3 \times 0) = 630 \]
- Expected Loss: \[ (0.3 \times 750) = 225 \]
- Net Expected Outcome (after investment): \[ 630 - 225 = 405 \] (which means Cora can expect a return of $405 on this option)
Summary
- Option A Expected Outcome: $100
- Option B Expected Outcome: $405
Recommendation:
Based on the expected outcomes, Cora's client should consider investing in Option B. Although it has a higher initial investment and a potential value lower than that of Option A, it has a lower risk of loss and a significantly higher expected return. The lower probability of loss (30% vs. 60%) and better expected outcomes make Option B the more favorable choice.
Cora should also consider the client’s risk tolerance, investment goals, and timeframe since these factors also play a crucial role in making a final decision. If the client is more risk-averse, Option B would be the more suitable choice.