Question
cora evalutes two investment options that have different initial costs potential returns and risks option a requires a $500 investment and carries a 60% risk of loss with potential value of 1,000 in two years option b requires a $750 investment and carries a 30% risk of loss wit potential value of $900 in two years based on the risks involved what advice should cora her client regarding theses options
Answers
GPT-4o mini
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.
### 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.