Question

Cora evaluates 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 a potential value of $1,000 in two years. Option B requires a $750 investment and
carries a 30% risk of loss, with a potential value of $900 in two years. Based on the
risks involved, what advice should Cora give her client regarding these options?

A) Option A has less risk.
B) Option B has less risk.
C) Both options have the same risk.
D) The client should not invest in either option.

Answer 1

To evaluate the risk associated with each investment option, we can consider both the probability of loss and the potential returns.

**Option A:**
- Initial Investment: $500
- Risk of Loss: 60%
- Potential Value in two years: $1,000

The expected outcome can be calculated as follows:
- Probability of gaining $1,000: 40% (100% - 60% risk of loss)
- Expected Value = (0.4 * $1,000) + (0.6 * $0) = $400

**Option B:**
- Initial Investment: $750
- Risk of Loss: 30%
- Potential Value in two years: $900

The expected outcome can be calculated as follows:
- Probability of gaining $900: 70% (100% - 30% risk of loss)
- Expected Value = (0.7 * $900) + (0.3 * $0) = $630

Now let's analyze the risk involved:

- For **Option A**, there is a 60% chance of losing the entire investment.
- For **Option B**, there is a 30% chance of losing the entire investment.

Since **Option B has a lower risk of loss at 30% compared to Option A's 60%**, the advice Cora should give her client would be:

**B) Option B has less risk.**