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?

Answer 1

First, make the assumption that “risk of loss” means the investor gets $0 in the losing scenario (if you mean something else, tell me and I’ll redo the numbers).

Compute expected terminal value and expected net gain (in 2 years):

- Option A: invest $500, 40% chance to end with $1,000, 60% chance to end with $0.
- Expected terminal value = 0.4×$1,000 + 0.6×$0 = $400
- Expected net = $400 − $500 = −$100 (an expected loss of $100; −20% on the capital)

- Option B: invest $750, 70% chance to end with $900, 30% chance to end with $0.
- Expected terminal value = 0.7×$900 + 0.3×$0 = $630
- Expected net = $630 − $750 = −$120 (an expected loss of $120; −16% on the capital)

Conclusions and advice:
- Under these assumptions, both options have negative expected returns, so neither is a good investment on average — Cora should advise the client to avoid both.
- If the client insists on choosing one:
- A has a smaller expected dollar loss (−$100 vs −$120), but a much higher chance of total loss (60% vs 30%).
- B has a lower probability of loss and a less negative percentage return (−16% vs −20%), so it is the less risky choice for a risk-averse client.
- Recommend clarifying what “loss” means (total loss or partial loss) and consider alternatives with positive expected return or lower downside risk.