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Suppose Alexander wants to invest his money on a profitable project. He selected 2 projects: project A and Project B and has to decide which one to select to invest his money in. The first and the second one have an average return or $100. The standard deviation of the first one is 15 and from the second is 5. If Alexander has $ 120, in which project he should invest it?

A) Project A
B) Project B
C) Both A and B
D) Not enough information
E) None of the above

1 answer

To compare the two projects, we can analyze their risk-to-return ratios. Both projects have the same average return of $100, but they have different levels of risk as represented by their standard deviations.

  • Project A: Average Return = $100, Standard Deviation = $15
  • Project B: Average Return = $100, Standard Deviation = $5

A lower standard deviation indicates less risk, meaning Project B has less variability in returns compared to Project A. This makes Project B a safer investment, even though they both have the same average return.

To analyze this further, we can calculate the coefficient of variation (CV) for each project, which is a measure of relative risk:

\[ \text{Coefficient of Variation (CV)} = \frac{\text{Standard Deviation}}{\text{Average Return}} \]

Calculating CV for both projects:

  • Project A: \[ \text{CV}_A = \frac{15}{100} = 0.15 \]

  • Project B: \[ \text{CV}_B = \frac{5}{100} = 0.05 \]

Since Project B has a lower coefficient of variation (0.05) compared to Project A (0.15), it has a more favorable risk-to-return profile.

Given that Alexander has $120 to invest and both projects have the same average return, he should invest in the project that minimizes risk relative to return. Thus, the better choice for Alexander is:

B) Project B