# Calculate best share based on return of investement and standard devation (Without risk free rate)

I have a microeconomics task in investment analysis. How do you pick the best share based on return of investment and standard deviations? The task is like this: 3 shares:

• Share A: 10% ROI & 20% std
• Share B: 15% ROI & 30% std
• Share C: 20% ROI & 40% std

Which share would a reasonable investor invest in? The correct answer is apparently B, but how do you calculate this? I know if a risk free rate was given, the investor invest in the share with the highest Sharpe Ratio, but in this task no risk free rate was given.

Any help would be appreciated.

• In a classic mean-variance optimization setup, the investor would be indifferent between all three, since they all offer the same risk/reward profiles. Typically in Microeconomics, however, one would also specify a utility function for the investor. In this case, you could easily ensure that B is the unique optimal choice. Could this be the case here? – AdB May 13 at 10:01