Consider a T-bill with a rate of return of 5% and the following risky securities:

Security A: E (r) = 0.15; Variance = 0.04

Security B: E (r) = 0.10; Variance = 0.0225

Security C: E (r) = 0.12; Variance = 0.01

Security D: E (r) = 0.13; Variance = 0.0625

From which set of portfolios, formed with the T-bill and any one of the four risky securities, would a risk-averse investor always choose his portfolio?

Security C: E (r) = 0.12; Variance = 0.01

Explanation:

As the investor is risk-averse, he/she will try to avoid risk, which is the lesser variance possible. Actually, he/she would prefer only T-bill investment, which is risk-free, but as he/she is diversifying and choosing one of the portfolios listed, he/she will choose C, as it is the lowest variance.

We can of course discard Security B, as it has a lower expectation (expected return) than Security C and higher variance (risk). No rational investor will invest in something that has lower return and higher risk. The same goes for Security D, it has lower return (expectancy) than Security A and higher risk (variance).

So the options are down to Security A and Security C. Security C has lower variance and lower expectancy than A, but as the investor is risk-averse, he/she will not care in resigning profit if it means lower risk. So the option is the one with the lowest variance, Security C.