An investor invests 70% of her wealth in a risky asset with an expected rate of return of 15% and a variance of 0.05 and she puts 30% in a Treasury bill that pays 5%. Her portfolio's expected rate of return and standard deviation are and respectively.

The portfolio's expected return is 12% and the standard deviation of the portfolio is 15.65%.

Explanation:

The expected rate of return of the portfolio is the weighted average of the individual stock returns that form up the portfolio. The formula for a two stock portfolio return is,

Portfolio return = wA * rA + wB * rB

Where,

Portfolio return = 0.7 * 0.15  +  0.3 * 0.05  =  0.12 or 12%

The portfolio which consists of a risky and a risk free asset has a standard deviation equal to the weight of the risky asset multiplied by its standard deviation. The risk free asset has no standard deviation. Thus, the formula for a portfolio standard deviation for such a portfolio is,

Standard deviation = weight of risky asset * standard deviation of risky asset

Standard deviation of portfolio = 0.7 * √0.05

Where standard deviation is the square root of variance.

Standard deviation of portfolio = 0.1565 or 15.65%

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