Question

An investor invests 40% of his wealth in a risky asset with an expected rate of return of 0.18 and a variance of 0.04 and 60% in a t-bill that pays 4%. his portfolio's expected return and standard deviation are ______ and ______, respectively.

Answer 1

The investor's portfolio has an expected return of 9.6% and a standard deviation, which is a measure of risk, of 8%.

Step-by-step explanation:

An investor who invests 40% of his wealth in a risky asset with an expected rate of return of 0.18 and a variance of 0.04, and 60% in a T-bill that pays 4%, has a portfolio's expected return calculated as follows:

• Expected return from risky asset = 40% * 18% = 7.2%
• Expected return from T-bill = 60% * 4% = 2.4%
• Total expected rate of return = 7.2% + 2.4% = 9.6%

The portfolio's standard deviation, which measures the risk, only considers the risky asset since T-bills are risk-free. The standard deviation of the portfolio is calculated using the square root of the variance of the risky asset times the square of its weight in the portfolio:

• Standard deviation of the portfolio = sqrt(0.04) * 40% = 20% * 40% = 8%

Therefore, the portfolio's expected return is 9.6% and its standard deviation is 8%.