Return and Standard Deviation of the Portfolio in an Index Fund

Question

Over the next year, expected return on the S&P 500 index (proxy for the optimal risky portfolio), the SMB portfolio, and the HML portfolio are 11%, 6%, and 3%; standard deviation of the returns on the S&P 500 is 27%; risk free return is 2%.

If you invest 80% of your investment budget in an index fund that tracks the S&P 500 and the remainder in the risk-free asset, what are the expected return and standard deviation of the “complete portfolio” that you have created? [Assume that the fund passes on the full return on the S&P 500 to investors.

Summary: This question belongs to financial management and discuses about expected return and standard deviation of the complete portfolio when invest in an index fund that tracks S&P 500.

Total word count: 20