Weights Required in the portfolio from SPX and the SWISX

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%.

To obtain greater diversification for your investments you consider forming a portfolio from two stock index funds, one that tracks the S&P 500 (SPX) and the other is the Schwab International Index Fund (SWISX) that tracks large stocks in markets around the world. Over the next year, the S&P 500 has an expected return of 14% and a standard deviation of return of 30%. The SWISX has an expected return of 18% and a standard deviation of return of 27% (in U.S. $ terms). Assume that the indices have a historic correlation of 0.20 and that is expected to hold in the near future.

If you wish to obtain an expected return of 15.5% on a portfolio formed with the two indices, what are the weights in the SPX and the SWISX that would be required to be in the portfolio?

Summary: This question belongs to financial management and discuses about weights in the SPX and the SWISX that would be required to be in the portfolio.

Total word count: 37