Question

Assume that as a US investor, you decide to hold a portfolio with 80 percent invested in the S&P 500 US stock index and the remaining 20 percent in the MSCI Emerging Markets index. The expected return is 9.93 percent for the S&P 500 and 18.20 percent for the Emerging Markets index. The risk (standard deviation) is 16.21 percent for the S&P 500 and 33.11 percent for the Emerging Markets index. What will be the portfolio’s expected return and risk given that the covariance between the S&P 500 and the Emerging Markets index is 0.5 percent or 0.0050? Note that units for covariance and variance are written as %2 when not expressed as a fraction. These are units of measure like squared feet and the numbers themselves are not actually squared.

Answer 1

The expected return for an 80/20 investment in the S&P 500 and MSCI Emerging Markets index is 11.584%. Risk calculation requires a detailed formula considering standard deviations and covariance of the two assets.

Step-by-step explanation:

If you're a US investor with 80 percent of your portfolio invested in the S&P 500 and the remaining 20 percent in the MSCI Emerging Markets index, the calculation of your portfolio's expected return and risk involves a weighted average of the returns and a formula considering the standard deviation and covariance of the two investments.

The expected return for the portfolio is a weighted average: (0.80 * 9.93%) + (0.20 * 18.20%) = 7.944% + 3.640% = 11.584%.

As for the risk (standard deviation) of the portfolio, it's calculated using the variances (squared standard deviations), the weights, and the covariance. This calculation is more complex and often requires financial calculator or software, but essentially combines the individual risks of the investments in the portfolio taking into account how the returns on the investments move together (covariance).