Question 1200774: [ LU
b) The company considers holding 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 returns are 9.93 percent and 18.20 percent for the S&P 500 and the Emerging Markets index, respectively. The standard deviations (risk) are 16.21 percent and 33.11 percent for the S&P 500 and the Emerging Markets index, respectively.
Calculate the portfolio's expected return and risk given that the covariance between the
S&P 500 and the Emerging Markets index is 0.005? Interpret the results that you have obtained.
(10 marks)
Answer by GingerAle(43)   (Show Source):
You can put this solution on YOUR website! **1. Calculate the Portfolio Expected Return:**
* **Formula:** Portfolio Expected Return = (Weight of S&P 500 * Expected Return of S&P 500) + (Weight of Emerging Markets * Expected Return of Emerging Markets)
* **Calculation:**
* Portfolio Expected Return = (0.80 * 0.0993) + (0.20 * 0.1820)
* Portfolio Expected Return = 0.07944 + 0.0364
* Portfolio Expected Return = 0.11584 or 11.584%
**2. Calculate the Portfolio Variance:**
* **Formula:** Portfolio Variance = (Weight of S&P 500)² * (Standard Deviation of S&P 500)² + (Weight of Emerging Markets)² * (Standard Deviation of Emerging Markets)² + 2 * (Weight of S&P 500) * (Weight of Emerging Markets) * Covariance
* **Calculation:**
* Portfolio Variance = (0.80)² * (0.1621)² + (0.20)² * (0.3311)² + 2 * (0.80) * (0.20) * 0.005
* Portfolio Variance = 0.016739 + 0.004372 + 0.00016
* Portfolio Variance = 0.021271
**3. Calculate the Portfolio Standard Deviation (Risk):**
* **Formula:** Portfolio Standard Deviation = √Portfolio Variance
* **Calculation:**
* Portfolio Standard Deviation = √0.021271
* Portfolio Standard Deviation = 0.1458 or 14.58%
**Interpretation:**
* **Expected Return:** The portfolio is expected to generate an average return of 11.584% per year. This return is higher than the return of the S&P 500 alone (9.93%) due to the inclusion of the higher-returning Emerging Markets index.
* **Risk:** The portfolio's risk (measured by standard deviation) is 14.58%. This is lower than the risk of the Emerging Markets index alone (33.11%) but higher than the risk of the S&P 500 (16.21%). This reduction in risk compared to the Emerging Markets index alone is due to the diversification effect of combining the two assets.
**Key Takeaway:**
This portfolio demonstrates a classic risk-return trade-off. By combining the higher-returning but riskier Emerging Markets index with the more stable S&P 500, the investor can potentially achieve a higher expected return while mitigating some of the overall risk. The positive covariance between the two indices indicates that they tend to move in the same direction, which limits the diversification benefits to some extent.
**Disclaimer:** This analysis is for illustrative purposes only and does not constitute financial advice. Investment decisions should be based on thorough research and consideration of individual risk tolerance and financial goals.
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