You own shares of Fidelity Magellan Fund (FMF), which concentrates on stocks of large American companies. Its monthly return is μFMF = 1.4% and sFMF = 4.70%.
You decided to diversify your portfolio by adding shares of the Fidelity Japan Fund (FJF), which has monthly returns μFJF = 1.6% and sFJF = 6.80%.
Show that having a mix of these two funds (40% FMF and 60% FJF) has both a higher mean return and less volatility (variability) than FMF alone. Consider that correlation between returns of FMF and FJF is r = 0.25.
To analyze the performance of the mixed portfolio (40% FMF and 60% FJF) compared to FMF alone, we need to calculate the mean return and volatility of both options.
1. Calculate the mean return:
The mean return of a portfolio is given by the weighted average of the mean returns of its individual components. In this case, we have:
Mean return of FMF = μFMF = 1.4%
Mean return of FJF = μFJF = 1.6%
To calculate the mean return of the mixed portfolio, we use the following formula:
Mean return of mixed portfolio = (weight of FMF * mean return of FMF) + (weight of FJF * mean return of FJF)
Substituting the values:
Mean return of mixed portfolio = (0.4 * 1.4%) + (0.6 * 1.6%)
2. Calculate the volatility (standard deviation):
The volatility (or variability) of a portfolio is a measure of how much the returns fluctuate over time. In this case, we have the standard deviations for each fund, sFMF and sFJF.
To calculate the volatility of the mixed portfolio, we use the following formula:
Volatility of mixed portfolio = sqrt((weight of FMF)^2 * (standard deviation of FMF)^2 + (weight of FJF)^2 * (standard deviation of FJF)^2 + 2 * (weight of FMF) * (weight of FJF) * (standard deviation of FMF) * (standard deviation of FJF) * correlation)
Substituting the values:
Volatility of mixed portfolio = sqrt((0.4)^2 * (4.70%)^2 + (0.6)^2 * (6.80%)^2 + 2 * 0.4 * 0.6 * 4.70% * 6.80% * 0.25)
After calculating the mean return and volatility for both options, we can compare the results to determine if the mixed portfolio has a higher mean return and lower volatility compared to investing in FMF alone.