Answer:
Step-by-step explanation:
To analyze the risk and return of a portfolio consisting of these three mutual funds, we need to calculate the expected return and standard deviation of the portfolio. The weights of each fund in the portfolio are denoted by w_s, w_b, and w_m for the stock fund, bond fund, and money market fund, respectively.
The expected return of the portfolio (E(R_p)) is given by the weighted sum of the expected returns of the individual funds:
E(Rp)=ws⋅E(Rs)+wb⋅E(Rb)+wm⋅E(Rm)E(Rp)=ws⋅E(Rs)+wb⋅E(Rb)+wm⋅E(Rm)
The standard deviation of the portfolio (SD_p) is given by:
SDp=ws2⋅SDs2+wb2⋅SDb2+wm2⋅SDm2+2⋅ws⋅wb⋅ρsb⋅SDs⋅SDbSDp=ws2⋅SDs2+wb2⋅SDb2+wm2⋅SDm2+2⋅ws⋅wb⋅ρsb⋅SDs⋅SDb
Where:
E(Rs),E(Rb),E(Rs),E(Rb), and E(Rm)E(Rm) are the expected returns of the stock, bond, and money market funds, respectively.
SDs,SDb,SDs,SDb, and SDmSDm are the standard deviations of the stock, bond, and money market funds, respectively.
ρsbρsb is the correlation coefficient between the stock and bond funds.
Given the information provided:
E(Rs)=15%,SDs=38%E(Rs)=15%,SDs=38%
E(Rb)=9%,SDb=29%E(Rb)=9%,SDb=29%
E(Rm)=5.5%,SDm=This is not provided but could be assumed to be 0 since it’s a risk-free rate.E(Rm)=5.5%,SDm=This is not provided but could be assumed to be 0 since it’s a risk-free rate.
ρsb=0.15ρsb=0.15
Assuming a risk-free money market fund has zero standard deviation (as it yields a sure rate), the standard deviation of the portfolio simplifies to:
SDp=ws2⋅SDs2+wb2⋅SDb2+2⋅ws⋅wb⋅ρsb⋅SDs⋅SDbSDp=ws2⋅SDs2+wb2⋅SDb2+2⋅ws⋅wb⋅ρsb⋅SDs⋅SDb
Now, you can choose weights for each fund (w_s, w_b, and w_m) and substitute the values into the formulas to find the expected return and standard deviation of the portfolio. The weights must satisfy the constraint ws+wb+wm=1ws+wb+wm=1.