Question

You are a financial advisor and offer two risky funds A and B, and a risk-free money market fund. Fund A has an expected return of 18% and standard deviation of 21%. Fund B has an expected return of 8% and a standard deviation of 12%. The correlation between the two funds is 0.1. The risk free rate is 4%. Your client Derek wants to earn 9% on his investments while taking as little risk as possible. With the above products your best suggestion would be

21.74 in A, 29.5 in B, 48.76 in RF

29.5 in A, 21.74 in B, 48.76 in Rf

40.58 in A, 42.02 in B, 17.4 in Rf

42.02 in A, 40.58 in B, 17.4 in Rf

Answer 1

Answer.

RA=18%,σA=21%

RB=8%,σB=8%

Correlation between two fund (rAB)=0.1

RRF= 4%

Option 1

WA=21.74, WB=29.50, WRF=48.76

Expected rate of return at this level = WA*RA+WB*RB+WFR*RRF

= 0.2174*18+.2950*8+0.4876*4= 8.2236%

Risk of the portfolio = (((WA*σA)^2+(WB*σB)^2+2*rAB*WA*σA*WB*σB)^0.5 )

= 6.05% (Please use above data in formula given for risk of portfolio)

Option 2

WA=29.50, WB=21.74, WRF=48.76

Expected rate of return at this level = WA*RA+WB*RB+WFR*RRF

= 0.2950*18+0.2174*8+0.4876*4= 8.9996%

Similarly Risk of portfolio=6.96%

Option 3

WA=40.58, WB=42.02, WRF=17.40

Expected rate of return at this level = WA*RA+WB*RB+WFR*RRF

= 0.4058*18+0.4202*8+0.1740*4=11.362%

Similarly Risk of portfolio in this case=10.33%

Option 4

WA=42.02, WB=40.58, WRF=17.40

Expected rate of return at this level = WA*RA+WB*RB+WFR*RRF

= 0.4202*18+0.4058*8+0.1740*4=11.506%

Similarly Risk of portfolio in this case=10.50%

As client expected rate of return is 9% so option 2 is acceptable.

Note.

As we know that standard deviation of risk free rate of security is zero so we have not incorporating the standard deviation of that security in said formula