Let X = the fraction of the portfolio to invest in Bond 1
Y = the fraction of the portfolio to invest in Bond 2
Z = the fraction of the portfolio to invest in Bond 3
s.t.
0.20X + 0.128Y + 0.067Z = R1
0.026X + 0.1Y + 0.7Z = R2
0.121X + 0.125Y + 0.226Z = R3
-0.139X-0.243Y-0.18Z = R4
-0.167X + 0.269Y + 0.234Z = R5
0.135X + 0.225Y-0.146Z = R6
0.152X + 0.204Y + 0.047Z = R7
0.175X + 0.186Y + 0.604Z = R8
X + Y + Z =1
X, Y, Z, ≥ 0
The efficient frontier is shown below. We see that as the expected return increases, the minimum variance (possible risk) also increases, and this increase is evident for expected returns of more than 8 percent.