Ralph Vince - Portfolio Mathematics

264 THE HANDBOOK OF PORTFOLIO MATHEMATICS

quarter equates to roughly a 6% risk-free rate for the year.). Thus, to work
out (8.01a) for the third set of coordinates (.00013, 1.002):

(AHPR−(1+RFR))/SD=(1. 002 −(1+.015))/. 00013

=(1. 002 − 1 .015)/. 00013

=−. 013 /. 00013

=− 100

The process is completed for each point along the efficient frontier.
Equation (8.01) peaks out at .502265, which is at the coordinates (02986,
1.03). These coordinates are the point where the CML line is tangent to the
efficient frontier, corresponding to point B in Figure 8.1. This tangent point
is a certain portfolio along the efficient frontier. The Sharpe ratio is the slope
of the CML, with the steepest slope being the tangent line to the efficient
frontier.

Efficient Frontier CML line

AHPR SD Eq. (8.1a) Percentage AHPR

RFR=.015
1.00000 0.00000 0 0.00% 1.0150
1.00100 0.00003 −421.902 0.11% 1.0150
1.00200 0.00013 −100.000 0.44% 1.0151
1.00300 0.00030 −40.1812 1.00% 1.0152
1.00400 0.00053 −20.7184 1.78% 1.0153
1.00500 0.00083 −12.0543 2.78% 1.0154
1.00600 0.00119 −7.53397 4.00% 1.0156
1.00700 0.00163 −4.92014 5.45% 1.0158
1.00800 0.00212 −3.29611 7.11% 1.0161
1.00900 0.00269 −2.23228 9.00% 1.0164
1.01000 0.00332 −1.50679 11.11% 1.0167
1.01100 0.00402 −0.99622 13.45% 1.0170
1.01200 0.00478 −0.62783 16.00% 1.0174
1.01300 0.00561 −0.35663 18.78% 1.0178
1.01400 0.00650 −0.15375 21.78% 1.0183
1.01500 0.00747 0 25.00% 1.0188
1.01600 0.00849 0.117718 28.45% 1.0193
1.01700 0.00959 0.208552 32.12% 1.0198
1.01800 0.01075 0.279036 36.01% 1.0204
1.01900 0.01198 0.333916 40.12% 1.0210
1.02000 0.01327 0.376698 44.45% 1.0217
1.02100 0.01463 0.410012 49.01% 1.0224
1.02200 0.01606 0.435850 53.79% 1.0231
1.02300 0.01755 0.455741 58.79% 1.0238
1.02400 0.01911 0.470873 64.01% 1.0246
1.02500 0.02074 0.482174 69.46% 1.0254