Assume that the yearly risk free rate is 2%. (A monthly risk free rate of 0.001652).

(a) Find the optimal investment portfolio in the risky assets. What are the mean and s.d. of the returns of this portfolio?

(b) Find the point on the efficient frontier that corresponds to a yearly risk free rate of 5% (0.004074 monthly). What is the correlation of this portfolio with the optimal investment portfolio?

(c) Plot the efficient frontier in the mean-s.d. plane (use the two-fund theorem).

(d) Find the global minimum variance portfolio. What is the expected return and variance of return of this portfolio?

(e) Write down the CAL equation for this case.

(f) What would be the capital allocation between the risk free asset and the optimal risky investment portfolio for individuals with risk aversion coefficients of 1, 3, 5, 10?

(g) If the initial investment is $100,000, how much money should each of these investors allocate to each of the 5 assets (risk free asset and 4 risky assets).

Date 2/3/1997 3/3/1997 4/1/1997 5/1/1997 6/2/1997 7/1/1997 8/1/1997 9/2/1997 10/1/1997 11/3/1997 12/1/1997 1/2/1998 2/2/1998 3/2/1998 4/1/1998 5/1/1998 6/1/1998 7/1/1998 8/3/1998 9/1/1998 10/1/1998 11/2/1998 12/1/1998 1/4/1999 2/1/1999 3/1/1999 4/1/1999 5/3/1999 6/1/1999 7/1/1999 8/2/1999 9/1/1999 10/1/1999 11/1/1999 12/1/1999 1/3/2000 2/1/2000 3/1/2000 4/3/2000 5/1/2000 6/1/2000 7/3/2000 8/1/2000 9/1/2000 10/2/2000 11/1/2000 12/1/2000 PG 0.039059 -0.044853 0.099732 0.096787 0.024472 0.080347 -0.124958 0.037519 -0.011808 0.120612 0.047318 -0.014954 0.08301 -0.005965 -0.022802 0.020264 0.085766 -0.125554 -0.036133 -0.070372 0.251503 -0.012154 0.042346 -0.001647 -0.015122 0.094361 -0.039286 -0.00478 -0.056297 0.031383 0.095943 -0.055278 0.122319 0.029724 0.014433 -0.074977 -0.130615 -0.354114 0.057826 0.113029 -0.146603 0.010385 0.084797 0.083695 0.071038 0.048299 0.047696 Microsof -0.043935 -0.05994 0.325186 0.02085 0.018853 0.118736 -0.064783 0.000737 -0.017673 0.088456 -0.086777 0.1546 0.135859 0.056354 0.007077 -0.058919 0.277427 0.014388 -0.127216 0.147283 -0.03807 0.152324 0.136981 0.261679 -0.142261 0.194093 -0.092688 -0.007789 0.117754 -0.048622 0.078932 -0.021842 0.02233 -0.016316 0.282236 -0.161694 -0.086859 0.18888 -0.34365 -0.103039 0.278816 -0.127284 0 -0.136078 0.141761 -0.166961 -0.243737 BAC 0.109771 -0.070109 0.088252 -0.024705 0.102423 0.102398 -0.160399 0.041554 -0.033679 0.00429 0.018687 -0.015199 0.143693 0.070731 0.042156 -0.006672 0.020991 0.039885 -0.279162 -0.063083 0.074941 0.133442 -0.07112 0.111743 -0.023267 0.088614 0.013567 -0.096287 0.141424 -0.0946 -0.088303 -0.072515 0.156916 -0.090737 -0.136175 -0.034898 -0.050499 0.152988 -0.06549 0.141377 -0.224239 0.101858 0.141786 -0.022429 -0.082261 -0.157317 0.149059 Exxon -0.025167 0.074816 0.051471 0.053613 0.033628 0.048801 -0.041224 0.046828 -0.040667 -0.000424 0.002969 -0.030867 0.082024 0.060887 0.080578 -0.029546 0.012323 -0.015754 -0.062932 0.079193 0.014029 0.05321 -0.024924 -0.039378 -0.047105 0.06 0.177287 -0.033565 -0.034418 0.029164 -0.001259 -0.03657 -0.025524 0.077569 0.015581 0.028843 -0.086191 0.035574 -0.003782 0.07814 -0.057805 0.021489 0.02378 0.091423 0.000819 -0.008451 -0.012098 1/2/2001 2/1/2001 3/1/2001 4/2/2001 5/1/2001 6/1/2001 7/2/2001 8/1/2001 9/4/2001 10/1/2001 11/1/2001 12/3/2001 1/2/2002 2/1/2002 3/1/2002 4/1/2002 5/1/2002 6/3/2002 7/1/2002 8/1/2002 9/3/2002 10/1/2002 11/1/2002 12/2/2002 1/2/2003 2/3/2003 3/3/2003 4/1/2003 5/1/2003 6/2/2003 7/1/2003 8/1/2003 9/2/2003 10/1/2003 11/3/2003 12/1/2003 1/2/2004 2/2/2004 3/1/2004 4/1/2004 5/3/2004 6/1/2004 7/1/2004 8/2/2004 9/1/2004 10/1/2004 11/1/2004 12/1/2004 -0.079901 -0.018512 -0.11214 -0.034762 0.069628 -0.006734 0.119397 0.044078 -0.018369 0.019041 0.049936 0.021479 0.037248 0.037938 0.0625 0.00604 -0.007831 0.004999 0.001571 -0.003921 0.008397 -0.005985 -0.044241 0.016708 0.000269 -0.043361 0.087838 0.013716 0.021956 -0.028728 -0.009774 -0.006494 0.063268 0.064175 -0.021026 0.037999 0.016598 0.014091 0.023158 0.013581 0.019141 0.009808 -0.037611 0.073223 -0.033013 -0.049866 0.044861 0.030013 0.407075 -0.03352 -0.07308 0.238753 0.021215 0.055282 -0.093427 -0.13802 -0.102904 0.136126 0.104315 0.031866 -0.038603 -0.08413 0.03382 -0.133683 -0.025641 0.074163 -0.122494 0.022843 -0.108685 0.22216 0.078815 -0.103885 -0.081998 0.002053 0.021516 0.056169 -0.037512 0.041934 0.02983 0.004138 0.048535 -0.054585 -0.016628 0.064819 0.010146 -0.040611 -0.060082 0.047942 0.004159 0.088357 -0.002114 -0.038983 0.012787 0.011319 0.068446 -0.003223 0.172544 -0.047261 0.079481 0.022977 0.067892 0.013384 0.059906 -0.033378 -0.041897 0.010091 0.040438 0.035665 0.001325 0.02425 0.063711 0.065561 0.045955 -0.06427 -0.055103 0.053799 -0.08106 0.093723 0.004265 0.001931 0.006936 -0.011864 -0.025174 0.107668 0.002152 0.074087 0.044652 -0.040191 -0.005317 -0.029402 -0.004131 0.077774 0.012829 0.005383 -0.001575 -0.005994 0.032688 0.027658 0.004785 0.058333 -0.026997 0.033526 0.032998 0.025717 -0.032007 -0.031915 -0.000594 0.093908 0.00652 -0.015385 -0.04386 -0.033257 -0.018683 0.001209 -0.046484 0.050965 -0.006325 0.063959 0.061254 -0.08349 -0.000293 0.024612 -0.101516 -0.029599 -0.100033 0.055029 0.04076 0.003983 -0.022479 0.003044 0.02731 0.00722 0.041382 -0.013454 -0.009198 0.066901 -0.029403 -0.000309 -0.003401 0.132485 -0.005205 0.040209 -0.013768 0.023087 0.023091 0.02693 0.042458 0.001677 0.048314 0.01848 0.046819 0.000214 1/3/2005 2/1/2005 3/1/2005 4/1/2005 5/2/2005 6/1/2005 7/1/2005 8/1/2005 9/1/2005 10/3/2005 11/1/2005 12/1/2005 1/3/2006 2/1/2006 3/1/2006 4/3/2006 5/1/2006 6/1/2006 7/3/2006 8/1/2006 9/1/2006 10/2/2006 11/1/2006 12/1/2006 1/3/2007 -0.02934 -0.002502 -0.001672 0.026795 0.018552 -0.043435 0.059845 -0.002567 0.071655 -0.053565 0.021468 0.012037 0.028318 0.01175 -0.038469 0.015852 -0.068178 0.02492 0.016534 0.101416 0.001216 0.027937 -0.009453 0.023517 0.0333 -0.016572 -0.039457 -0.039367 0.046771 0.022979 -0.037438 0.031115 0.072087 -0.060203 -0.001248 0.080383 -0.055127 0.076295 -0.042077 0.012663 -0.112544 -0.058565 0.028531 0.032742 0.072215 0.064066 0.049788 0.026103 0.017198 0.041916 -0.013196 0.005884 -0.045467 0.021448 0.028361 -0.005834 -0.044012 -0.001395 -0.021794 0.039132 0.060473 0.005702 -0.041753 0.036848 0.00415 0.096099 -0.020504 -0.006015 0.071169 0.009718 0.040734 0.005591 0.010051 -0.008469 0.003844 0.006632 0.232944 -0.058611 -0.043032 -0.009568 0.022604 0.022294 0.02458 0.060606 -0.116327 0.038876 -0.032049 0.117129 -0.048826 0.025036 0.036549 -0.029497 0.007162 0.104232 0.003455 -0.008296 0.064394 0.080071 -0.002334 -0.040457