is the risk free rate requiring to change from monthly to annual

I have question on q1 optimal weight and q2.

could u give me more detail

Thanks

Date 1/31/1995 2/28/1995 3/31/1995 4/28/1995 5/31/1995 6/30/1995 7/31/1995 8/31/1995 9/29/1995 10/31/1995 11/30/1995 12/29/1995 1/31/1996 2/29/1996 3/29/1996 4/30/1996 5/31/1996 6/28/1996 7/31/1996 8/30/1996 9/30/1996 10/31/1996 11/29/1996 12/31/1996 1/31/1997 2/28/1997 3/31/1997 4/30/1997 5/30/1997 6/30/1997 7/31/1997 8/29/1997 9/30/1997 10/31/1997 11/28/1997 12/31/1997 1/30/1998 2/27/1998 3/31/1998 4/30/1998 5/29/1998 6/30/1998 7/31/1998 8/31/1998 S&P500 0.02600 0.03923 0.02933 0.02940 0.03981 0.02416 0.03341 0.00350 0.04210 -0.00344 0.04403 0.01764 0.03486 0.01009 0.00959 0.01513 0.02526 0.00413 -0.04444 0.02193 0.05604 0.02680 0.07646 -0.01982 0.06278 0.00775 -0.04165 0.06027 0.06140 0.04410 0.08039 -0.05497 0.05389 -0.03261 0.04632 0.01715 0.01199 0.07196 0.05134 0.01128 -0.01767 0.04097 -0.01011 -0.14312 S&P GSCI The MSCI EM Bond Index -0.02485 -0.10707 0.01736 0.00808 -0.02667 0.02113 0.01362 0.00395 0.00664 0.03062 0.04302 0.01220 -0.00844 0.05055 0.03720 -0.01784 0.00091 0.00796 0.02612 0.02100 -0.00270 0.02120 -0.02493 0.01073 0.00422 -0.00612 0.00897 0.01006 -0.03924 0.01410 0.02700 -0.01879 0.01481 0.10227 0.04248 0.01325 -0.00162 0.07014 0.00725 0.04009 -0.01753 -0.01829 0.06500 0.00598 -0.00743 0.05773 0.03643 -0.00539 -0.00790 -0.00691 -0.00135 0.03880 0.00411 0.01161 -0.04732 -0.07019 0.00253 0.03220 0.02417 -0.00089 0.03547 0.00731 0.01493 -0.00248 -0.02744 0.02023 0.08322 0.01557 0.01643 0.00964 0.00337 -0.00895 -0.01470 0.06741 0.00185 -0.06894 0.04217 0.00119 0.01687 -0.02878 -0.01000 0.02313 -0.00177 0.01432 0.00715 0.02591 0.00892 -0.05410 0.05144 0.01137 0.04097 0.01299 0.02937 0.02529 -0.12841 -0.01056 0.02529 0.02618 0.01544 0.02751 -0.16490 0.01753 -0.09859 -0.03718 0.00519 -0.06757 0.02178 0.01058 -0.01612 -0.07918 0.01545 -0.06598 0.10382 -0.00320 -0.00519 0.04005 0.00278 -0.02727 -0.01287 0.00448 -0.04718 -0.14012 0.01057 -0.03546 -0.10694 0.01172 -0.07861 0.02817 0.00178 -0.05902 -0.29285 0.02664 DXY Currency -0.00823 -0.02341 -0.04690 -0.00122 0.00941 -0.01199 -0.00012 0.04904 -0.01496 -0.00747 0.01913 -0.00586 0.03091 -0.01225 0.00243 0.01734 -0.00273 0.00046 -0.02186 0.00536 0.01830 -0.00580 0.00560 0.00227 0.05583 0.01988 -0.00179 0.02597 -0.02398 0.00865 0.04056 -0.00552 -0.01909 -0.01514 0.02227 0.01923 0.01074 -0.00884 0.01673 -0.01764 0.00772 0.00687 -0.00030 -0.00929 9/30/1998 10/30/1998 11/30/1998 12/31/1998 1/29/1999 2/26/1999 3/31/1999 4/30/1999 5/31/1999 6/30/1999 7/30/1999 8/31/1999 9/30/1999 10/29/1999 11/30/1999 12/31/1999 1/31/2000 2/29/2000 3/31/2000 4/28/2000 5/31/2000 6/30/2000 7/31/2000 8/31/2000 9/29/2000 10/31/2000 11/30/2000 12/29/2000 1/31/2001 2/28/2001 3/30/2001 4/30/2001 5/31/2001 6/29/2001 7/31/2001 8/31/2001 9/28/2001 10/31/2001 11/30/2001 12/31/2001 1/31/2002 2/28/2002 3/29/2002 4/30/2002 5/31/2002 0.06318 0.08011 0.06217 0.05967 0.04280 -0.03194 0.03898 0.03756 -0.02316 0.05443 -0.03022 -0.00499 -0.02808 0.06424 0.02082 0.06258 -0.04961 -0.01747 0.09849 -0.03159 -0.02241 0.02622 -0.01200 0.06370 -0.05194 -0.00422 -0.07832 0.00566 0.03225 -0.09111 -0.06350 0.07777 0.00703 -0.02442 -0.00933 -0.06344 -0.08043 0.01956 0.07879 0.00905 -0.01432 -0.01948 0.03757 -0.06102 -0.00780 0.10221 -0.04691 -0.12167 -0.01721 0.00437 -0.04606 0.16893 0.04133 -0.05457 0.06432 0.03587 0.07038 0.05304 -0.05157 0.04046 0.04224 0.07231 0.06248 -0.01161 -0.00911 0.11197 0.07127 -0.07680 0.15409 -0.01369 0.00225 0.09215 -0.02062 -0.05307 -0.01396 -0.03919 0.05370 -0.02848 -0.07234 0.00239 0.00956 -0.10956 -0.05043 -0.05371 -0.01326 -0.03120 0.04368 0.13482 0.01107 -0.04351 0.06059 0.10409 0.08220 -0.01826 -0.01692 0.00902 0.12878 0.12221 -0.00886 0.11141 -0.02868 0.00836 -0.03511 0.02041 0.08934 0.12588 0.00403 0.01292 0.00334 -0.09620 -0.04356 0.03201 -0.05261 0.00351 -0.08861 -0.07300 -0.08800 0.02277 0.13550 -0.07915 -0.10280 0.04653 0.00864 -0.02314 -0.06572 -0.01160 -0.15686 0.06150 0.10331 0.07802 0.03261 0.01532 0.05607 0.00401 -0.01859 0.02841 -0.00326 0.00055 0.00220 0.00550 -0.02656 0.00433 0.00308 -0.01095 -0.00205 -0.00145 -0.00028 0.00833 0.00148 -0.00168 -0.00629 -0.00319 0.01303 0.01406 -0.00311 0.00004 0.02023 0.00872 0.01540 0.00590 0.00714 0.01691 0.02004 0.01573 0.00875 0.00544 -0.00510 0.00562 0.00388 0.02247 0.01116 0.01336 0.02105 -0.01460 -0.00653 0.00814 0.01015 -0.01758 0.02101 0.00852 -0.04022 -0.02589 0.02690 -0.02110 0.02028 0.02737 0.01408 0.00899 0.01267 0.00557 -0.03014 0.00201 -0.01411 0.00528 0.02958 -0.00118 0.03200 0.00751 -0.00453 0.04458 -0.01271 -0.01747 0.02593 0.02728 0.00577 0.03002 -0.01209 -0.04929 0.00876 0.01348 0.04785 -0.01372 0.02859 0.00336 -0.01917 -0.03209 -0.00009 0.01279 0.01106 0.00534 0.02964 -0.00873 -0.00453 -0.02892 -0.02934 6/28/2002 7/31/2002 8/30/2002 9/30/2002 10/31/2002 11/29/2002 12/31/2002 1/31/2003 2/28/2003 3/31/2003 4/30/2003 5/30/2003 6/30/2003 7/31/2003 8/29/2003 9/30/2003 10/31/2003 11/28/2003 12/31/2003 1/30/2004 2/27/2004 3/31/2004 4/30/2004 5/31/2004 6/30/2004 7/30/2004 8/31/2004 9/30/2004 10/29/2004 11/30/2004 12/31/2004 1/31/2005 2/28/2005 3/31/2005 4/29/2005 5/31/2005 6/30/2005 7/29/2005 8/31/2005 9/30/2005 10/31/2005 11/30/2005 12/30/2005 1/31/2006 2/28/2006 -0.07135 -0.07398 0.00704 -0.10902 0.08860 0.05902 -0.05883 -0.02658 -0.01525 0.01031 0.08277 0.05325 0.01282 0.01793 0.01960 -0.01074 0.05556 0.00926 0.05184 0.01908 0.01440 -0.01501 -0.01558 0.01371 0.01949 -0.03293 0.00381 0.01082 0.01497 0.04056 0.03373 -0.02382 0.02115 -0.01724 -0.01893 0.03199 0.00172 0.03737 -0.00916 0.00800 -0.01555 0.03837 -0.00006 0.02643 0.00243 0.03417 0.00578 0.06048 0.04567 -0.04719 -0.00217 0.08531 0.08991 0.12123 -0.14411 -0.06137 0.09588 0.00219 0.00712 0.04086 -0.04084 0.02191 0.02559 0.06245 0.00392 0.07420 0.02010 0.02758 0.04627 -0.04700 0.07753 -0.03883 0.12614 0.04148 -0.04837 -0.09989 0.06762 0.06226 0.07559 -0.09051 -0.00733 0.05795 0.05495 0.15143 0.00018 -0.10325 -0.03848 0.02869 0.04334 -0.10104 -0.07661 -0.07859 0.01449 -0.10967 0.06407 0.06781 -0.03397 -0.00565 -0.03150 -0.03207 0.08411 0.06867 0.05465 0.05994 0.06494 0.00562 0.08336 0.01032 0.07125 0.03254 0.04493 0.00906 -0.08455 -0.02275 0.00218 -0.02096 0.03925 0.05549 0.02180 0.09210 0.04676 0.00020 0.08556 -0.06793 -0.03044 0.03038 0.03105 0.06616 0.00609 0.09087 -0.06640 0.08192 0.05762 0.10940 -0.00212 0.00793 0.01395 0.01767 0.01606 -0.00336 -0.00086 0.02108 0.00033 0.01398 -0.00124 0.00835 0.01751 -0.00170 -0.03470 0.00788 0.02681 -0.00967 0.00210 0.01056 0.00808 0.01094 0.00776 -0.02670 -0.00424 0.00644 0.01052 0.01970 0.00308 0.00900 -0.00845 0.01006 0.00670 -0.00614 -0.00527 0.01463 0.01131 0.00570 -0.00919 0.01312 -0.01030 -0.00865 0.00472 0.01015 -0.00019 0.00357 -0.05098 0.01225 -0.00400 -0.00103 -0.00215 -0.00244 -0.04258 -0.01905 -0.00200 -0.00832 -0.01709 -0.04013 0.01544 0.02280 0.01249 -0.05352 -0.00129 -0.02696 -0.03668 0.00322 0.00126 0.00344 0.03276 -0.01746 -0.00112 0.01306 -0.01134 -0.01765 -0.02816 -0.03639 -0.01186 0.03364 -0.01268 0.01879 0.00440 0.03944 0.01515 0.00292 -0.01981 0.02215 0.00614 0.01665 -0.00437 -0.02424 0.01293 3/31/2006 4/28/2006 5/31/2006 6/30/2006 7/31/2006 8/31/2006 9/29/2006 10/31/2006 11/30/2006 12/29/2006 1/31/2007 2/28/2007 3/30/2007 4/30/2007 5/31/2007 6/29/2007 7/31/2007 8/31/2007 9/28/2007 10/31/2007 11/30/2007 12/31/2007 1/31/2008 2/29/2008 3/31/2008 4/30/2008 5/30/2008 6/30/2008 7/31/2008 8/29/2008 9/30/2008 10/31/2008 11/28/2008 12/31/2008 1/30/2009 2/27/2009 3/31/2009 4/30/2009 5/29/2009 6/30/2009 7/31/2009 8/31/2009 9/30/2009 10/30/2009 11/30/2009 0.01291 0.01206 -0.02832 0.00156 0.00555 0.02417 0.02649 0.03251 0.01839 0.01376 0.01535 -0.01927 0.01090 0.04399 0.03446 -0.01662 -0.03119 0.01511 0.03749 0.01736 -0.04122 -0.00610 -0.06118 -0.03141 -0.00349 0.04863 0.01299 -0.08282 -0.00731 0.01496 -0.08547 -0.16698 -0.07351 0.01200 -0.08262 -0.10358 0.08763 0.09423 0.05464 0.00248 0.07448 0.03476 0.03656 -0.01826 0.06026 0.05130 0.06333 -0.00770 0.01162 0.02005 -0.07257 -0.10706 -0.02568 0.05528 -0.07118 -0.02290 0.04297 0.03234 -0.00275 -0.01553 0.03221 0.05546 -0.04187 0.10226 0.09607 -0.03697 0.05765 -0.00025 0.11258 -0.01174 0.07965 0.09104 0.09231 -0.12238 -0.07102 -0.12442 -0.28199 -0.14841 -0.13319 -0.08940 -0.06099 0.04505 -0.00919 0.19667 0.00569 0.00444 -0.02364 0.00172 0.05872 0.01524 0.00728 0.06827 -0.10763 -0.00461 0.01110 0.02286 0.00652 0.04662 0.07323 0.04413 -0.01224 -0.00659 0.03740 0.04402 0.04624 0.04426 0.05009 -0.02318 0.10848 0.11016 -0.07145 0.00284 -0.12594 0.07251 -0.05402 0.07872 0.01553 -0.10158 -0.04163 -0.08217 -0.17708 -0.27500 -0.07633 0.07604 -0.06615 -0.05709 0.14154 0.16275 0.16657 -0.01529 0.10866 -0.00540 0.08885 0.00023 0.04252 -0.01034 -0.00246 -0.00119 0.00242 0.01390 0.01601 0.00863 0.00691 0.01186 -0.00614 -0.00052 0.01582 -0.00013 0.00528 -0.00800 -0.00369 0.00919 0.01374 0.00734 0.00956 0.02086 0.00108 0.01967 0.00389 0.00321 -0.00412 -0.00897 0.00154 -0.00080 0.01087 -0.01108 -0.01963 0.04616 0.03424 -0.01000 -0.00259 0.01546 0.00038 0.00559 0.00633 0.01423 0.00961 0.01072 0.00453 0.01343 -0.00422 -0.04034 -0.01614 0.00519 0.00164 -0.00293 0.01152 -0.00825 -0.02778 0.00844 0.01136 -0.01217 -0.00766 -0.01788 0.01049 -0.00463 -0.01404 0.00026 -0.03802 -0.01595 -0.00434 0.00720 -0.01978 -0.01947 -0.02594 0.00985 0.00510 -0.00571 0.01054 0.05673 0.02671 0.07785 0.01032 -0.06021 0.05769 0.02336 -0.02929 -0.00955 -0.06224 0.00989 -0.02229 -0.00223 -0.01943 -0.00461 -0.01862 12/31/2009 0.01898 0.00865 0.03813 -0.01760 0.03981 Problem: Suppose you are an associate at a prestigious investment firm. One day, your boss gives you the following exercise to test your basic quantitive skill: find optimal portfolio based on sharpe ratio. Your investment opportunities are limited to five assets (1) A index; (2) S&P GSCI; (3)The MSCI EM ; (4) Bond Index; (5)DXY Currency. (See the Description sheet for details of these assets). He gives you the time series of 5 asset class monthly returns between 01/1995 and 12/2009. (a). Find the optimal allocation among these assets, and also report the resulting complete portfolio expected return, standard deviation and sharpe ratio. (b). Do (a) again, but this time you are not allowed to short assets. How the results (e.g. expected return and sharpe ratio) change? Hints: use Excel's solver function to generate \"optimal\" portfolio weights(make sure your excel solver add-ins is active.) u the following exercise ent opportunities are rrency. (See the monthly returns between (a). Find expected return, (b). Do (a) urn and sharpe ratio) Hints: use Excel's ns is active.) DATA: S&P GSCI The S&P GSCI is a composite index of commodity sector returns representing an unleve the spectrum of commodities. The returns are calculated on a fully collateralized basis representative and realistic picture of realizable returns attainable in the commodities The MSCI EM The MSCI Emerging Markets Index is a free float-adjusted market capitalization index. A indices: Argentina, Brazil, Chile, China, Colombia, Czech Republic, Egypt, Hungary, India Philippines, Poland, Russia, South Africa, Taiwan, Thailand, Turkey and Venezuela. The i worldwide. The MSCI Emerging Markets Index has a base date of December 31, 1987. A of USD 1,387,304 million. DXY Currency IntercontinentalExchange (ICE) is the world's centralized price discovery point for the U benchmark for traders, analysts and economists worldwide. I use return of US dollar in futures contract is an index that weighs dollar exchange rates with six component curre franc). Bond Index J.P. Morgan Aggregate U.S. Bond Index Risk Free Rate 0.3% average 1-month TBill return from Ibbotson and Associates, Inc. between 1995-2 or returns representing an unleveraged, long-only investment in commodity futures that is broadly diversified across ted on a fully collateralized basis with full reinvestment. The combination of these attributes provides investors with a ns attainable in the commodities markets. sted market capitalization index. As of August 2005, the index consisted of the following 26 emerging market country ch Republic, Egypt, Hungary, India, Indonesia, Israel, Jordan, Korea, Malaysia, Mexico, Morocco, Pakistan, Peru, land, Turkey and Venezuela. The index represents companies within these countries that are available to investors ase date of December 31, 1987. As of August 31, 2005 it contained 823 constituents with a total market capitalization ed price discovery point for the U.S. Dollar Index (USDX). The ICE USDX futures contract is a recognized currency dwide. I use return of US dollar index futures traded on ICE to track price fluctuation of US dollar. The underlying of this ge rates with six component currencies (euro, Japanese yen, British pound, Canadian dollar, Swedish krona and Swiss Associates, Inc. between 1995-2009 Variance-Covariance Matrix (5x5) ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? S&P500 S&P GSCI The MSCI EM Bond Index DXY Currency Optimal Weights ? ? ? ? Portfolio Std Dev (Annualized) Portfolio Expected Excess Return (Annualized) Portfolio Sharpe ? ? ? ? DXY Currency Variance-Covariance Matrix (5x5) ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? S&P500 S&P GSCI The MSCI EM Bond Index DXY Currency Optimal Weights ? ? ? ? Portfolio Std Dev (Annualized) Portfolio Expected Excess Return (Annualized) Portfolio Sharpe ? ? ? ? DXY Currency Variance-Covariance Matrix (5x5) ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? S&P500 S&P GSCI The MSCI EM Bond Index DXY Currency Optimal Weights ? ? ? ? Portfolio Std Dev (Annualized) Portfolio Expected Excess Return (Annualized) Portfolio Sharpe ? ? ? ? DXY Currency