Please follow these 4 file to finish a project. Read those file carefully and meet all requirements

Assignment 1 International Portfolio Allocation You should write a polished and persuasive letter to your client and show your work with detailed technical Appendix. Late assignments will not be accepted. Suppose you are a _nancial advisor working for a client with 90% of his wealth invested in the S&P 500 and 10% of his wealth invested in Microsoft stock. Prepare a brief letter to your client advising why a portfolio reallocation into international stocks might be favorable. The _rst step is to obtain data on the returns of relevant assets. A common way is to prepare the daily holding period return (HPR) of the following exchange traded funds (ETFs) and Microsoft stock: 1. MSFT - Microsoft stock 2. SPY - The SPDR ETF which tracks the S&P 500 index. 3. MDY - An ETF that tracks the midcap S&P index. 4. EWA - An ETF that tracks the MSCI Australia index. 5. EWC - An ETF that tracks the MSCI Canada index. 6. EWQ - An ETF that tracks the MSCI France index. 7. EWG - An ETF that tracks the MSCI Germany index. 8. EWJ - An ETF that tracks the MSCI Japan index. 9. EWU - An ETF that tracks the MSCI United Kingdom index. 10. EWS - An ETF that tracks the MSCI Singapore index. 11. EWW - An ETF that tracks the MSCI Mexico index. 12. EWH - An ETF that tracks the MSCI Hong Kong index. 13. EWM - An ETF that tracks the MSCI Malaysia index. For Microsoft Stock (MSFT), you can _nd the historical return from Yahoo Finance. For the ETFs, let us take SPY as an example. ETFs are traded on NYSE, so we go to the NYSE website, https://www.nyse.com/quote/ARCX:SPY To simplify this assignment, I have prepared you the daily return series in several Excel _les uploaded on blackboard. To write the letter, include the following analysis into your technical appendix: 1. Calculate the mean and standard deviation of each daily return series. 2. Calculate the correlation between each of the return series. Hints: You can create a 13 by 13 matrix and calculate the correlation coe_cient by Excel. Or if you have learned Matlab or other softwares, it's also _ne to use those. 3. Calculate and plot the minimum standard deviation portfolios both with and without short-selling allowed using the following securities (plot as many points as you feel appropriate): Hints: For this question, you need to build mean-variance frontiers by changing the number of risky stocks in the portfolio. You need to build the plots of the frontiers just as what we plotted on the board. Basically for each of the following case, you are solving a variance minimization problem, with the sum of weights constrained by 1. We will demonstrate this optimization problem in class. (a) Large U.S. Stocks - S&P 500 and Microsoft. (b) Large U.S. Stocks and Midcaps - S&P 500, Microsoft, and S&P Midcaps. (c) North American Stocks - MS&P 500, Microsoft, S&P Midcaps, Canada, and Mexico. (d) North American Stocks and European Stocks - MS&P 500, Microsoft, S&P Midcaps, Canada, Mexico, France, Germany, and the U.K. (e) All 12 ETFs and Microsoft stock. The purpose of this tutorial note is to describe how Excel's Solver tool can be used to solve some simple problems in the area of portfolio management. We will use an example involving four stocks: A, B, C, and D. The expected returns and standard deviation of returns for these stocks are as follows: Expected return Standard deviation Stock A .07 .13 Stock B .05 .11 Stock C .15 .19 Stock D .20 .25 In addition, correlations between the four stocks are as follows: Stock A Stock B Stock C Stock D Stock A 1.00 0.60 0.40 -0.20 Stock B 0.60 1.00 0.30 -0.50 Stock C 0.40 0.30 1.00 -0.05 Stock D -0.20 -0.50 -0.05 1.00 The first step is to ensure that the Solver tool is available. Click on Tools and look for it. If it is not there, click on Add-ins and tick the appropriate checkbox. The next step is to enter the necessary statistical information in the spreadsheet. The expected returns for the four stocks are entered in cells B3-E3 and the standard deviations are one line below in cells B4-E4. The correlations are entered in cells B8-E11. Based on the standard deviations and the correlations, the covariances are calculated in cells B15-E18. Overall Minimum Variance Portfolio The first portfolio management problem we will attempt is to find the overall minimum variance portfolio. Recall that in a portfolio with N risky assets, portfolio variance is given by N N P2 = Xi X j i j . i=1 j=1 As Solver relies on numerical algorithms, we must provide an initial guess. We will use an equally-weighted portfolio with 0.25 invested in each of the four stocks. These weights are entered in cells B25-E25. A table of weighted covariances is provided below these weights in cells B27-E30. The entries of this table correspond to Xi X j i j in the portfolio variance formula. Next to the portfolio weights is cell F25, which simply contains the sum of the weights (we need this to ensure that Solver finds weights which do add up to 1). Beside this, in cell G25, is the portfolio variance (given the weights). This is just the sum of all of the elements in the weighted covariance table (i.e. cells B27-E30). The standard deviation given in cell H25 is just the square root of the variance in G25. The expected return (given the weights) is calculated in cell I25 using the formula N E(RP ) = Xi E(Ri ). i=1 Now we want to use Solver to find the minimum variance portfolio. The necessary steps are: 1. Click Tools Solver; 2. Set Target Cell to portfolio variance (cell G25), and specify that a minimum is required (check Equal to Min); 3. By Changing Cells (portfolio weights) cells B25-E25; 4. Subject to the Constraints (portfolio weights add up to one). Add a constraint that the sum of the portfolio weights in cell F25 equals 1; 5. Click Solve and the OK when Solver reports that it has found a solution. Risk/Return Tradeoff The next problem is to solve for the minimum variance portfolio given a target portfolio return (we will use target values of .05, .10, .15, .20). The problem is set up as above for the overall minimum variance portfolio except that now we have to add the target returns. In particular, cells B38-E38 contain the portfolio weights, cells B40-E43 contain the weighted covariance table, cell F38 has the sum of the portfolio weights, cells G38 and H38 contain the portfolio variance and standard deviation respectively, cell I38 has the target portfolio return, and cell J38 has the portfolio expected return. Assuming that short sales are allowed, the following steps should be followed: 1. Click Tools Solver; 2. Set Target Cell to portfolio variance (cell G38), and specify that a minimum is required (check Equal to Min); 3. By Changing Cells (portfolio weights) cells B38-E38; 4. Subject to the Constraints (portfolio weights add up to one). Add a constraint that the sum of the portfolio weights in cell F38 equals 1 and a second constraint that the portfolio expected return in cell J38 equals the target return in cell I38; 5. Click Solve and the OK when Solver reports that it has found a solution. 6. To store this solution, copy the range of cells B38-J38 to some place lower down (e.g. cells B48-J48). It is critical to use the Paste Special Values feature of Excel when doing this. In particular, highlight cells B38-J38, click Edit Copy. Then go to cell B48 and click Edit Paste Special and then check Values. 7. Repeat for another value of target return by changing the entry in cell I38. You should just have to do Tools Solver Solve (i.e. you should not need to change any constraints or specify the weights again). Copy and paste special this solution below (in cell B49) and continue as needed. A related problem where short positions are not allowed can also be easily solved. Just add another constraint that the portfolio weights must be at least zero (i.e. in step 4 above, add a constraint that cells B48-E48 must be 0), and proceed as above. A 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 Expected return Standard deviation B C D E F G H I J Stock A Stock B Stock C Stock D 0.07 0.05 0.15 0.20 0.13 0.11 0.19 0.25 Correlations Stock A Stock B Stock C Stock D Stock A Stock B Stock C Stock D 1.00 0.60 0.40 -0.20 0.60 1.00 0.30 -0.50 0.40 0.30 1.00 -0.05 -0.20 -0.50 -0.05 1.00 Covariances Stock A Stock B Stock C Stock D Stock A Stock B Stock C Stock D 0.0169 0.0086 0.0099 -0.0065 0.0086 0.0121 0.0063 -0.0138 0.0099 0.0063 0.0361 -0.0024 -0.0065 -0.0138 -0.0024 0.0625 Overall Minimum Variance Portfolio Portfolio weights Weighted Covariance table Sum of Portfolio Standard Expected Stock A Stock B Stock C Stock D weights variance Deviation Return 0.0563 0.6666 0.0359 0.2412 1 0.005458 0.0739 0.0909 0.000054 0.000322 0.000020 -0.000088 0.000322 0.005377 0.000150 -0.002211 0.000020 0.000150 0.000046 -0.000021 -0.000088 -0.002211 -0.000021 0.003636 Risk/Return Tradeoff Portfolio weights 0.0000 0.0000 0.0000 1.0000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.062500 Sum of weights Portfolio Standard Target Expected variance Deviation Return Return 1 0.062500 0.2500 0.20 0.20 Sum of weights 1 1 1 1 Portfolio Standard Target Expected variance Deviation Return Return 0.009667 0.0983 0.05 0.05 0.005667 0.0753 0.10 0.10 0.014253 0.1194 0.15 0.15 0.035427 0.1882 0.20 0.20 1 1 1 1 Portfolio Standard Target Expected variance Deviation Return Return 0.012100 0.1100 0.05 0.05 0.005667 0.0753 0.10 0.10 0.014294 0.1196 0.15 0.15 0.062500 0.2500 0.20 0.20 Short sales allowed Portfolio weights 0.1394 0.0378 -0.0638 -0.1655 0.9500 0.6035 0.2571 -0.0894 -0.2124 0.0912 0.3948 0.6983 0.1230 0.2675 0.4120 0.5565 No short sales allowed Sum of weights Portfolio weights 0.0000 0.0378 0.0000 0.0000 1.0000 0.6035 0.2042 0.0000 0.0000 0.0912 0.3874 0.0000 0.0000 0.2675 0.4084 1.0000 ETF Ticker Date S&P 500 SPY MidCap Microsoft Australia Canada France Germany Japan S&P Stock MDY MSFT EWA EWC EWQ EWG EWJ 20100104 0.01696 0.016775 0.01542 0.038529 20100105 0.002647 0.002538 0.000323 0.002951 20100106 0.000704 0.005436 -0.006137 0.003783 20100107 0.004221 0.00474 -0.010335 -0.004606 20100108 0.003328 0.006266 0.00683 0.01178 20100111 0.001397 -0.001978 -0.01272 0.009979 20100112 -0.009326 -0.011377 -0.006607 -0.032935 20100113 0.008446 0.01277 0.009312 0.015326 20100114 0.002705 0.001906 0.020099 0.012579 20100115 -0.011224 -0.01339 -0.00323 -0.021118 20100119 0.012496 0.012756 0.007777 0.014805 20100120 -0.010169 -0.007835 -0.01656 -0.029596 20100121 -0.019229 -0.01299 -0.0188 -0.033505 20100122 -0.022292 -0.021012 -0.034988 -0.020444 20100125 0.005128 0.003055 0.012431 0.015336 20100126 -0.004191 -0.003807 0.006139 -0.017785 20100127 0.004757 0.001452 0.005763 -0.00455 20100128 -0.011472 -0.012518 -0.017189 -0.009141 20100129 -0.010869 -0.014455 -0.033608 -0.026753 20100201 0.015551 0.014902 0.008162 0.024171 20100202 0.012103 0.014065 0.00176 0.006941 20100203 -0.004983 -0.004649 0.005973 -0.012408 20100204 -0.030866 -0.032769 -0.027593 -0.047464 20100205 0.002067 0.002771 0.006466 0.005862 20100208 -0.007219 -0.007262 -0.010707 -0.006314 20100209 0.01256 0.012643 0.010462 0.029326 20100210 -0.001959 -0.000236 -0.000714 -0.006173 20100211 0.010466 0.013823 0.004645 0.034878 20100212 -0.000832 0.006275 -0.006757 -0.017544 20100216 0.015735 0.017014 0.019692 0.040413 20100217 0.004739 0.007116 0.008466 0.01084 20100218 0.005895 0.007366 0.013256 0.007596 20100219 0.002074 0.001791 -0.006869 -0.007539 20100222 0.00018 0.001415 -0.00139 0.013405 20100223 -0.012145 -0.013537 -0.013923 -0.020282 20100224 0.009198 0.009048 0.010589 0.005401 20100225 -0.001354 0.002316 -0.001048 -0.023277 20100226 0.000633 -0.001416 0.002448 0.014665 20100301 0.010385 0.01844 0.012208 0.028455 20100302 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