Question #2: Markowitz Optimization:

Open the associated Excel file named QPS2 Data Fall I 2015 Problem 2 in My Course Content: Problem Set Spreadsheets. T

All students will do problem 2 using 9 of the above ETFs; all students will include the first 8 ETFs listed above: SPY, MDY, IWM, QQQ, EFA, VWO, VNQ, and BND. All students will include one of the last 3 ETFs: PFF, GLD, and JNK as instructed on your version.

Version A: Include PFF and exclude GLD and JNK.

Use the data on your 9 ETFs to answer the following questions:

1. What is the average return for each of the nine indexes?

2. Show the covariance matrix of returns. Briefly describe how you constructed the covariance matrix.

Consider the simple case where short sales are allowed, but short positions must be greater than or equal to ?50% and long positions must be less than or equal to 50%. Use Excel Solver to find the Minimum Variance Portfolio (MVP).

3. What is the expected portfolio return for the MVP portfolio?

4. What is the portfolio standard deviation for the MVP portfolio?

5. What is the portfolio composition (i.e., what are the weights for the nine ETFs)?

Consider the simple case where short sales are allowed, but short positions must be greater than or equal to ?30% and long positions must be less than or equal to 30%. Use Excel Solver to find the Maximum return portfolio with a standard deviation of exactly 4.50%.

6. What is the expected portfolio return for this portfolio?

7. What is the portfolio composition (i.e., what are the weights for the nine ETFs)?

Consider the more realistic case where short sales are NOT allowed and no more than 30% of the portfolio and no less than 4% is invested in any ETF. Use Excel Solver to find the Minimum Variance Portfolio (MVP).

8. What is the expected portfolio return for the MVP portfolio?

9. What is the portfolio standard deviation for the MVP portfolio?

10. What is the portfolio composition (i.e., what are the weights for the nine ETFs)?

Consider the simple case where short sales are NOT allowed and no more than 25% and no less than 3% of the portfolio is invested in any ETF. Use Excel Solver to find the Market Portfolio if the risk-free rate is 0.15%/month (1.80%/year).

11. What is the expected portfolio return for this portfolio?

12. What is the portfolio standard deviation for this portfolio?

13. What is the portfolio composition (i.e., what are the weights for the nine ETFs)?

14. What is the maximum Sharpe ratio?

FIN 5550 - Jack De Jong: Fall I 2015 Data for Problem 2 on QPS #2 Ticker 1 SPY 2 MDY 3 IWM 4 QQQ 5 EFA 6 VWO 7 VNQ 8 BND 9 PFF 10 GLD 11 JNK Name of Exchange Traded Fund SPDR S&P 500 ETF SPDR S&P MidCap 400 ETF iShares Russell 2000 ETF Power Shares QQQ ETF iShares MSCI EAFE ETF Vanguard FTSE Emerging Markets Stock Index ETF Vanguard REIT Index ETF Vanguard Total Bond Market ETF iShares US Preferred Stock ETF SPDR Gold Shares ETF SPDR Barclays High Yield Bond ETF Adjusted Closing Prices: Date SPY 8/2/2010 $ 94.61 9/1/2010 $ 103.09 10/1/2010 $ 107.02 11/1/2010 $ 107.02 12/1/2010 $ 114.18 1/3/2011 $ 116.84 2/1/2011 $ 120.90 3/1/2011 $ 120.91 4/1/2011 $ 124.41 5/2/2011 $ 123.02 6/1/2011 $ 120.94 7/1/2011 $ 118.52 8/1/2011 $ 112.01 9/1/2011 $ 104.23 10/3/2011 $ 115.61 11/1/2011 $ 115.14 12/1/2011 $ 116.34 1/3/2012 $ 121.74 2/1/2012 $ 127.02 3/1/2012 $ 131.11 4/2/2012 $ 130.23 5/1/2012 $ 122.41 6/1/2012 $ 127.38 7/2/2012 $ 128.89 8/1/2012 $ 132.11 9/4/2012 $ 135.46 10/1/2012 $ 133.00 11/1/2012 $ 133.75 12/3/2012 $ 134.95 1/2/2013 $ 141.85 2/1/2013 $ 143.66 3/1/2013 $ 149.12 4/1/2013 $ 151.98 5/1/2013 $ 155.57 6/3/2013 $ 153.50 7/1/2013 $ 161.43 8/1/2013 $ 156.59 9/3/2013 $ 161.54 10/1/2013 $ 169.02 11/1/2013 $ 174.03 12/2/2013 $ 178.54 1/2/2014 $ 172.25 2/3/2014 $ 180.09 3/3/2014 $ 181.58 4/1/2014 $ 182.85 5/1/2014 $ 187.09 6/2/2014 $ 190.95 7/1/2014 $ 188.39 8/1/2014 $ 195.82 9/2/2014 $ 193.12 10/1/2014 $ 197.67 11/3/2014 $ 203.10 12/1/2014 $ 202.58 1/2/2015 $ 196.58 2/2/2015 $ 207.63 3/2/2015 $ 204.37 4/1/2015 $ 206.38 5/1/2015 $ 209.03 6/1/2015 $ 204.82 MDY $ 123.49 $ 137.41 $ 142.07 $ 146.28 $ 155.86 $ 158.86 $ 166.07 $ 170.37 $ 174.85 $ 173.25 $ 168.85 $ 163.01 $ 151.33 $ 135.48 $ 153.84 $ 153.47 $ 152.55 $ 162.60 $ 169.93 $ 173.21 $ 172.72 $ 161.57 $ 164.69 $ 164.65 $ 170.49 $ 173.37 $ 171.76 $ 175.71 $ 179.73 $ 192.45 $ 194.05 $ 203.45 $ 204.66 $ 209.35 $ 204.54 $ 218.18 $ 209.75 $ 220.98 $ 228.98 $ 231.82 $ 239.14 $ 233.84 $ 245.21 $ 246.05 $ 242.39 $ 246.36 $ 256.63 $ 245.38 $ 257.80 $ 246.09 $ 254.78 $ 259.46 $ 261.62 $ 258.74 $ 271.76 $ 275.38 $ 271.32 $ 275.83 $ 272.30 IWM $ 55.82 $ 62.77 $ 65.37 $ 67.65 $ 73.08 $ 72.81 $ 76.85 $ 78.79 $ 80.86 $ 79.41 $ 77.50 $ 74.86 $ 68.21 $ 60.60 $ 69.75 $ 69.49 $ 69.85 $ 74.84 $ 76.76 $ 78.67 $ 77.40 $ 72.30 $ 75.96 $ 74.80 $ 77.45 $ 79.97 $ 78.24 $ 78.67 $ 81.51 $ 86.60 $ 87.47 $ 91.55 $ 91.23 $ 94.81 $ 94.04 $ 100.93 $ 97.74 $ 104.08 $ 106.60 $ 110.82 $ 113.06 $ 109.92 $ 115.18 $ 114.31 $ 110.03 $ 110.89 $ 116.74 $ 109.67 $ 114.97 $ 108.15 $ 115.28 $ 115.41 $ 118.75 $ 114.86 $ 121.69 $ 123.84 $ 120.67 $ 123.37 $ 124.31 QQQ $ 41.13 $ 46.54 $ 49.49 $ 49.41 $ 51.76 $ 53.22 $ 54.91 $ 54.66 $ 56.23 $ 55.54 $ 54.42 $ 55.33 $ 52.52 $ 50.16 $ 55.38 $ 53.89 $ 53.56 $ 58.07 $ 61.79 $ 64.91 $ 64.15 $ 59.64 $ 61.80 $ 62.41 $ 65.65 $ 66.23 $ 62.74 $ 63.56 $ 63.26 $ 64.95 $ 65.17 $ 67.14 $ 68.85 $ 71.31 $ 69.60 $ 74.00 $ 73.70 $ 77.27 $ 81.10 $ 83.98 $ 86.43 $ 84.77 $ 89.14 $ 86.70 $ 86.43 $ 90.30 $ 93.13 $ 94.23 $ 98.95 $ 98.20 $ 100.79 $ 105.37 $ 103.01 $ 100.87 $ 108.15 $ 105.36 $ 107.38 $ 109.80 $ 107.07 EFA $ 42.82 $ 47.09 $ 48.88 $ 46.52 $ 50.38 $ 51.44 $ 53.27 $ 51.99 $ 54.92 $ 53.71 $ 53.06 $ 51.80 $ 47.26 $ 42.15 $ 46.21 $ 45.21 $ 44.22 $ 46.55 $ 48.80 $ 49.01 $ 47.99 $ 42.64 $ 45.65 $ 45.68 $ 47.14 $ 48.42 $ 48.95 $ 50.31 $ 52.52 $ 54.48 $ 53.77 $ 54.48 $ 57.21 $ 55.48 $ 54.00 $ 56.87 $ 55.76 $ 60.12 $ 62.08 $ 62.42 $ 63.78 $ 60.46 $ 64.17 $ 63.88 $ 64.94 $ 65.98 $ 66.58 $ 64.85 $ 64.97 $ 62.44 $ 62.28 $ 62.32 $ 59.83 $ 60.20 $ 64.02 $ 63.10 $ 65.41 $ 65.53 $ 63.49 VWO $ 35.82 $ 39.91 $ 41.15 $ 39.98 $ 43.01 $ 41.53 $ 41.46 $ 43.72 $ 45.20 $ 43.87 $ 43.43 $ 43.16 $ 39.24 $ 32.01 $ 37.10 $ 36.46 $ 34.95 $ 38.71 $ 40.82 $ 39.76 $ 38.92 $ 34.77 $ 36.52 $ 36.59 $ 36.68 $ 38.63 $ 38.42 $ 38.91 $ 41.66 $ 41.69 $ 40.70 $ 40.19 $ 40.99 $ 38.91 $ 36.83 $ 37.09 $ 35.82 $ 38.42 $ 40.09 $ 39.71 $ 39.60 $ 36.26 $ 37.43 $ 39.17 $ 39.51 $ 40.74 $ 42.03 $ 42.61 $ 44.24 $ 41.07 $ 41.99 $ 41.53 $ 39.58 $ 39.50 $ 41.34 $ 40.49 $ 43.50 $ 41.95 $ 40.88 VNQ $ 41.64 $ 43.50 $ 45.57 $ 44.72 $ 46.76 $ 48.28 $ 50.55 $ 49.74 $ 52.59 $ 53.32 $ 51.56 $ 52.36 $ 49.42 $ 44.06 $ 50.36 $ 48.45 $ 50.80 $ 54.04 $ 53.42 $ 56.19 $ 57.80 $ 55.20 $ 58.24 $ 59.41 $ 59.40 $ 58.29 $ 57.76 $ 57.61 $ 59.75 $ 61.99 $ 62.74 $ 64.54 $ 68.89 $ 64.77 $ 63.49 $ 64.06 $ 59.59 $ 61.66 $ 64.45 $ 61.07 $ 61.13 $ 63.74 $ 66.97 $ 67.30 $ 69.52 $ 71.18 $ 71.99 $ 72.05 $ 74.24 $ 69.76 $ 76.69 $ 78.22 $ 79.71 $ 85.17 $ 82.05 $ 83.47 $ 78.59 $ 78.35 $ 74.69 BND $ 71.40 $ 71.40 $ 71.62 $ 71.14 $ 70.41 $ 70.47 $ 70.68 $ 70.57 $ 71.61 $ 72.45 $ 72.18 $ 73.35 $ 74.57 $ 75.07 $ 75.15 $ 75.11 $ 75.99 $ 76.48 $ 76.51 $ 76.12 $ 76.96 $ 77.67 $ 77.73 $ 78.68 $ 78.81 $ 78.95 $ 78.87 $ 78.92 $ 78.23 $ 77.69 $ 78.10 $ 78.17 $ 78.96 $ 77.44 $ 76.16 $ 76.45 $ 75.80 $ 76.64 $ 77.30 $ 77.07 $ 76.58 $ 77.77 $ 78.13 $ 78.00 $ 78.62 $ 79.45 $ 79.52 $ 79.30 $ 80.20 $ 79.75 $ 80.32 $ 80.99 $ 81.03 $ 82.98 $ 81.90 $ 82.34 $ 82.08 $ 81.67 $ 80.76 PFF $ 29.18 $ 29.28 $ 29.33 $ 29.15 $ 29.23 $ 29.44 $ 29.92 $ 30.21 $ 30.69 $ 30.87 $ 30.70 $ 30.12 $ 29.56 $ 28.02 $ 29.53 $ 28.60 $ 28.63 $ 30.66 $ 31.59 $ 31.65 $ 31.72 $ 31.35 $ 32.11 $ 32.59 $ 33.08 $ 33.32 $ 33.66 $ 33.54 $ 33.67 $ 34.12 $ 34.30 $ 34.69 $ 35.05 $ 34.82 $ 34.05 $ 33.87 $ 33.13 $ 33.35 $ 33.66 $ 33.77 $ 33.33 $ 34.32 $ 35.10 $ 35.72 $ 36.37 $ 36.83 $ 37.05 $ 36.87 $ 37.53 $ 37.22 $ 37.61 $ 38.08 $ 38.03 $ 38.53 $ 38.91 $ 39.03 $ 39.03 $ 39.03 $ 38.63 GLD $ 122.08 $ 127.91 $ 132.62 $ 135.42 $ 138.72 $ 129.87 $ 137.66 $ 139.86 $ 152.37 $ 149.64 $ 146.00 $ 158.29 $ 177.72 $ 158.06 $ 167.34 $ 170.13 $ 151.99 $ 169.31 $ 164.29 $ 162.12 $ 161.88 $ 151.62 $ 155.19 $ 156.49 $ 164.22 $ 171.89 $ 166.83 $ 166.05 $ 162.02 $ 161.20 $ 153.00 $ 154.45 $ 142.77 $ 133.92 $ 119.11 $ 127.96 $ 134.62 $ 128.18 $ 127.74 $ 120.70 $ 116.12 $ 120.09 $ 127.62 $ 123.61 $ 124.22 $ 120.43 $ 128.04 $ 123.39 $ 123.86 $ 116.21 $ 112.66 $ 112.11 $ 113.58 $ 123.45 $ 116.16 $ 113.66 $ 113.47 $ 114.10 $ 112.37 JNK $ 27.34 $ 28.31 $ 29.14 $ 28.58 $ 29.37 $ 29.94 $ 30.35 $ 30.33 $ 30.82 $ 31.00 $ 30.69 $ 30.90 $ 29.97 $ 28.14 $ 30.50 $ 29.83 $ 30.86 $ 31.68 $ 32.36 $ 31.96 $ 32.46 $ 31.33 $ 32.64 $ 33.18 $ 33.59 $ 33.84 $ 34.14 $ 34.32 $ 34.83 $ 34.92 $ 35.17 $ 35.54 $ 36.28 $ 35.44 $ 34.66 $ 35.54 $ 35.17 $ 35.50 $ 36.39 $ 36.68 $ 36.87 $ 37.08 $ 37.93 $ 37.92 $ 38.14 $ 38.48 $ 38.85 $ 37.93 $ 38.88 $ 37.93 $ 38.29 $ 37.72 $ 37.15 $ 37.47 $ 38.46 $ 38.09 $ 38.49 $ 38.66 $ 37.87 7/1/2015 $ 209.36 $ 272.55 $ 122.91 $ 111.95 $ 64.78 $ 38.31 $ 79.00 $ 81.47 $ 39.16 $ 104.93 $ 37.60 8/3/2015 $ 196.52 $ 257.11 $ 115.18 $ 104.31 $ 59.97 $ 34.54 $ 74.03 $ 81.27 $ 38.87 $ 108.82 $ 36.82 Monthly Returns in %: Date SPY MDY IWM QQQ EFA VWO VNQ BND PFF GLD JNK 9/1/2010 8.96% 11.27% 12.45% 13.17% 9.97% 11.42% 4.47% 0.00% 0.37% 4.78% 3.55% 10/1/2010 3.82% 3.39% 4.15% 6.34% 3.81% 3.10% 4.74% 0.32% 0.15% 3.68% 2.91% 11/1/2010 0.00% 2.96% 3.49% -0.17% -4.82% -2.84% -1.85% -0.68% -0.62% 2.11% -1.91% 12/1/2010 6.69% 6.55% 8.03% 4.76% 8.31% 7.57% 4.55% -1.02% 0.27% 2.44% 2.74% 1/3/2011 2.33% 1.92% -0.37% 2.83% 2.10% -3.45% 3.25% 0.09% 0.72% -6.38% 1.96% 2/1/2011 3.47% 4.54% 5.54% 3.16% 3.55% -0.17% 4.71% 0.29% 1.65% 6.00% 1.35% 3/1/2011 0.01% 2.59% 2.52% -0.45% -2.39% 5.47% -1.61% -0.15% 0.97% 1.60% -0.04% 4/1/2011 2.90% 2.63% 2.64% 2.87% 5.63% 3.37% 5.75% 1.46% 1.58% 8.94% 1.60% 5/2/2011 -1.12% -0.92% -1.79% -1.22% -2.21% -2.94% 1.37% 1.18% 0.59% -1.79% 0.58% 6/1/2011 -1.69% -2.54% -2.40% -2.03% -1.21% -1.00% -3.30% -0.38% -0.55% -2.43% -1.01% 7/1/2011 -2.00% -3.46% -3.41% 1.67% -2.38% -0.62% 1.56% 1.63% -1.89% 8.42% 0.71% 8/1/2011 -5.50% -7.16% -8.89% -5.07% -8.75% -9.09% -5.62% 1.66% -1.87% 12.27% -3.03% 9/1/2011 -6.94% -10.48% -11.15% -4.49% -10.81% -18.44% -10.84% 0.66% -5.20% -11.06% -6.09% 10/3/2011 10.91% 13.56% 15.10% 10.40% 9.63% 15.91% 14.29% 0.11% 5.37% 5.87% 8.38% 11/1/2011 -0.41% -0.24% -0.38% -2.69% -2.18% -1.71% -3.80% -0.06% -3.14% 1.67% -2.19% 12/1/2011 1.04% -0.60% 0.52% -0.61% -2.17% -4.16% 4.85% 1.18% 0.12% -10.66% 3.45% 1/3/2012 4.64% 6.59% 7.15% 8.42% 5.27% 10.78% 6.38% 0.63% 7.07% 11.40% 2.65% 2/1/2012 4.34% 4.51% 2.57% 6.41% 4.83% 5.43% -1.15% 0.04% 3.04% -2.96% 2.13% 3/1/2012 3.22% 1.93% 2.48% 5.05% 0.42% -2.60% 5.20% -0.51% 0.18% -1.32% -1.21% 4/2/2012 -0.67% -0.28% -1.62% -1.17% -2.08% -2.09% 2.86% 1.10% 0.22% -0.15% 1.54% 5/1/2012 -6.01% -6.45% -6.58% -7.04% -11.14% -10.67% -4.51% 0.93% -1.17% -6.34% -3.48% 6/1/2012 4.06% 1.93% 5.05% 3.62% 7.04% 5.02% 5.52% 0.07% 2.42% 2.35% 4.19% 7/2/2012 1.18% -0.02% -1.52% 1.00% 0.08% 0.20% 2.00% 1.23% 1.51% 0.84% 1.67% 8/1/2012 2.51% 3.54% 3.54% 5.19% 3.20% 0.25% -0.01% 0.16% 1.48% 4.94% 1.24% 9/4/2012 2.54% 1.69% 3.26% 0.89% 2.71% 5.31% -1.86% 0.18% 0.73% 4.67% 0.73% 10/1/2012 -1.82% -0.93% -2.17% -5.28% 1.09% -0.55% -0.91% -0.10% 1.02% -2.94% 0.88% 11/1/2012 0.57% 2.30% 0.55% 1.31% 2.78% 1.28% -0.26% 0.06% -0.35% -0.47% 0.55% 12/3/2012 0.89% 2.29% 3.62% -0.47% 4.38% 7.07% 3.72% -0.88% 0.39% -2.43% 1.46% 1/2/2013 5.12% 7.08% 6.24% 2.67% 3.73% 0.07% 3.74% -0.69% 1.34% -0.51% 0.27% 2/1/2013 1.28% 0.83% 1.00% 0.34% -1.29% -2.36% 1.22% 0.54% 0.53% -5.09% 0.72% 3/1/2013 3.80% 4.84% 4.66% 3.02% 1.31% -1.27% 2.87% 0.08% 1.12% 0.95% 1.04% 4/1/2013 1.92% 0.60% -0.35% 2.54% 5.02% 2.00% 6.73% 1.02% 1.05% -7.56% 2.07% 5/1/2013 2.36% 2.29% 3.93% 3.58% -3.02% -5.07% -5.98% -1.93% -0.66% -6.20% -2.31% 6/3/2013 -1.33% -2.30% -0.82% -2.40% -2.68% -5.35% -1.98% -1.65% -2.21% -11.06% -2.20% 7/1/2013 5.17% 6.67% 7.33% 6.31% 5.32% 0.70% 0.90% 0.38% -0.54% 7.43% 2.53% 8/1/2013 -3.00% -3.86% -3.16% -0.40% -1.96% -3.43% -6.98% -0.86% -2.19% 5.20% -1.03% 9/3/2013 3.16% 5.35% 6.49% 4.83% 7.82% 7.28% 3.48% 1.11% 0.68% -4.78% 0.95% 10/1/2013 4.63% 3.62% 2.42% 4.96% 3.26% 4.34% 4.52% 0.86% 0.92% -0.34% 2.50% 11/1/2013 2.96% 1.24% 3.96% 3.55% 0.55% -0.93% -5.25% -0.29% 0.32% -5.51% 0.78% 12/2/2013 2.59% 3.16% 2.02% 2.93% 2.18% -0.28% 0.10% -0.64% -1.29% -3.79% 0.51% 1/2/2014 -3.52% -2.22% -2.77% -1.92% -5.20% -8.43% 4.28% 1.55% 2.96% 3.42% 0.57% 2/3/2014 4.55% 4.86% 4.78% 5.15% 6.13% 3.24% 5.07% 0.47% 2.28% 6.27% 2.31% 3/3/2014 0.83% 0.34% -0.75% -2.73% -0.46% 4.63% 0.50% -0.17% 1.75% -3.14% -0.02% 4/1/2014 0.70% -1.49% -3.75% -0.32% 1.67% 0.89% 3.29% 0.80% 1.84% 0.49% 0.55% 5/1/2014 2.32% 1.64% 0.79% 4.49% 1.60% 3.10% 2.40% 1.05% 1.25% -3.05% 0.92% 6/2/2014 2.06% 4.17% 5.27% 3.12% 0.92% 3.17% 1.13% 0.08% 0.61% 6.32% 0.95% 7/1/2014 -1.34% -4.39% -6.05% 1.18% -2.60% 1.37% 0.08% -0.28% -0.50% -3.63% -2.38% 8/1/2014 3.95% 5.06% 4.83% 5.01% 0.18% 3.84% 3.04% 1.14% 1.79% 0.38% 2.51% 9/2/2014 -1.38% -4.54% -5.93% -0.76% -3.88% -7.17% -6.04% -0.57% -0.83% -6.18% -2.44% 10/1/2014 2.36% 3.53% 6.59% 2.64% -0.27% 2.23% 9.94% 0.72% 1.07% -3.05% 0.93% 11/3/2014 2.75% 1.84% 0.11% 4.55% 0.06% -1.10% 2.00% 0.83% 1.24% -0.49% -1.47% 12/1/2014 -0.25% 0.83% 2.89% -2.24% -3.99% -4.68% 1.90% 0.06% -0.12% 1.31% -1.52% 1/2/2015 -2.96% -1.10% -3.28% -2.08% 0.62% -0.20% 6.85% 2.40% 1.32% 8.69% 0.85% 2/2/2015 5.62% 5.03% 5.95% 7.22% 6.34% 4.66% -3.67% -1.31% 0.98% -5.91% 2.64% 3/2/2015 -1.57% 1.33% 1.77% -2.58% -1.43% -2.06% 1.73% 0.55% 0.30% -2.15% -0.94% 4/1/2015 0.98% -1.48% -2.56% 1.92% 3.65% 7.41% -5.85% -0.32% 0.02% -0.17% 1.05% 5/1/2015 1.29% 1.66% 2.24% 2.25% 0.20% -3.55% -0.30% -0.50% -0.02% 0.56% 0.43% 6/1/2015 -2.01% -1.28% 0.77% -2.48% -3.12% -2.55% -4.67% -1.11% -1.01% -1.52% -2.05% 7/1/2015 2.21% 0.09% -1.13% 4.56% 2.03% -6.29% 5.77% 0.88% 1.36% -6.62% -0.71% 8/3/2015 -6.13% -5.66% -6.29% -6.82% -7.43% -9.84% -6.29% -0.25% -0.75% 3.71% -2.06%