Please just focus on question 3d and question 4 and its individual parts

Variance Microsoft Corporation returns Month Opening Price Monthly Return 01-Oct-17 83.18 01-Nov-17 84.17 1.19% 01-Dec-17 85.54 1.63% 01-Jan-18 11.07% 01-Feb-18 93.77 -1.31% 01-Mar-18 91.27 -2.67% 01-Apr-18 93.52 2.47% 01-May-18 98.84 5.69% 01-Jun-18 98.61 -0.23% 01-Jul-18 106.08 7.58% 01-Aug-18 112.33 5.89% 01-Sep-18 114.37 1.82% -1.82% -1.38% 8.06% -4.32% -5.68% -0.55% 2.68% -3.24% 4.56% 2.88% -1.19% Month Opening Price 01-Oct-17 01-Nov-17 01-Dec-17 01-Jan-18 01-Feb-18 01-Mar-18 01-Apr-18 01-May-18 01-Jun-18 01-Jul-18 01-Aug-18 01-Sep-18 Monthly Returns Variance 12.27 12.52 2.04% 4.45% 12.49 -0.24% 2.17% 10.97 -12.17% -9.76% 10.61 -3.28% -0.87% 11.08 4.43% 6.84% 11.24 1.44% 3.85% 11.55 2.76% 5.17% 11.07 -4.16% -1.75% 10.04 -9.30% -6.90% 9.48 -5.58% -3.17% 9.25 -2.43% -0.02% Low Date 2017-10-02 2017-10-03 2017-10-04 2017-10-05 2017-10-06 2017-10-09 2017-10-10 2017-10-11 2017-10-12 2017-10-13 2017-10-16 2017-10-17 2017-10-18 2017-10-19 2017-10-20 2017-10-23 2017-10-24 2017-10-25 2017-10-26 2017-10-27 2017-10-30 2017-10-31 2017-11-01 2017-11-02 2017-11-03 2017-11-06 2017-11-07 2017-11-08 2017-11-09 2017-11-10 2017-11-13 2017-11-14 2017-11-15 2017-11-16 2017-11-17 2017-11-20 Sp500 Prices Open High Close Adj Close Volume 2521.2 2529.23 2520.4 2529.12 2529.12 3.2 E+09 2530.34 2535.13 2528.85 2534.58 2534.58 3.07 E+09 2533.48 2540.53 2531.8 2537.74 2537.74 3.02 E+09 2540.86 2552.51 2540.02 2552.07 2552.07 3.05E+09 2547.44 2549.41 2543.79 2549.33 2549.33 2.88E+09 2551.39 2551.82 2541. 6 2544.73 2544.73 2.48E+09 2549.99 2555.23 2544.86 2550.64 2550.64 2.96E+09 2550.62 2555.24 2547.95 2555.24 2555.24 2.98 E+09 2552.88 2555.33 2548.31 2550.93 2550.93 3.15 E+09 2555.66 2557.65 2552.09 2553.17 2553.17 3.15 E+09 2555.57 2559.47 2557.64 2557.64 2.92 E+09 2557.17 2559.71 2554.69 2559.36 2559.36 2.89E+09 2562.87 2564.11 2559.67 2561.26 2561.26 3E+09 2553.39 2562.36 2547.92 2562.1 2562.1 2.99E+09 2567.56 2575.44 2567.56 2575.21 2575.21 3.38E+09 2578.08 2578.29 2564.33 2564.98 2564.98 3.21E+09 2568.66 2572.18 2565.58 2569.13 2569.13 3.43 E+09 2566.52 2567.4 2544 2557.15 2557.15 3.87E+09 2560.08 2567.07 2559.8 2560.4 2560.4 3.87E+09 2570.26 2582.98 2565.94 2581.07 2581.07 3.89E+09 2577.75 2580.03 2568.25 2572.832572.83 3.66E+09 2575.99 2578.29 2572.15 2575.26 2575.26 3.83E+09 2583.21 2588.4 2574.92 2579.36 2579.36 3.81E+09 2579.46 2581.11 2566.17 2579.85 2579.85 4.05E+09 2581.93 2588.42 2587.84 2587.84 3.57E+09 2587.47 2593.38 2585.66 2591.13 2591.13 3.54E+09 2592.11 2597.02 2584.35 2590.64 2590.64 3.81E+09 2588.71 2595.47 2585.02 2594.38 2594.38 3.9E+09 2584 2586.5 2566.33 2584.62 2584.62 3.83E+09 2580.18 2583.81 2575.57 2582.3 2582.3 3.49E+09 2576.53 2587.66 2574.48 2584.84 2584.84 3.4E+09 2577.752579.66 2566.56 2578.87 2578.87 3.64E+09 2569.45 2572.84 2557.45 2564.62 2564.62 3.56E+09 2572.95 2590.09 2572.95 2585.64 2585.64 3.31E+09 2582.94 2583.96 2577.62 2578.85 2578.85 3.3E+09 2579.49 2584.64 2578.24 2582.14 2582.14 3E+09 | 2018-01-18 | 2018-01-19 2018-01-22 2018-01-23 | 2018-01-24 | 2018-01-25 2018-01-26 | 2018-01-29 | 2018-01-30 | 2018-01-31 | 2018-02-01 | 2018-02-02 | 2018-02-05 | 2018-02-06 | 2018-02-07 | 2018-02-08 | 2018-02-09 | 2018-02-12 | 2018-02-13 | 2018-02-14 | 2018-02-15 | 2018-02-16 | 2018-02-20 | 2018-02-21 | 2018-02-22 | 2018-02-23 | 2018-02-26 | 2018-02-27 | 2018-02-28 | 2018-03-01 | 2018-03-02 2018-03-05 | 2018-03-06 | 2018-03-07 | 2018-03-08 | 2018-03-09 | 2018-03-12 2802.4 2805.83 2802.6 2810.33 2809.16 2833.03 2835.05 2842.24 2845.42 2852.97 2846.24 2848.56 2847.48 2872.87 2867.23 2870.62 2832.74 2837.75 2832.41 2839.26 2816.45 2835.96 2808.92 2808.92 2741.06 2763.39 2614.78 2701.04 2690.95 2727.67 2685.01] 2685.27 2601.78 2638.67 2636.75 2672.61 2646.27 2668.84 2651.21 2702. 1 2713.46 2731.51 2727.142754.42 2722.99 2737.6 2720.53 2747.75 2710.42 2731.26 2715.8 2747.76 2757.37 2780.64 2780.452789.15 2753.78 2761.52 2715.22 2730.89 2658.89 2696.25 2681.06 2728.09 2730.18 2732.08 2710.18 2730.6 2732.75 2740.45 2752.91 2786.57 2790.54 | 2796.98 2792.56 2798.03 2798.03 3.68E+09 2798.08 2810.3 2810.3 3.64E+09 12808.12 2832.97 2832.97 3.47E409 2830.59 2839.13 2839.13 3.52E+09 2824.81 2837.54 2837.54 4.01E+09 2830.94 2839.25 2839.25 3.84E+09 2846.18 2872.87 2872.87 3.44E+09 2851.48 2853.53 2853.53 3.57E+09 2818.27 2822.43 2822.43 3.99E+09 2813.04 2823.81 2823.81 4.26E+09 2812.7 2821.98 2821.98 3.94E+09 2759.97 2762.13 2762.13 4.3E+09 2638.17 2648.94 2648.94 5.28E+09 2593.07 2695.142695.145.89E+09 2681.33 2681.66 2681.66 4.63E09. 2580.56 2 581 2 581531E+09 2532.69 2619.55 2619.55 5.68E+09 2622.45 2656 2 656 4.06E+09 2637.08 2662.94 2662.94 3.47E+09 2648.87 2698.63 2698.63 4 E+09 2689.82 2731. 2 2731.2 3.68E+09 2725.11| 2732.222732.22 3.64E+09 2706.76 2716.26 2716.26 3.63E+09 2701.29 2701.332701.33 3.78E+09 2697.77 2703.96 2703.96 3.7E+09 2713.742747. 3 27473 3.19F+09 2753.78 2779.6 2779.6 3.42E+09 2744.22 2744.28 2744.28 3.75E+09 2713.54 2713.83 2713.83 4.23E+09 2659.65 2677.67 2677.67 4.5E+09 2647.32 2691.25 2691.25 3.88E+09 2675.75 2720.94 2720.94 3.71E+09 2711.26 2728.12 2728.12 3.37E+09 2701.74 2726.8 2726.8 3.39E+09 2722.65 2738.97 2738.97 3.21E+09 2751.54 2786.57 2786.57 3.36E+09 2779.26 2783.02 2783.02 3.19E+09 | 2018-03-13 | 2018-03-14 | 2018-03-15 2018-03-16 2018-03-19 2018-03-20 | 2018-03-21 2018-03-22 2018-03-23 2018-03-26 | 2018-03-27 2018-03-28 2018-03-29 2018-04-02 | 2018-04-03 2018-04-04 2018-04-05 2018-04-06 2018-04-09 2018-04-10 | 2018-04-11 2018-04-12 2018-04-13 2018-04-16 | 2018-04-17 2018-04-18 | 2018-04-19 2018-04-20 | 2018-04-23 2018-04-24 2018-04-25 2018-04-26 | 2018-04-27 | 2018-04-30 2018-05-01 | 2018-05-02 2018-05-03 2018-05-04 2792.31 2801.9 2774.06 2777.11 2754.27 2763.03 2750.57 2761.85 2741.38 2741.38 2715.05 2724.22 2714.99 2739.14 2691.36 2695.68 2646.71 2657.67 2619.35 2661.36 2667.57 2674.78 2611.3 2632.65 2614.41 2659.07 2633.45 2638.3 2592.17 2619.14 2584.04 2649.86 2657.36 2672.08 2645.82 2656.88 2617.18 2653.55 2638.41 2665.45 2643.89 2661.43 2653.83 2674.72 2676.9 2680.26 2670.1 2686.49 2692.74 2713.34 2710.11 2717.49 2701.16 2702.84 2692.56 2693.94 2675.4 2682.86 2680.8 2683.55 2634.92 2645.3 2651.65 2676.48 2675.47 2677.35 2682.51 2682.87 2642.96 2655.27 2654.24 2660.87 2628.08 2637.14 2621.452670.93 2758.68 2744.38 2741.47 2749.97 2694.59 2710.05 2709.79 2641.59 2585.89 2601.81 2596.12 2593.06 2609.72 2553.8 2575.49 2573.61 2649.58 2586.27 2610.79 2635.78 2639.25 2653.83 2645.05 2665.16 2692.05 2703.63 2681.9 2660.61 2657.99 2617.32 2612.67 2647.16 2659.01 2648.04 2625.41 2631.7 2594.62 2615.32 2765.31 2749.48 2747.33 2752.01 2712.92 2716.94 2711.93 2643.69 2588.26 2658.55 2612.62 2605 2640.87 2581.88 2614.45 2644.69 2662.84 2604.47 2613.16 2656.87 2642.19 2663.99 2656.3 2677.84 2706.39 2708.64 2693.13 2670.14 2670.29 2634.56 2639.4 2666.94 2669.91 2648.05 2654.8 2635.67 2629.73 2663.42 2765.31 2749.48 2747.33 2752.01 2712.92 2716.94 2711.93 2643.69 2588.26 2658.55 2612.62 2605 2640.87 2581.88 2614.45 2644.69 2662.84 2604.47 2613.16 2656.87 2642.19 2663.99 2656.3 2677.84 2706.39 2708.64 2693.13 2670.14 2670.29 2634.56 2639.4 2666.94 2669.91 2648.05 2654.8 2635.67 2629.73 2663.42 3.3E+09 3.39E+09 3.5E+09 5.37E+09 3.3E+09 3.26E+09 3.42 E+09 3.74E+09 3.82 E+09 3.51E+09 3.71E+09 3.86E+09 3.57E+09 3.6E+09 3.39E+09 3.35E+09 3.18E+09 3.3E+09 3.06E+09 3.54E+09 3.02 E+09 3.02E+09 2.96E+09 3.02 E+09 3.23E+09 3.38E+09 3.35E+09 3.39E+09 3.02 E+09 3.71E+09 3.5 E+09 3.67E+09 3.22E+09 3.73E+09 3.56E+09 4.01 E+09 3.85E+09 3.33E+09 | 2018-05-07 2018-05-08 2680.34 2670.26 2683.35 2676.34 2664.7 2655.2 2672.63 2671.92 2672.63 3.24E+09 2671.92 | 13.72E+09 | 2018-05-10 | 2018-05-11 | 2018-05-14 | 2018-05-15 | 2018-05-16 | 2018-05-17 | 2018-05-18 | 2018-05-21 | 2018-05-22 | 2018-05-23 | 2018-05-24 | 2018-05-25 | 2018-05-29 | 2018-05-30 | 2018-05-31 | 2018-06-01 | 2018-06-04 | 2018-06-05 | 2018-06-06 | 2018-06-07 | 2018-06-08 | 2018-06-11 | 2018-06-12 | 2018-06-13 | 2018-06-14 | 2018-06-15 | 2018-06-18 | 2018-06-19 | 2018-06-20 | 2018-06-21 | 2018-06-22 | 2018-06-25 2018-06-26 2018-06-27 | 2018-06-28 2705.02 2722.7 2738.47 2718.59 2712.62 2719.71 2717.35 2735.39 2738.34 2713.98 2730.94 2723.6 2705.11 2702.43 2720.98 2718.7 2741.67 2748.46 2753.25 2774.84 2765.84 2780.18 2785.6 2787.94 2783.21 2777.78 2765.79 2752.01 2769.73 2769.28 2760.79 2742.94 2722.12 2728.45 2698.69 2726.11 2732.86 2742. 1 2718.59 2727.76 2731.96 2719.5 2739.19 2742.24 2733.33 2731.97 2727.36 2710.67 2729.34 2722.5 2736.93 2749.16 2752.61 2772.39 2779.9 2779.39 2790.21 2789.8 2791.47 2789.06 2782.81 2774.99 2765.05 2774.86 2769.28 2764.17 2742.94 2732.91 2746.09 2724.34 2704.54 2723.07 2723.07 3.33E+09 2717.45 2727.72 2727.72 2.86E+09 2725.47 2730.132730.13297E+09 2701.91 2711.45 2711.45 3.29E+09 2712.17 2722.46 2722.46 3.2E+09 2711.36 2720.13 2720.13 3.48E+09 2709.18 2712.97 271297 337E+09 2 725.7 2733.01 2733.01] 3.02E+09 2721.88 2724.44 2724.44 3.37E+09 2709.54 2733.29 2733.29 3.33E+09 2707.38 2727.76 2727.76 3.26E+09 2714.99 2721.33272133 3 E+09 2676.81 2689.86 2689.86 3.74E+09 2702.43 2724.01 2724.01 3.56E+09 2700.68 2705.27 2705.27 4.24E+09 2718.7 2734.62 2734.62 3.68E+09 2740.54 2746.87 2746.87 3.38E+09 2739.51 2748.8 2748.8 3.52E+09 2748.46 2772.35 2772.35 3.65E+09 2760.16 2770.372770.37 3.71E+09 2763.59 2779.03 2779.03 3.12E+09 2780.17 2 782 2 782 3.23E+09 2778.78 2786.852786.85 3.4E+09 2774.65 2775.63 2775.63 3.78E+09 2776.52 2782.49 2782.49 3.53E+09 2761.73 2779.66 2779.66 5.43E409 2757.122773.75 2773.75 3.29F+09 2743.19 2762.59 2762.59 3.66E+09 2763.91 2767.322767.32 333E+09 2744.39 2749.76 2749.76 3.3E+09 2752.68 2754.88 2754.88 5.45E+09 2698.67 2717.07 2717.07 3.66E+09 2715.6| 2723.06 2723.06 13.56E+09 12699.38 2699.63 2699.63 13.78E+09 2691.99 2716.31 2716.31 3.43E409 | 2018-06-29 2018-07-02 | 2018-07-03 | 2018-07-05 | 2018-07-06 | 2018-07-09 | 2018-07-10 | 2018-07-11 | 2018-07-12 | 2018-07-13 | 2018-07-16 | 2018-07-17 | 2018-07-18 | 2018-07-19 | 2018-07-20 2727.13 2743.26 2704.95 2727.26 2733.27 2736.58 2724.192737.83 2737.68 2764.41 2775.62] 2784.65 2788.56 2795.58 2779.82 2785.91 2783.14 2799.22 2796.93 2804.53 2797.36 2801.19 2789.34 2814.19 2811.35 2816.76 2809.37 2812.05 2804.55 2809.7 2718.03 2698.95 2711.16 2716.02 2733.52 2770.73 2786.24 2770.77 2781.53 2791.69 2793.39 2789.24 2805.89 2799.77 2800.01 2718.37 2718.37 3.57E+09 2726.71 2726.71| 3.07E+09 2713.222713.22 191E+09 2736.612736.61| 295E+09 2759.822759.82 255E+09 2784.172784.17 3.05E+09 2793.842793.84 3.06E+09 2774.02 2774.02 2.96E+09 2798.29 2798.29 2.82E+09 2801.31 2801.31 2.61E+09 2798.43 2798.43 2.81E+09 2809.55 2809.55 3.05E+09 2815.62 2815.62 3.09E+09 2804.49 2804.49 3.27E+09 2801.83 2801.83 3.23E+09 | 2018-07-24 | 2018-07-25 | 2018-07-26 | 2018-07-27 | 2018-07-30 | 2018-07-31 | 2018-08-01 | 2018-08-02 | 2018-08-03 | 2018-08-06 | 2018-08-07 | 2018-08-08 | 2018-08-09 | 2018-08-10 | 2018-08-13 | 2018-08-14 | 2018-08-15 | 2018-08-16 | 2018-08-17 | 2018-08-20 | 2018-08-21 | 2018-08-22 2820.68 2817.73 2835.49 2842.35 2819 2809.73 2821.17 2800.48 2829.62 2840.29 2855.92 2856.79 2857.19 2838.9 2835.46 2827.88 2827.95 2831.44 2838.32 2853.93 2861.51 2860.99 2829.99 2848.03 2845.57 2843.17 2821.74 2824.46 2825.83 2829.91 2840.38 2853.29 2863.43 2862.44 2862.48 2842. 2 2843.4 2843.11 2827.95 2850.49 2855.63 2859.76 2873.23 2867.54 2811.12 2820.4 2817.73 2846.07 2835.26 2837.44 2808.34 2818.82 2798.112802.6 2808.06 2816.29 2805.85 2813.36 2796.34 2827.22 2827.37 2840.35 2835.98 2850. 4 2855.92 2858.45 2853.09 2857.7 2851.98 2853.58 2825.81| 2833.28 2819.88 2821.93 2826.58 2839.96 2802.49 2818.37 2831.44 2840.69 2833.73 2850.13 2850.62 2857.05 2861.32 2862.96 2856.05 2861.82 2820.4 2846.07 2837.44 2818.82 2802.6 2816.29 2813.36 2827.22 2840.35 2850.4 2858.45 2857. 7 2853.58 2833.28 2821.93 2839.96 2818.37 2840.69 2850.13 2857.05 2862.96 2861.82 3.42E+09 3.55E+09 3.65E+09 3.42E+09 3.25E+09 3.89E+09 3.5E+09 3.47E+09 3.03E+09 2.87E+09 3.16E+09 2.97E+09 3.05E+09 3.26E+09 3.16E+09 2.98E+09 3.65E+09 3.22E+09 3.02E+09 2.75E+09 3.15E+09 2.69E+09 | 2018-08-23 | 2018-08-24 | 2018-08-27 2018-08-28 2018-08-29 2018-08-30 | 2018-08-31 2018-09-04 2018-09-05 | 2018-09-06 | 2018-09-07 2018-09-10 | 2018-09-11 2018-09-12 | 2018-09-13 2018-09-14 2018-09-17 2018-09-18 2018-09-19 2018-09-20 2018-09-21 | 2018-09-24 2018-09-25 | 2018-09-26 2018-09-27 | 2018-09-28 2860.29 2862.35 2884.69 2901.45 2900.62 2908.94 2898.37 2896.96 2891.59 2888.64] 2868.26 2881.39 2871.57 2888.29 2896.85 2906.38 2903.83 2890.74 2868.78 2854.03 2856.98 2856.98 2876.162862.35 2874.69 2874.69 2898.25 2884.69 2896.74 2896.74 2903.77 2893.5 2897.52 2897.52 2916.5 2898.4 2914.04 2914.04 2912.46 2895.22 2901.13 2901.13 2906.32 2891.732901.52 290152 2900.18 2885.13 2896.72 2896.72 2894.21 2876.92 2888.6 12888.6 2892.05 2867.29 2878.05 2878.05 2883.81| 2864.122871.6882871.68 2886.93 2875.94 2877.13 2877.13 2892.52 2866.78 2887.89 2887.89 2894.65 2879.2 2888.92 2888.92 2906.76 2896.39 2904.18 2904.18 2908.3 2895.77 2904.98 2904.98 2904.65 2886.16 2888.8 2888.8 2911.17 2890.43 | 2904.31 2904.31 2912.36 2903.82 2907.95 2907.95 2934.8 2919.73 2930.75 2930.75 2940.91 2927.11 | 2929.67 2929.67 2923.79 2912.63 2919.372919.37 2923.95 2913.7 2915.56 2915.56 2931.15 2903.28 2905.97 2905.97 2927.22 2909.27 2914 2914 2920.53 2 907.5 2913.98 2913.98 2.71E+09 2.6E+09 2.85E+09 2.68E+09 2.79EA09 2.8E+09 2.88E+09 3.08E+09 3.24E+09 314E+09 295E+09 2.73E+09 2.9E+09 3.26E+09 3.25E409 3.15E+09 2.95E+09 3.07EH09 3. 28E+09 3.34E09 5.61E+09 337E+09 3.29F+09 339E+09 3.06E+09 3.43E409 2919.73 2936.76 2921.83 2921.75 2916.98 2911.65 2910.03 Exercise 3 On October 1, 2017, you invested $1000 into a portfolio with initial weight of 40% - Microsoft a. What is the value of your portfolio on September 30, 2018? b. What is the annualized monthly volatility of your portfolio? c. What are the portfolio weights on September 30, 2018? d. Assume that the return on your portfolio is normally distributed with mean y = 0.19% and standard deviation 0, = 2.17%. What is the value-at-risk with probability p= 5%? Exercise 4 a. Draw a histogram of daily S&P500 returns with 20 equal-sized bins. b. Calculate the average and the standard deviation of daily return on S&P500. c. Assume that daily S&P500 returns are normally distributed with the mean and the standard deviation calculated in 4b). You observe a return on S&P500 of (-1.51%). Is it extreme? How often can we expect to observe returns of (-1.51% or lower? d. Assume again that daily S&P500 returns are normally distributed with the mean and the standard deviation calculated in 4b). Can we be certain that the average daily return on S&P500 is different from (-0.02%) ? Variance Microsoft Corporation returns Month Opening Price Monthly Return 01-Oct-17 83.18 01-Nov-17 84.17 1.19% 01-Dec-17 85.54 1.63% 01-Jan-18 11.07% 01-Feb-18 93.77 -1.31% 01-Mar-18 91.27 -2.67% 01-Apr-18 93.52 2.47% 01-May-18 98.84 5.69% 01-Jun-18 98.61 -0.23% 01-Jul-18 106.08 7.58% 01-Aug-18 112.33 5.89% 01-Sep-18 114.37 1.82% -1.82% -1.38% 8.06% -4.32% -5.68% -0.55% 2.68% -3.24% 4.56% 2.88% -1.19% Month Opening Price 01-Oct-17 01-Nov-17 01-Dec-17 01-Jan-18 01-Feb-18 01-Mar-18 01-Apr-18 01-May-18 01-Jun-18 01-Jul-18 01-Aug-18 01-Sep-18 Monthly Returns Variance 12.27 12.52 2.04% 4.45% 12.49 -0.24% 2.17% 10.97 -12.17% -9.76% 10.61 -3.28% -0.87% 11.08 4.43% 6.84% 11.24 1.44% 3.85% 11.55 2.76% 5.17% 11.07 -4.16% -1.75% 10.04 -9.30% -6.90% 9.48 -5.58% -3.17% 9.25 -2.43% -0.02% Low Date 2017-10-02 2017-10-03 2017-10-04 2017-10-05 2017-10-06 2017-10-09 2017-10-10 2017-10-11 2017-10-12 2017-10-13 2017-10-16 2017-10-17 2017-10-18 2017-10-19 2017-10-20 2017-10-23 2017-10-24 2017-10-25 2017-10-26 2017-10-27 2017-10-30 2017-10-31 2017-11-01 2017-11-02 2017-11-03 2017-11-06 2017-11-07 2017-11-08 2017-11-09 2017-11-10 2017-11-13 2017-11-14 2017-11-15 2017-11-16 2017-11-17 2017-11-20 Sp500 Prices Open High Close Adj Close Volume 2521.2 2529.23 2520.4 2529.12 2529.12 3.2 E+09 2530.34 2535.13 2528.85 2534.58 2534.58 3.07 E+09 2533.48 2540.53 2531.8 2537.74 2537.74 3.02 E+09 2540.86 2552.51 2540.02 2552.07 2552.07 3.05E+09 2547.44 2549.41 2543.79 2549.33 2549.33 2.88E+09 2551.39 2551.82 2541. 6 2544.73 2544.73 2.48E+09 2549.99 2555.23 2544.86 2550.64 2550.64 2.96E+09 2550.62 2555.24 2547.95 2555.24 2555.24 2.98 E+09 2552.88 2555.33 2548.31 2550.93 2550.93 3.15 E+09 2555.66 2557.65 2552.09 2553.17 2553.17 3.15 E+09 2555.57 2559.47 2557.64 2557.64 2.92 E+09 2557.17 2559.71 2554.69 2559.36 2559.36 2.89E+09 2562.87 2564.11 2559.67 2561.26 2561.26 3E+09 2553.39 2562.36 2547.92 2562.1 2562.1 2.99E+09 2567.56 2575.44 2567.56 2575.21 2575.21 3.38E+09 2578.08 2578.29 2564.33 2564.98 2564.98 3.21E+09 2568.66 2572.18 2565.58 2569.13 2569.13 3.43 E+09 2566.52 2567.4 2544 2557.15 2557.15 3.87E+09 2560.08 2567.07 2559.8 2560.4 2560.4 3.87E+09 2570.26 2582.98 2565.94 2581.07 2581.07 3.89E+09 2577.75 2580.03 2568.25 2572.832572.83 3.66E+09 2575.99 2578.29 2572.15 2575.26 2575.26 3.83E+09 2583.21 2588.4 2574.92 2579.36 2579.36 3.81E+09 2579.46 2581.11 2566.17 2579.85 2579.85 4.05E+09 2581.93 2588.42 2587.84 2587.84 3.57E+09 2587.47 2593.38 2585.66 2591.13 2591.13 3.54E+09 2592.11 2597.02 2584.35 2590.64 2590.64 3.81E+09 2588.71 2595.47 2585.02 2594.38 2594.38 3.9E+09 2584 2586.5 2566.33 2584.62 2584.62 3.83E+09 2580.18 2583.81 2575.57 2582.3 2582.3 3.49E+09 2576.53 2587.66 2574.48 2584.84 2584.84 3.4E+09 2577.752579.66 2566.56 2578.87 2578.87 3.64E+09 2569.45 2572.84 2557.45 2564.62 2564.62 3.56E+09 2572.95 2590.09 2572.95 2585.64 2585.64 3.31E+09 2582.94 2583.96 2577.62 2578.85 2578.85 3.3E+09 2579.49 2584.64 2578.24 2582.14 2582.14 3E+09 | 2018-01-18 | 2018-01-19 2018-01-22 2018-01-23 | 2018-01-24 | 2018-01-25 2018-01-26 | 2018-01-29 | 2018-01-30 | 2018-01-31 | 2018-02-01 | 2018-02-02 | 2018-02-05 | 2018-02-06 | 2018-02-07 | 2018-02-08 | 2018-02-09 | 2018-02-12 | 2018-02-13 | 2018-02-14 | 2018-02-15 | 2018-02-16 | 2018-02-20 | 2018-02-21 | 2018-02-22 | 2018-02-23 | 2018-02-26 | 2018-02-27 | 2018-02-28 | 2018-03-01 | 2018-03-02 2018-03-05 | 2018-03-06 | 2018-03-07 | 2018-03-08 | 2018-03-09 | 2018-03-12 2802.4 2805.83 2802.6 2810.33 2809.16 2833.03 2835.05 2842.24 2845.42 2852.97 2846.24 2848.56 2847.48 2872.87 2867.23 2870.62 2832.74 2837.75 2832.41 2839.26 2816.45 2835.96 2808.92 2808.92 2741.06 2763.39 2614.78 2701.04 2690.95 2727.67 2685.01] 2685.27 2601.78 2638.67 2636.75 2672.61 2646.27 2668.84 2651.21 2702. 1 2713.46 2731.51 2727.142754.42 2722.99 2737.6 2720.53 2747.75 2710.42 2731.26 2715.8 2747.76 2757.37 2780.64 2780.452789.15 2753.78 2761.52 2715.22 2730.89 2658.89 2696.25 2681.06 2728.09 2730.18 2732.08 2710.18 2730.6 2732.75 2740.45 2752.91 2786.57 2790.54 | 2796.98 2792.56 2798.03 2798.03 3.68E+09 2798.08 2810.3 2810.3 3.64E+09 12808.12 2832.97 2832.97 3.47E409 2830.59 2839.13 2839.13 3.52E+09 2824.81 2837.54 2837.54 4.01E+09 2830.94 2839.25 2839.25 3.84E+09 2846.18 2872.87 2872.87 3.44E+09 2851.48 2853.53 2853.53 3.57E+09 2818.27 2822.43 2822.43 3.99E+09 2813.04 2823.81 2823.81 4.26E+09 2812.7 2821.98 2821.98 3.94E+09 2759.97 2762.13 2762.13 4.3E+09 2638.17 2648.94 2648.94 5.28E+09 2593.07 2695.142695.145.89E+09 2681.33 2681.66 2681.66 4.63E09. 2580.56 2 581 2 581531E+09 2532.69 2619.55 2619.55 5.68E+09 2622.45 2656 2 656 4.06E+09 2637.08 2662.94 2662.94 3.47E+09 2648.87 2698.63 2698.63 4 E+09 2689.82 2731. 2 2731.2 3.68E+09 2725.11| 2732.222732.22 3.64E+09 2706.76 2716.26 2716.26 3.63E+09 2701.29 2701.332701.33 3.78E+09 2697.77 2703.96 2703.96 3.7E+09 2713.742747. 3 27473 3.19F+09 2753.78 2779.6 2779.6 3.42E+09 2744.22 2744.28 2744.28 3.75E+09 2713.54 2713.83 2713.83 4.23E+09 2659.65 2677.67 2677.67 4.5E+09 2647.32 2691.25 2691.25 3.88E+09 2675.75 2720.94 2720.94 3.71E+09 2711.26 2728.12 2728.12 3.37E+09 2701.74 2726.8 2726.8 3.39E+09 2722.65 2738.97 2738.97 3.21E+09 2751.54 2786.57 2786.57 3.36E+09 2779.26 2783.02 2783.02 3.19E+09 | 2018-03-13 | 2018-03-14 | 2018-03-15 2018-03-16 2018-03-19 2018-03-20 | 2018-03-21 2018-03-22 2018-03-23 2018-03-26 | 2018-03-27 2018-03-28 2018-03-29 2018-04-02 | 2018-04-03 2018-04-04 2018-04-05 2018-04-06 2018-04-09 2018-04-10 | 2018-04-11 2018-04-12 2018-04-13 2018-04-16 | 2018-04-17 2018-04-18 | 2018-04-19 2018-04-20 | 2018-04-23 2018-04-24 2018-04-25 2018-04-26 | 2018-04-27 | 2018-04-30 2018-05-01 | 2018-05-02 2018-05-03 2018-05-04 2792.31 2801.9 2774.06 2777.11 2754.27 2763.03 2750.57 2761.85 2741.38 2741.38 2715.05 2724.22 2714.99 2739.14 2691.36 2695.68 2646.71 2657.67 2619.35 2661.36 2667.57 2674.78 2611.3 2632.65 2614.41 2659.07 2633.45 2638.3 2592.17 2619.14 2584.04 2649.86 2657.36 2672.08 2645.82 2656.88 2617.18 2653.55 2638.41 2665.45 2643.89 2661.43 2653.83 2674.72 2676.9 2680.26 2670.1 2686.49 2692.74 2713.34 2710.11 2717.49 2701.16 2702.84 2692.56 2693.94 2675.4 2682.86 2680.8 2683.55 2634.92 2645.3 2651.65 2676.48 2675.47 2677.35 2682.51 2682.87 2642.96 2655.27 2654.24 2660.87 2628.08 2637.14 2621.452670.93 2758.68 2744.38 2741.47 2749.97 2694.59 2710.05 2709.79 2641.59 2585.89 2601.81 2596.12 2593.06 2609.72 2553.8 2575.49 2573.61 2649.58 2586.27 2610.79 2635.78 2639.25 2653.83 2645.05 2665.16 2692.05 2703.63 2681.9 2660.61 2657.99 2617.32 2612.67 2647.16 2659.01 2648.04 2625.41 2631.7 2594.62 2615.32 2765.31 2749.48 2747.33 2752.01 2712.92 2716.94 2711.93 2643.69 2588.26 2658.55 2612.62 2605 2640.87 2581.88 2614.45 2644.69 2662.84 2604.47 2613.16 2656.87 2642.19 2663.99 2656.3 2677.84 2706.39 2708.64 2693.13 2670.14 2670.29 2634.56 2639.4 2666.94 2669.91 2648.05 2654.8 2635.67 2629.73 2663.42 2765.31 2749.48 2747.33 2752.01 2712.92 2716.94 2711.93 2643.69 2588.26 2658.55 2612.62 2605 2640.87 2581.88 2614.45 2644.69 2662.84 2604.47 2613.16 2656.87 2642.19 2663.99 2656.3 2677.84 2706.39 2708.64 2693.13 2670.14 2670.29 2634.56 2639.4 2666.94 2669.91 2648.05 2654.8 2635.67 2629.73 2663.42 3.3E+09 3.39E+09 3.5E+09 5.37E+09 3.3E+09 3.26E+09 3.42 E+09 3.74E+09 3.82 E+09 3.51E+09 3.71E+09 3.86E+09 3.57E+09 3.6E+09 3.39E+09 3.35E+09 3.18E+09 3.3E+09 3.06E+09 3.54E+09 3.02 E+09 3.02E+09 2.96E+09 3.02 E+09 3.23E+09 3.38E+09 3.35E+09 3.39E+09 3.02 E+09 3.71E+09 3.5 E+09 3.67E+09 3.22E+09 3.73E+09 3.56E+09 4.01 E+09 3.85E+09 3.33E+09 | 2018-05-07 2018-05-08 2680.34 2670.26 2683.35 2676.34 2664.7 2655.2 2672.63 2671.92 2672.63 3.24E+09 2671.92 | 13.72E+09 | 2018-05-10 | 2018-05-11 | 2018-05-14 | 2018-05-15 | 2018-05-16 | 2018-05-17 | 2018-05-18 | 2018-05-21 | 2018-05-22 | 2018-05-23 | 2018-05-24 | 2018-05-25 | 2018-05-29 | 2018-05-30 | 2018-05-31 | 2018-06-01 | 2018-06-04 | 2018-06-05 | 2018-06-06 | 2018-06-07 | 2018-06-08 | 2018-06-11 | 2018-06-12 | 2018-06-13 | 2018-06-14 | 2018-06-15 | 2018-06-18 | 2018-06-19 | 2018-06-20 | 2018-06-21 | 2018-06-22 | 2018-06-25 2018-06-26 2018-06-27 | 2018-06-28 2705.02 2722.7 2738.47 2718.59 2712.62 2719.71 2717.35 2735.39 2738.34 2713.98 2730.94 2723.6 2705.11 2702.43 2720.98 2718.7 2741.67 2748.46 2753.25 2774.84 2765.84 2780.18 2785.6 2787.94 2783.21 2777.78 2765.79 2752.01 2769.73 2769.28 2760.79 2742.94 2722.12 2728.45 2698.69 2726.11 2732.86 2742. 1 2718.59 2727.76 2731.96 2719.5 2739.19 2742.24 2733.33 2731.97 2727.36 2710.67 2729.34 2722.5 2736.93 2749.16 2752.61 2772.39 2779.9 2779.39 2790.21 2789.8 2791.47 2789.06 2782.81 2774.99 2765.05 2774.86 2769.28 2764.17 2742.94 2732.91 2746.09 2724.34 2704.54 2723.07 2723.07 3.33E+09 2717.45 2727.72 2727.72 2.86E+09 2725.47 2730.132730.13297E+09 2701.91 2711.45 2711.45 3.29E+09 2712.17 2722.46 2722.46 3.2E+09 2711.36 2720.13 2720.13 3.48E+09 2709.18 2712.97 271297 337E+09 2 725.7 2733.01 2733.01] 3.02E+09 2721.88 2724.44 2724.44 3.37E+09 2709.54 2733.29 2733.29 3.33E+09 2707.38 2727.76 2727.76 3.26E+09 2714.99 2721.33272133 3 E+09 2676.81 2689.86 2689.86 3.74E+09 2702.43 2724.01 2724.01 3.56E+09 2700.68 2705.27 2705.27 4.24E+09 2718.7 2734.62 2734.62 3.68E+09 2740.54 2746.87 2746.87 3.38E+09 2739.51 2748.8 2748.8 3.52E+09 2748.46 2772.35 2772.35 3.65E+09 2760.16 2770.372770.37 3.71E+09 2763.59 2779.03 2779.03 3.12E+09 2780.17 2 782 2 782 3.23E+09 2778.78 2786.852786.85 3.4E+09 2774.65 2775.63 2775.63 3.78E+09 2776.52 2782.49 2782.49 3.53E+09 2761.73 2779.66 2779.66 5.43E409 2757.122773.75 2773.75 3.29F+09 2743.19 2762.59 2762.59 3.66E+09 2763.91 2767.322767.32 333E+09 2744.39 2749.76 2749.76 3.3E+09 2752.68 2754.88 2754.88 5.45E+09 2698.67 2717.07 2717.07 3.66E+09 2715.6| 2723.06 2723.06 13.56E+09 12699.38 2699.63 2699.63 13.78E+09 2691.99 2716.31 2716.31 3.43E409 | 2018-06-29 2018-07-02 | 2018-07-03 | 2018-07-05 | 2018-07-06 | 2018-07-09 | 2018-07-10 | 2018-07-11 | 2018-07-12 | 2018-07-13 | 2018-07-16 | 2018-07-17 | 2018-07-18 | 2018-07-19 | 2018-07-20 2727.13 2743.26 2704.95 2727.26 2733.27 2736.58 2724.192737.83 2737.68 2764.41 2775.62] 2784.65 2788.56 2795.58 2779.82 2785.91 2783.14 2799.22 2796.93 2804.53 2797.36 2801.19 2789.34 2814.19 2811.35 2816.76 2809.37 2812.05 2804.55 2809.7 2718.03 2698.95 2711.16 2716.02 2733.52 2770.73 2786.24 2770.77 2781.53 2791.69 2793.39 2789.24 2805.89 2799.77 2800.01 2718.37 2718.37 3.57E+09 2726.71 2726.71| 3.07E+09 2713.222713.22 191E+09 2736.612736.61| 295E+09 2759.822759.82 255E+09 2784.172784.17 3.05E+09 2793.842793.84 3.06E+09 2774.02 2774.02 2.96E+09 2798.29 2798.29 2.82E+09 2801.31 2801.31 2.61E+09 2798.43 2798.43 2.81E+09 2809.55 2809.55 3.05E+09 2815.62 2815.62 3.09E+09 2804.49 2804.49 3.27E+09 2801.83 2801.83 3.23E+09 | 2018-07-24 | 2018-07-25 | 2018-07-26 | 2018-07-27 | 2018-07-30 | 2018-07-31 | 2018-08-01 | 2018-08-02 | 2018-08-03 | 2018-08-06 | 2018-08-07 | 2018-08-08 | 2018-08-09 | 2018-08-10 | 2018-08-13 | 2018-08-14 | 2018-08-15 | 2018-08-16 | 2018-08-17 | 2018-08-20 | 2018-08-21 | 2018-08-22 2820.68 2817.73 2835.49 2842.35 2819 2809.73 2821.17 2800.48 2829.62 2840.29 2855.92 2856.79 2857.19 2838.9 2835.46 2827.88 2827.95 2831.44 2838.32 2853.93 2861.51 2860.99 2829.99 2848.03 2845.57 2843.17 2821.74 2824.46 2825.83 2829.91 2840.38 2853.29 2863.43 2862.44 2862.48 2842. 2 2843.4 2843.11 2827.95 2850.49 2855.63 2859.76 2873.23 2867.54 2811.12 2820.4 2817.73 2846.07 2835.26 2837.44 2808.34 2818.82 2798.112802.6 2808.06 2816.29 2805.85 2813.36 2796.34 2827.22 2827.37 2840.35 2835.98 2850. 4 2855.92 2858.45 2853.09 2857.7 2851.98 2853.58 2825.81| 2833.28 2819.88 2821.93 2826.58 2839.96 2802.49 2818.37 2831.44 2840.69 2833.73 2850.13 2850.62 2857.05 2861.32 2862.96 2856.05 2861.82 2820.4 2846.07 2837.44 2818.82 2802.6 2816.29 2813.36 2827.22 2840.35 2850.4 2858.45 2857. 7 2853.58 2833.28 2821.93 2839.96 2818.37 2840.69 2850.13 2857.05 2862.96 2861.82 3.42E+09 3.55E+09 3.65E+09 3.42E+09 3.25E+09 3.89E+09 3.5E+09 3.47E+09 3.03E+09 2.87E+09 3.16E+09 2.97E+09 3.05E+09 3.26E+09 3.16E+09 2.98E+09 3.65E+09 3.22E+09 3.02E+09 2.75E+09 3.15E+09 2.69E+09 | 2018-08-23 | 2018-08-24 | 2018-08-27 2018-08-28 2018-08-29 2018-08-30 | 2018-08-31 2018-09-04 2018-09-05 | 2018-09-06 | 2018-09-07 2018-09-10 | 2018-09-11 2018-09-12 | 2018-09-13 2018-09-14 2018-09-17 2018-09-18 2018-09-19 2018-09-20 2018-09-21 | 2018-09-24 2018-09-25 | 2018-09-26 2018-09-27 | 2018-09-28 2860.29 2862.35 2884.69 2901.45 2900.62 2908.94 2898.37 2896.96 2891.59 2888.64] 2868.26 2881.39 2871.57 2888.29 2896.85 2906.38 2903.83 2890.74 2868.78 2854.03 2856.98 2856.98 2876.162862.35 2874.69 2874.69 2898.25 2884.69 2896.74 2896.74 2903.77 2893.5 2897.52 2897.52 2916.5 2898.4 2914.04 2914.04 2912.46 2895.22 2901.13 2901.13 2906.32 2891.732901.52 290152 2900.18 2885.13 2896.72 2896.72 2894.21 2876.92 2888.6 12888.6 2892.05 2867.29 2878.05 2878.05 2883.81| 2864.122871.6882871.68 2886.93 2875.94 2877.13 2877.13 2892.52 2866.78 2887.89 2887.89 2894.65 2879.2 2888.92 2888.92 2906.76 2896.39 2904.18 2904.18 2908.3 2895.77 2904.98 2904.98 2904.65 2886.16 2888.8 2888.8 2911.17 2890.43 | 2904.31 2904.31 2912.36 2903.82 2907.95 2907.95 2934.8 2919.73 2930.75 2930.75 2940.91 2927.11 | 2929.67 2929.67 2923.79 2912.63 2919.372919.37 2923.95 2913.7 2915.56 2915.56 2931.15 2903.28 2905.97 2905.97 2927.22 2909.27 2914 2914 2920.53 2 907.5 2913.98 2913.98 2.71E+09 2.6E+09 2.85E+09 2.68E+09 2.79EA09 2.8E+09 2.88E+09 3.08E+09 3.24E+09 314E+09 295E+09 2.73E+09 2.9E+09 3.26E+09 3.25E409 3.15E+09 2.95E+09 3.07EH09 3. 28E+09 3.34E09 5.61E+09 337E+09 3.29F+09 339E+09 3.06E+09 3.43E409 2919.73 2936.76 2921.83 2921.75 2916.98 2911.65 2910.03 Exercise 3 On October 1, 2017, you invested $1000 into a portfolio with initial weight of 40% - Microsoft a. What is the value of your portfolio on September 30, 2018? b. What is the annualized monthly volatility of your portfolio? c. What are the portfolio weights on September 30, 2018? d. Assume that the return on your portfolio is normally distributed with mean y = 0.19% and standard deviation 0, = 2.17%. What is the value-at-risk with probability p= 5%? Exercise 4 a. Draw a histogram of daily S&P500 returns with 20 equal-sized bins. b. Calculate the average and the standard deviation of daily return on S&P500. c. Assume that daily S&P500 returns are normally distributed with the mean and the standard deviation calculated in 4b). You observe a return on S&P500 of (-1.51%). Is it extreme? How often can we expect to observe returns of (-1.51% or lower? d. Assume again that daily S&P500 returns are normally distributed with the mean and the standard deviation calculated in 4b). Can we be certain that the average daily return on S&P500 is different from (-0.02%)