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fm3_problems21

# fm3_problems21 - UN-14P A 1 2 3 4 5 6 7 8 9 10 11 12 13 14...

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UN-14P CHOOSING A SYNTHETIC PUT EXERCISE PRICE z 0.9500 Insurance level S 100 Current stock price X 106.473 Exercise price r 6.00% Risk-free rate of interest T 1 Time to maturity of option (in years) Sigma 30% Stock volatility 0.1409 <--(LN(S/X)+(r+0.5*sigma^2)*T)/(sigma*SQRT(T)) -0.1591 0.5560 0.4368 Equation 0.0000 Calculating the portfolio insurance proportions Omega 43.59% #MACRO? 56.41% #MACRO? Extra calculations Stock 100.0000 #MACRO? Put price 12.0763 #MACRO? Stock + put 112.0763 #MACRO? If you have \$1000, you can buy: Number of shares+puts 8.9225 #MACRO? 950.0007 #MACRO? d 1 d 2 <--d 1 - sigma*SQRT(T) N(d 1 ) <---Uses formula NormSDist(d 1 ) N(d 2 ) <---Uses formula NormSDist(d 2 ) <--1/z - S/X*N(d 1 )-exp(-r*T)*(1-N(d 2 )) Note : Excel's Solver was used to find X so that the insurance level would be 95%. Note that omega = S/(S+P) In the worst case situation, you exercise all the puts, getting A B C 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

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Exercise 2 Page 2 PORTFOLIO INSURANCE S X 106.47 Sigma 40% r 6% Initial 1000 Portfolio va beginning of Week Time Stock price Put price Omega Stocks Bonds 0 0.0000 100.00 0.1932 16.0099 0.4970 497.03 502.97 1 0.0192 101.98 0.2379 15.1019 0.5174 522.78 487.65 2 0.0385 102.10 0.2364 14.9634 0.5176 523.59 488.02 3 0.0577 100.85 0.2001 15.3910 0.5026 505.50 500.27 4 0.0769 105.55 0.3136 13.4243 0.5528 569.31 460.58 5 0.0962 97.52 0.1017 16.6830 0.4615 455.58 531.51 6 0.1154 99.20 0.1412 15.8328 0.4796 477.48 518.10 7 0.1346 96.40 0.0585 17.0331 0.4448 437.06 545.63 8 0.1538 103.41 0.2426 13.8553 0.5254 533.36 481.73 9 0.1731 107.91 0.3552 12.0244 0.5747 597.09 441.79 10 0.1923 102.47 0.2080 14.0317 0.5122 516.98 492.29 11 0.2115 111.66 0.4447 10.5004 0.6140 648.50 407.71 12 0.2308 114.39 0.5114 9.5144 0.6421 688.63 383.90 13 0.2500 117.41 0.5854 8.5071 0.6721 733.42 357.74 14 0.2692 116.14 0.5535 8.7384 0.6603 715.59 368.08 15 0.2885 103.61 0.2145 12.9941 0.5198 523.33 483.55 16 0.3077 119.96 0.6495 7.4290 0.6987 761.59 328.40 17 0.3269 123.23 0.7326 6.4912 0.7297 810.80 300.38 18 0.3462 117.94 0.5992 7.6903 0.6811 733.31 343.38 19 0.3654 117.43 0.5861 7.6899 0.6768 726.79 347.10 20 0.3846 115.97 0.5468 7.9611 0.6623 705.49 359.77 21 0.4038 119.28 0.6380 6.8956 0.6979 757.82 328.01 22 0.4231 122.54 0.7284 5.9398 0.7314 809.55 297.36 23 0.4423 123.55 0.7593 5.5581 0.7427 827.36 286.56 24 0.4615 131.40 0.9736 3.8906 0.8109 946.18 220.69 25 0.4808 137.45 1.1382 2.8734 0.8546 1034.67 176.00 26 0.5000 135.26 1.0937 3.0296 0.8440 1008.13 186.27 27 0.5192 135.68 1.1168 2.8364 0.8502 1018.30 179.44 28 0.5385 146.43 1.4103 1.5980 0.9108 1164.59 114.00 29 0.5577 154.51 1.6326 0.9814 0.9427 1266.13 76.90 30 0.5769 151.74 1.5893 1.0431 0.9376 1237.95 82.44 31 0.5962 148.56 1.5329 1.1370 0.9302 1204.23 90.33 32 0.6154 146.62 1.5070 1.1601 0.9268 1185.29 93.67 33 0.6346 155.09 1.7671 0.6366 0.9575 1290.16 57.32 34 0.6538 160.57 1.9517 0.3968 0.9721 1354.31 38.85 35 0.6731 152.31 1.7657 0.5904 0.9576 1267.40 56.17 36 0.6923 163.87 2.1376 0.2284 0.9824 1394.77 25.05 37 0.7115 159.94 2.0821 0.2513 0.9798 1358.37 28.01 38 0.7308 159.05 2.1154 0.2196 0.9814 1353.29 25.58 39 0.7500 166.60 2.4136 0.0926 0.9916 1430.93 12.19 40 0.7692 153.70 2.0785 0.2164 0.9798 1305.36 26.93 41 0.7885 156.26 2.2464 0.1306 0.9868 1336.30 17.83 42 0.8077 161.72 2.5364 0.0535 0.9941 1392.53 8.31 The cells in column P have the function N to simulate the standard normal deviates F9 produces a new simulat d 1 0 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
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