Study Questions for Itos Dilemma Case

1. Using the Black-Scholes pricing function in Excel, compute an option value for each strike price and maturity date in case Exhibit 2. For simplicity, assume zero dividend yield. Also, use Louise Itos volatility estimates, provided in case Exhibit 1.

Exhibit 1 ITO'S DILEMMA Weekly Prices and Returns for Duke Energy, IBM and Microsoft 6 Week No Date Prices Duke Enerx IBM Close Close Returns (In Duke Enero IBM Microsoft Microsoft Close 3.57% 4.13% -0.16% 6.87% 7.27% 1.25% 2.18% 1.25% 5.96% 7.20% 1.14% -6.86% 12.25% -4.72% 3.97% 1.39% -3.91% 2.45% 2.83% 1 31-7-00 33.16 115.47 69.13 2 07-8-00 33.58 120.34 72.44 14-8-00 34.32 120.15 71.00 21-8-00 34.75 128.69 70.63 28-8-00 36.89 133.30 70.19 6 04-9-00 39.64 129.19 69.31 7 11-9-00 40.10 124.70 64.19 8 18-9-00 37.44 123.58 63.25 9 25-9-00 42.32 112.35 60.31 10 02-10-00 40.37 115.72 55.56 11 09-10-00 42.00 108.80 53.75 12 16-10-00 42.599 4.52 65.19 13 23-10-00 40.95 93.46 67.69 14 30-10-00 41.97 99.88 68.25 15 06-11-00 43.17 92.89 67.38 16 13-11-0043.83 101.82 69.06 17 20-11-00 42.71 99.82 69.94 18 27-11-0043.33 95.52 56.63 -12.00 42.59 96.89 54.44 2011-12-00 41.06 87.71 49.19 21 18-12-00 41.96 88 90 46.44 22 25-12-0036.2593.8949.13 01-1-01 41.10 84.72 43.38 08-1-01 3 4.83 93.71 25 15-1-01 36.16 11.12 61.00 26 22-1-01 38.24 114.06 64.00 27 29-1-01 37.33 110.14 60.81 28 05-2-01 41.02112.00 59.13 12-2-01 41.16 115.00 57.31 30 19-2-01 42.27 108.90 55.19 -0.81% 4.68% -2.00% -0.53% -0.62% -1.25% -7.68% -1.47% 4.76% -8.20% -3.32% 19.29% 3.76% 0.83% -1.29% 2.47% 1.26% -21.12% -3.94% -10.14% -5.75% 5.63% -12.45% 20.98% 13.12% 4.80% -5.11% -2.81% -3.11% 3.78% -3.14% -3.54% -0.90% -9.52% 2.95% -6.17% -14.07% -1.13% 6.65% -7.25% 9.18% -1.98% 4.41% 1.43% -9.95% 1.34% 5.47% -10.29% 10.09% 17.05% 2.61% -3.49% 1.67% 2.64% -5.45% 1.51% -2.58% 1.44% -1.73% -3.64% 2.17% -14.63% 12.54% -16.55% 3.76% 5.59% -2.42% 9.44% 0.34% 2.66% 23 Weekly Sigma of Returns Annualized standard deviation of retur 6.34% 45.75% 6.69% 48.24% 8.26% 59.56% Oo vou -WN- A B C D E F G H I J Exhibit 2 ITO'S DILEMMA Option Premium and Market Data for February 20, 2001 Call Premiums Put Premiums Mar Apr July Mar Apr July Duke Energy 42.27 40 4.30 5.30 0.75 1.30 2.25 42.27 42.5 2.70 3.90 4.80 2.40 . . 42.27 45 1.25 2.40 3.30 IBM 108.90 100 12.00 14.10 18.70 2.20 4.30 7.00 108.90 110 4.40 8.10 11.40 5.30 8.10 10.50 108.90 120 1.10 3.60 7.50 12.20 13.90 15.60 Microsoft 55.19 50 6.50 8.13 10.00 1.19 2.50 4.00 55.19 55 3.00 4.50 6.88 2.69 4.136.00 55.19 60 0.94 2.38 4.50 5.38 6.75 8.13 16 17 18 19 20 21 T-bill rates Expiration date Days to expiration 4.92% 17-3 25 4.85% 21-4 6 0 4.91% 21-7 151 4.92% 17- 3 25 4.85% 2 1-4 60 4.91% 21-7 151 Exhibit 1 ITO'S DILEMMA Weekly Prices and Returns for Duke Energy, IBM and Microsoft 6 Week No Date Prices Duke Enerx IBM Close Close Returns (In Duke Enero IBM Microsoft Microsoft Close 3.57% 4.13% -0.16% 6.87% 7.27% 1.25% 2.18% 1.25% 5.96% 7.20% 1.14% -6.86% 12.25% -4.72% 3.97% 1.39% -3.91% 2.45% 2.83% 1 31-7-00 33.16 115.47 69.13 2 07-8-00 33.58 120.34 72.44 14-8-00 34.32 120.15 71.00 21-8-00 34.75 128.69 70.63 28-8-00 36.89 133.30 70.19 6 04-9-00 39.64 129.19 69.31 7 11-9-00 40.10 124.70 64.19 8 18-9-00 37.44 123.58 63.25 9 25-9-00 42.32 112.35 60.31 10 02-10-00 40.37 115.72 55.56 11 09-10-00 42.00 108.80 53.75 12 16-10-00 42.599 4.52 65.19 13 23-10-00 40.95 93.46 67.69 14 30-10-00 41.97 99.88 68.25 15 06-11-00 43.17 92.89 67.38 16 13-11-0043.83 101.82 69.06 17 20-11-00 42.71 99.82 69.94 18 27-11-0043.33 95.52 56.63 -12.00 42.59 96.89 54.44 2011-12-00 41.06 87.71 49.19 21 18-12-00 41.96 88 90 46.44 22 25-12-0036.2593.8949.13 01-1-01 41.10 84.72 43.38 08-1-01 3 4.83 93.71 25 15-1-01 36.16 11.12 61.00 26 22-1-01 38.24 114.06 64.00 27 29-1-01 37.33 110.14 60.81 28 05-2-01 41.02112.00 59.13 12-2-01 41.16 115.00 57.31 30 19-2-01 42.27 108.90 55.19 -0.81% 4.68% -2.00% -0.53% -0.62% -1.25% -7.68% -1.47% 4.76% -8.20% -3.32% 19.29% 3.76% 0.83% -1.29% 2.47% 1.26% -21.12% -3.94% -10.14% -5.75% 5.63% -12.45% 20.98% 13.12% 4.80% -5.11% -2.81% -3.11% 3.78% -3.14% -3.54% -0.90% -9.52% 2.95% -6.17% -14.07% -1.13% 6.65% -7.25% 9.18% -1.98% 4.41% 1.43% -9.95% 1.34% 5.47% -10.29% 10.09% 17.05% 2.61% -3.49% 1.67% 2.64% -5.45% 1.51% -2.58% 1.44% -1.73% -3.64% 2.17% -14.63% 12.54% -16.55% 3.76% 5.59% -2.42% 9.44% 0.34% 2.66% 23 Weekly Sigma of Returns Annualized standard deviation of retur 6.34% 45.75% 6.69% 48.24% 8.26% 59.56% Oo vou -WN- A B C D E F G H I J Exhibit 2 ITO'S DILEMMA Option Premium and Market Data for February 20, 2001 Call Premiums Put Premiums Mar Apr July Mar Apr July Duke Energy 42.27 40 4.30 5.30 0.75 1.30 2.25 42.27 42.5 2.70 3.90 4.80 2.40 . . 42.27 45 1.25 2.40 3.30 IBM 108.90 100 12.00 14.10 18.70 2.20 4.30 7.00 108.90 110 4.40 8.10 11.40 5.30 8.10 10.50 108.90 120 1.10 3.60 7.50 12.20 13.90 15.60 Microsoft 55.19 50 6.50 8.13 10.00 1.19 2.50 4.00 55.19 55 3.00 4.50 6.88 2.69 4.136.00 55.19 60 0.94 2.38 4.50 5.38 6.75 8.13 16 17 18 19 20 21 T-bill rates Expiration date Days to expiration 4.92% 17-3 25 4.85% 21-4 6 0 4.91% 21-7 151 4.92% 17- 3 25 4.85% 2 1-4 60 4.91% 21-7 151