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62

Изменение ОЛ

Среднее значение % изменения

Количество изменений

к = (а*Ь) / 2

z = x*f

-3.00%

-2.90%

-3.00%

-2.95%

-67.85%

-2.98%

8.89%

205.49%

-2.80%

-2.90%

-2.85%

-71.25%

-2.88%

8.31%

208.66%

-2.70%

-2.80%

-2.75%

-71.50%

-2.78%

7.74%

202.25%

-2.60%

-2.70%

-2.65%

-71.55%

-2.68%

7.19%

19523%

-2.50%

-2 60%

-2.55%

-96.90%

-2.58%

6.67%

254 72%

-240%

-2 50%

-2.45%

-117.60%

-2.48%

6.16%

297.37%

-2.30%

-2.40%

-2.35%

-110.45%

-2.38%

5.67%

26a25%

-2.20%

-2.30%

-2.25%

-112.50%

-2.28%

521%

261 98%

-2.10%

-2.20%

-2.15%

-98.90%

-2.18%

4.76%

220 43%

-2.00%

-2.10%

-2.05%

-133.25%

-2.08%

4.33%

28366%

-1 90%

-2.00%

-1.95%

-159.90%

-1.98%

3.93%

324.41%

-1.80%

-1.90%

-1.85%

-162.80%

-1.88%

3.54%

314.02%

-1.70%

-1 80%

-1 75%

-159.25%

-1.78%

3.18%

291.26%

-1.60%

-1.70%

-1.65%

-229.35%

-1.88%

2 63%

396.54%

-1.50%

-1.60%

-1.55%

-207.70%

-1.58%

2.50%

338.35%

-1.40%

-1.50%

-1.45%

-243.60%

-1 48%

2.20%

372.49%

-1.30%

-1.40%

-1.35%

-270.00%

-1.38%

1.91%

385.88%

-1.20%

-1.30%

-1.25%

.30a75%

-1 28%

! 64%

410.42%

изменений индекса DJI очень похож на нормальное распределение, поэтому мы будем исходить из закона нормального распределения.

Рисунок 3.17 Фактическое распределение вероятностен дневных изменений фондового индекса DJl с 04 января 1915г. по 27 августа 1999 года



-1.10%

-1.20%

-1.15%

-300.15%

-1.18%

1.40%

369.00%

-1.00%

-1.10%

-1.05%

-338.10%

-1.08%

1.17%

381.89%

-0.90%

-1.00%

-0.95%

-352.45%

-0.98%

0.96%

36Z91%

-0.80%

-0.90%

-0.85%

-387.60%

-0.88%

0.78%

360-41%

-0.70%

-0.80%

-0.75%

-384.00%

-0.78%

0.61%

318.76%

-0.60%

-0.70%

-0.65%

-391.30%

-0.68%

0.47%

285.81%

-0.50%

-0.60%

-0.55%

-358.60%

-0.58%

0.34%

226.22%

-0.40%

-050%

-0.45%

-352.80%

-048%

0.23%

187.50%

-0.30%

-0.40%

-0.35%

-304.85%

-038%

0.15%

131.82%

-0.20%

-0.30%

-025%

1081

-270.25%

Ч).28%

0.08%

90.31%

-0.10%

-0.20%

-0.15%

1128

-169.20%

-0.18%

0.03%

40.31%

0.00%

-0.10%

-0.05%

1419

-70.95%

-0.08%

0.01%

11.25%

0.10%

0.00%

0.05%

44.70%

0.02%

0.00%

0.11%

0.20%

0.10%

0.15%

1237

185.55%

0.12%

0.01%

15.23%

0.30%

0.20%

0.25%

1065

266.25%

0.22%

0.05%

47.40%

0.40%

0.30%

0.35%

1034

361.90%

0.32%

0.10%

99.99%

0 50%

0 40%

0 45%

426.15%

0.42%

0.17%

159.94%

0.60%

0.50%

0.55%

451.55%

0.52%

0.27%

214-35%

0.70%

0.60%

0.65%

463.45%

0.62%

0.38%

266.15%

0.80%

0.70%

0.75%

439.50%

0.72%

0 52%

296.21%

0.90%

0.80%

0.85%

4S9.6S%

0.82%

0.67%

355.80%

1.00%

0.90%

0.95%

454.10%

0.92%

0.84%

39667%

1.10%

1.00%

1.05%

428.40%

1-02%

1.04%

417.00%

1.20%

1.10%

1.15%

376.05%

1.12%

1.25%

403.60%

1.30%

1.20%

1.25%

323.75%

1.22%

1.48%

379.81%

1.40%

1.30%

1.35%

299.70%

1.32%

1.74%

381.54%

1.50%

1.40%

1.45%

266.80%

1.42%

2.01%

366.31%

1.60%

1.50%

1.55%

243 35%

1.62%

2.30%

358.43%

1.70%

1.60%

1.65%

240.90%

1.62%

2.62%

378.90%

1.80%

1.70%

1 75%

215.25%

1.72%

2.95%

360.07%

1.90%

1.80%

1.85%

177.60%

1.82%

3.31%

314.84%

2.00%

1.90%

1.95%

150.15%

1.92%

3.68%

281.19%

2.10%

Z00%

2.05%

141.45%

2.02%

4.07%

279-03%

2.20%

2.10%

2.15%

12470%

2.12%

4.49%

258.46%

2.30%

2.20%

2.25%

130.50%

2.22%

4.92%

28353%

2.40%

2.30%

235%

96.35%

2-32%

5-37%

21896%

2.50%

2.40%

2.45%

102.90%

2.42%

5.85%

244.14%

2.60%

Z50%

2.65%

94.35%

252%

6.34%

233.28%

270%

2.60%

2.65%

79.50%

2.62%

6.85%

204 51%

2.80%

2.70%

2.75%

44.00%

2.72%

7.39%

117.59%

2.90%

2.80%

2.85%

48.45%

2.82%

7.94%

134.33%

3.00%

2.90%

2.95%

44.25%

2.92%

8.52%

127.11%

3.10%

Сумма

20701

808.06%

16592.09%

Среднее значение

0.04%



Найдем вероятность роста фондового индекса DJI на 1% и более, лля чего в том числе необходимо рассчитать среднеарифметическое значение данного ряда и стандартное отклонетие. Так как ряд интервальный, то для расчета стандартного отклонения примшим формулу (3.11).

808 05%

Средневзвешенное: Т = -=--- = 0.04%

20701

Сумма разности квадратов: /,{х, ~ 15592.09%

ft 15592.09% Дисперсия. --=-=0.75%

20700

Стандартное отклонение: сг=

--=0.87%

Зная средаеарифметическое и стандартное отклотения ряда можно определить искомую вероятность роста фондового индекса DJI на 1% и более.

х-а 1%-0.04%[

= 1.11

сг 0.87%

По таблице находим значение вероятности, соответствующее полученной величине z: О 1335 или 13.35%.

Если сравнить это значение вероятности с фактической вероятностью данного события, полученной на основании эмпирических данных суммарной вероятности за прошлый пфнод (12.33%), то ввдно достаточно точное соответствие этих величин.

Используя Z можно получать доееритепьные пределы. Последние определяют верхнюю и нижнюю границу интервала от среднеарифметического значения ряда, в котором находится необходимое количество значений ряда. Доверительные пределы используются, кода есть величина необходимой вероятности, ио неизвестно значение интервала, при 1«ггором возможно получить эту вероятность.

Например.

Для приведенной выше совокупности значений изменений фондового индекса DJI необходимо найти те крайние границы интервала, с тем, чтобы в него поместилось 90% всех значений ряда.

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