Problem 12-05 (Algorithmic) The price of a share of a particular stock listed on
ID: 3295354 • Letter: P
Question
Problem 12-05 (Algorithmic) The price of a share of a particular stock listed on the New York Stock Exchange is currently $39. The following probability distribution shows how the price per share is expected to change over a three-month period: Stock Price Change ($) Probability 0.15 0.10 0.25 0.10 0.20 0.15 0.05 -4 -2 a. Set up intervals of random numbers that can be used to generate the change in stock price over a three-month period. If required, round your answers to two decimal places. Stock Price Change Probability Interval 0.15 0.10 0.25 0.10 0.20 0.15 0.05 but less than but less than but less than but less than but less than but less than but less than -4 -3 -2 b. With the current price of $39 per share and the random numbers 0.8091, 0.8941, 0.8917 and 0.9459, simulate the price per share for the next four 3-month periods.Explanation / Answer
Part (a)
Price Change
Probability
Cumulative Probability
Random Numbers
- 4
0.15
0.15
00
but less than
15
- 3
0.10
0.25
15
but less than
25
- 2
0.25
0.50
25
but less than
50
- 1
0.10
0.60
50
but less than
60
0
0.20
0.80
60
but less than
80
+ 1
0.15
0.95
80
but less than
95
+ 2
0.05
1.00
95
but less than
100
Note:
Two digit random numbers are preferred because all probability figures are 2-digit numbers.
ANSWER
Part (b)
Random
Number
Price Change
Ending Price
Note for understanding
Price change belongs to
Ending Price
0.8091
+ 1
40
[80 – 95)
39 + 1
0.8941
+ 1
41
[80 – 95)
40 + 1
0.8917
+ 1
42
[80 – 95)
41 + 1
0.9459
+ 1
43
[80 – 95)
42 + 1
So, the ending price = $43 ANSWER
Price Change
Probability
Cumulative Probability
Random Numbers
- 4
0.15
0.15
00
but less than
15
- 3
0.10
0.25
15
but less than
25
- 2
0.25
0.50
25
but less than
50
- 1
0.10
0.60
50
but less than
60
0
0.20
0.80
60
but less than
80
+ 1
0.15
0.95
80
but less than
95
+ 2
0.05
1.00
95
but less than
100