The price of a share of a particular stock listed on the New York Stock Exchange

Question

The price of a share of a particular stock listed on the New York Stock Exchange is currently $44. The following probability distribution shows how the price per share is expected to change over a three-month period:

Stock Price Change ($)/ Probability

-4/.05

-3/.05

-2/.10

-1/.25

0/.20

1/.15

2/.20

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

-4/.05/__ but less than__

-3/.05/__but less than__ -

2/.10/__but less than__

-1/.25/__but less than__

0/.15/__but less than__

+1/.15/__but less than__

+2/.20/__but less than__

b. With the current price of $44 per share and the random numbers 0.4527, 0.1923, 0.4529 and 0.5823, simulate the price per share for the next four 3-month periods.

Random number/Price Change/Ending Price per Share

.4527/__/$__

.1923/__/$__

.4529/__/$__

.5823/__/$__

What is the ending simulated price per share?

$__

Explanation / Answer

We need to assign the random numbers in a way that the number of random numbers in an interval divided by the total number of random numbers of 2 digits i.e. 100 is equal to the probability for that event.

e.g. for the first case a change of -4 is associated with prob of 0.05. So the interval should be 00 to <05 i.e. one of the random numbers 00,01,02,03,04 - so 5 random numbers out of 100, hence the probability of that event is 5/100 = 0.05.

Proceeding in this way we can complete the table as follows:

Change Prob. lower bound upper bound (equality on both lower and upper bound)

-4 0.05 00 04

-3 0.05 05 09

-2 0.10 10 19

-1 0.25 20 44

0 0.20 45 64  

1 0.15 65 79

2 0.20 80 99

Lets consider each random number after multiplication by 100 to give 2 digit random numbers and then compare with the above table to determine the change that will be affected on the share price:

45.27 / 0 / $4

19.23 / -2 / $2

45.29 / 0 / $2

58.23 / 0 / $2

So the ending price of the simulated share price is $2

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