Question

Over a five-year period, the quarterly change in the price per share of common stock for a major oil company ranged from -8% to 12%. A financial analyst wants to learn what can be expected for price appreciation of this stock over the next two years. Using the fiveyear history as a basis, the analyst is willing to assume that the change in price for each quarter is uniformly distributed between -8% and 12%. Use simulation to provide information about the price per share for the stock over the coming two-year period (eight quarters).

(a)	Use the random numbers 0.52, 0.99, 0.12, 0.15, 0.50, 0.77, 0.40, and 0.52 to simulate the quarterly price change for each of the eight quarters.
	If required, round your answers to one decimal places. For those boxes in which you must enter subtractive or negative numbers use a minus sign. (Example: -300)

Quarter	r	Return %
1	0.52	%
2	0.99	%
3	0.12	%
4	0.15	%
5	0.5	%
6	0.77	%
7	0.4	%
8	0.52	%

Answer 1

We assume that the change in price for each quarter is uniformly distributed between a=-8% and b=12%.

To simulate random numbers from a uniform distribution in the interval (a,b) we use the following steps

• Generate r, a random number from uniform distribution in the interval (0,1)
• a+(b-a)*r is a random number generated from a uniform distribution in the interval (a,b)

We can do the following calculations, knowing that r is drawn from uniform(0,1)

Quarter	r	Return %
1	0.52	-8+(12-(-8))*0.52=2.4
2	0.99	-8+(12-(-8))*0.99=11.8
3	0.12	-8+(12-(-8))*0.12=-5.6
4	0.15	-8+(12-(-8))*0.15=-5
5	0.5	-8+(12-(-8))*0.5=2
6	0.77	-8+(12-(-8))*0.77=7.4
7	0.4	-8+(12-(-8))*0.4=0
8	0.52	-8+(12-(-8))*0.52=2.4

ans:  the simulated quarterly price change for each of the eight quarters is

Quarter	r	Return %
1	0.52	2.4%
2	0.99	11.8%
3	0.12	-5.6%
4	0.15	-5%
5	0.5	2%
6	0.77	7.4%
7	0.4	0%
8	0.52	2.4%