Question

1. Given 2 projects, their probability distribution and their possible returns for various states of the economy, your task is to choose one of them for investment.

State of the Economy	Probability of occurrence of state of economy (Pi)	Profit of project A if state of economy occurs	Profit of project B if state of economy occurs
BOOM	0.2	600	1000
NORMAL	0.6	500	500
RECESSION	0.2	400	0

The investor is expected to select the project that is less risky. In this case the project with the lowest standard deviation will be selected. Therefore, compute the standard deviation of each project.

Answer 1

State of the economy	Probability of occurrence of state of economy	Profit of project A if state of economy occurs	Probability*Profit	(Profit - Expected profit)^2
BOOM	0.2	600	120	10000
NORMAL	0.6	500	300	0
RECESSION	0.2	400	80	10000
		SUM	500	20000
The expected profit for project A is 500.
The variance for project A is (Profit - Expected profit)^2
The variance for project A is 20000.
Standard deviation = (20000)^(.5)
Standard deviation = 141.42.
The standard deviation for project A is equal to 141.42.
State of the economy	Probability of occurrence of state of economy	Profit of project B if state of economy occurs	Probability*Profit	(Profit - Expected profit)^2
BOOM	0.2	1000	200	250000
NORMAL	0.6	500	300	0
RECESSION	0.2	0	0	250000
		SUM	500	500000
The expected profit for project B is 500.
The variance for project B is (Profit - Expected profit)^2
The variance for project B is 500000.
Standard deviation = (500000)^(.5)
Standard deviation = 707.11
The standard deviation for project B is equal to 707.11.
Project A is less risky because the standard deviation for project A is less than the standard deviation of project B.