Question

Consider the following probability distribution of returns estimated for a proposed project that involves a new ultrasound machine: State of the Probability Rate of economy of occurrence return Very poor 0.1 -10% Poor 0.2 0% Average 0.4 10% Good 0.2 20% Very good 0.1 30% a. What is the expected rate of return on the project? b. What is the project's standard deviation of returns? c. What is the project's coefficient of variation (CV) of returns? d. What type of risk does the standard deviation and CV measure? e. In what situation is this risk relevant?

Answer 1

a. Expected rate of return on the project

State of economy	Probability	Rate of Return(%)	Probability*Rate of Return
Very poor	0.1	10	1
Poor	0.2	0	0
Average	0.4	10	4
Good	0.2	20	4
Very good	0.1	30	3

Expected rate of return = $\sum$ Probability*Rate of Return

= 1+0+4+4+3

= 12%

b. Project's standard deviation of returns

State of economy	Probability	Rate of Return(%)	Deviation from expected return (D)	PD^2
Very poor	0.1	10	-2	0.40
Poor	0.2	0	-12	28.80
Average	0.4	10	-2	1.60
Good	0.2	20	8	12.80
Very good	0.1	30	18	32.40

Variance = $\sum$ PD^2

= .40+28.80+1.60+1.60+12.80+32.40

= 76

standard deviation = $\sqrt{}$ Variance

= $\sqrt{}$ 76

= 8.72

c) Project's coefficient of variation (CV) of returns

Coefficient of variation = Standard deviation / Expected return

= 8.72 / 12

= .7267

= 72.67%

d. What type of risk does the standard deviation and CV measure?

Standard deviation measures the variability of probability distribution with respect to its expected value.Whereas CV measuresan investment's standalone risk. It is helpful in comaparing two alternatives of investment.

e. In what situation is this risk relevant?

Where we need to choose between two alternatives that have same expected return but have different standard deviation, we use CV for decision making.