Consider the following probability distribution of returns estimated for a propo
ID: 2674416 • Letter: C
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?
Explanation / Answer
a) Expected rate of return on the project =pi X Ri
Expected rate of return on the project =.1*-10 +.2*0+.4*10+.2*20+.1*30 = 10%
b) Standard deviation = (pi*(x-)^2)
= (.1*(-10-10)^2 + .2*(0-10)^2 + .4*(10-10)^2+ .2*(20-10)^2+ .1*(30-10)^2)
= 10.95 %
c) coefficient of variation = / = 10.95/10 =
CV = 1.095
d) Standard deviation measures investment risk in terms of the volatility of returns.
CV measures how much risk is assumed in comparison to the amount of return expected from investment.
e) these risks are relevant when market is volatile.
CV = 1.095