2.Variance: sum all ...probability of return(return - E(r))^2
3.Std. deviation = square root of variance
4.coefficient of variation: std. dev. / E(r)
Rate of Return
Probability
-20%
0.25
0%
0.30
+20%
0.25
+40%
0.20
where * = multiply...
1) (0.25*-0.20) + (0.30*0) + (0.25*0.20) + (0.20*0.40) = 0.08
2) 0.25(-0.20-0.08)^2) + 0.30(0 - 0.08)^2 + 0.25(0.20 - 0.08)^2 + 0.20(0.40 - 0.08)^2 = variance
for the "order" of these...e.g. for the first one (-0.20-0.08) = -0.28, then square...-0.28^2 = 0.0784, then multiply by the probability 0.25*0.0784 = 0.01960...do this for each and then add them together to get the variance
3) variance^1/2 = std dev.
4) cv = answer in #3 / 0.08
see the link for an example
Phoenix Company common stock is currently selling for $20 per share. Security analysts at Smith Blarney have assigned the following probability distribution to the rate of return on Phoenix stock one year from now:
Rate of Return
Probability
-20%
0.25
0%
0.30
+20%
0.25
+40%
0.20
Assuming that Phoenix is not expected to pay any dividends during the coming year, determine the coefficient of variation for the rate of return on Phoenix stock. (Points : 3)
0.0
2.68
2.61
0.275
