Question

Suppose the following distribution describes the possible returns from a portfolio in 1 year: there is a 32% chance of the portfolio return being -1%, a 21% chance the portfolio return is 5%, otherwise the portfolio return is 9%. What is the standard deviation of the return on this portfolio? (please express your answer as a percentage and use 2 decimal places)

Answer 1

X	P(X)	X*P(X)	X² * P(X)
-1	0.3200	-0.32	0.320
5	0.2100	1.05	5.250
9	0.4700	4.23	38.0700

mean = E[X] = Σx*P(X) =            4.96000
          
E [ X² ] = ΣX² * P(X) =            43.6400
          
variance = E[ X² ] - (E[ X ])² =            19.0384
          
std dev = √(variance) =            4.36 (answer)