Suppose you have a project that has a 09 chance of tripling

Suppose you have a project that has a 0.9 chance of tripling your investment in a year and a 0.1 chance of halving your investment in a year. What is the standard deviation of the rate of return on this investment?

Solution

standard deviation of the rate of return on this investment is

x=3 with probability 0.9

x=0.5 with probablity 0.1

Let X is the rate of return on this investment

E(X)=0.9*3+0.1*1/2

      =2.75

E(X²)=9*0.9+0.25*0.1=8.125

Var(X)=8.125-7.5625=0.5625

SD=sqrt(Var(X))=0.75