Question

An investment firm wants to limit its losses by diversifying. It is considering three investments. You can assume that each investment follows a normal distribution and is independent of each other.
Investment 1: mean = $6 million; standard deviation = $6.9 million
Investment 2: mean = $1 million; standard deviation = $1.03 million
Investment 3: mean = $9 million; standard deviation = $8.55 million
If the firm invests an equal amount of money in each of the three investments, what is the probability the investment firm loses money from these investments?

Answer 1

Let A, B and C represent Investment 1, Investment 2 and Investment 3.

Let X = A + B + C

the probability the investment firm loses money from these investments is given by: P(X<0).

Mean () of X is given by:

= 6 + 1 + 9 = 16

Standard deviation () is given by:

To find P(X<0):

Z = (0 - 16)/11.0351

= - 1.4499

Table of Area Under Standard Normal Cuve gives area = 0.4265

So,

the probability the investment firm loses money from these investments = 0.4265