The rate of return of an asset is the change in price divided by the initial price (denoted as r ). Suppose that $10,000 is used to purchase shares in three stocks with rates of returns x1 , x2 , x3. Initially, $2500, $3000, and $4500 are allocated to each one, respectively. After one year, the distribution of the rate of return for each is normally distributed with the following parameters:

Step 1 of 4</p>

Let are the rates of returns of three stocks

Here all are following the normal distribution

Then

Let Y be the total rate of return after one year

Then

Step 2 of 4</p>

a) We have to find mean and variance of the rate of return after one year

Now

=0.12+0.04+0.07

=0.23

Variance (Y)=

=(0.14)2+(0.02)2+(0.08)2

=0.0264

Hence mean=0.23 and variance=0.0264