# expected return on stocks

#### Tascja

##### New member
Suppose an individual has $14,000 to invest and decides to put$1000 in each of 14 stocks picked at random from a large group listed on the local stock exchange. the mean return of the stocks in the group is 10% per year and the variance of the returns of the stocks in the group is 4% per year.

a)Calculate the expected return and variance of the 14 stock portfolios.
... do i have to break down the mean return and variance for each group?

b)Calculate a 90% confidence interval for the portfolio return.

:? any help with equations, i really appreciate your time.

thank you.

#### tkhunny

##### Moderator
Staff member
Sure, break it down, but eventually you will see that with equal variances it will make no differences.

How's your independence assumption?

#### Tascja

##### New member
what is an independence assumption?

can you give me some direction of how to start to find the expected return and variance?
is my N = 14,000 and my n = 1,000?

i know how to do the confidence interval but i dont know where to start to find the expected return or variance.

thank you,
tascja

#### tkhunny

##### Moderator
Staff member
You should have these:

$$\displaystyle E[nX] = nE[X]$$

$$\displaystyle Var(nX) = n^{2}Var(X)$$

Are we ringing any bells, yet?

#### Tascja

##### New member
no, i've not used these before. how do i use these?

#### tkhunny

##### Moderator
Staff member
You have:

For a single stock:

E[X] = 1000*0.10 = 100

Var(X) = 1000*0.04 = 40

For the Entire Portfolio:

n = 14

E[nX] = nE[X} = 14*100 = 1400

Var(nX) = (n^2)Var(x) = (14^2)*40 = 196*40 = 7840

StandardDeviation = sqrt(Variance) = 88.54

Still, I'm a little worried about the Independence of the individual investments.

1) If none of your textbook, teacher, or other course materials has addressed linear combinations of expectation or variance, I have to wonder how they expect you to solve the problem.

2) If you don't have any reference for "independence", I have to wonder what it is you are studying.

A little background might help. Are you sure you have all the prerequisites for this material? Why are you in this material?