This is stat question I am having trouble with, can someone please help explain how to do this?

Question

Here is the question

$1 in a stock yeilds Rs, $1 in a bond yeilds Rb

Rs is random with a mean .08 and SD of .07

Rb is random with a mean .05 and SD of .04

Correlation of Rs and Rb is .25

If you place a fraction w of your money in the stock fund and the rest, 1-w, in the bond fund, then your return on you investment is

R=wRs+(1-w)Rb

A. Suppose that w=.5 Compute the mean and SD of R.??
B Suppose that w=.75 Compute the mean and SD of R.??
C What value of w makes the mean of R as large as possible? What is the SD of R for this value of w?
D. What us the value of w that minimizes the SD of R??

Answer 1

This is your homework!....anyway...look for capital structure calculations and the CAPM model

Answer 2

This is a finance question, so there's probably a good example in your text.

In pure statistics, you have two random variables, Rb and Rs, which relate to rates of return. In all truth, rates of return aren't randomly selected, but are determined by a process that cannot be easily understood nor that exhibit a pattern (distribution) that can be easily modeled. As such, it is useful to present them as random variables.

Because R is composed of Rs and Rb, R behaves like a random variable, and therefore a mean and standard deviation can be computed. These are parts A and B.

Part C is an optimization problem. Finding the standard deviation should be a matter of algebra.

Part D is also an optimization problem.