Prove that E[(˜ r r) 2 ] E(˜ r 2 ) r 2 using the following steps: a. Show the E[(˜ r r) 2 ] E(˜ r…

Prove that E[(˜ r r) 2 ]  E(˜ r 2 ) r 2 using the following steps:

a. Show the E[(˜ r r) 2 ]  E(˜ r 2 2r˜ r r 2 )

b. Show that the expression in part a is equal to

E(˜ r 2 ) 2E(r ˜ r) r 2

c. Show that the expression in part b is equal to

E(˜ r 2 ) 2r 2 r 2

Then add.

Derive a formula for the weights of the minimum variance portfolio of two stocks using the following steps:

a. Compute the variance of a portfolio with weights x and 1 x on stocks 1 and 2, respectively. Show that you get

b. Take the derivative with respect to x of the expression in part a. Show that the value of x that makes the derivative 0 is

c. Compute the covariance of the return of this minimum variance portfolio with stocks 1 and 2.