Let wa and wb be any two distinct minimum-variance portfolio vectors. For suitable constants a and b, these vectors can be expressed in the following form:

wa =(1a)wG +awD, wb =(1b)wG +bwD, where wG and wD are the global minimum-variance and diversified portfolio

vectors, respectively. a) Show that any minimum-variance portfolio vector w can be expressed as

w=1A+b1wa + 1a1Awb.ba ba

b) Show that the covariance is given as follows: 1 AC B2

Cov(RP(wa), RP(wb)) = A + ab AB2 ,

where A = eTV1e, B = TV1e, and C = TV1.

Here is the question, with a hint to the answer.

3.31. Let Wa and w, be any two distinct minimum-variance portfolio vectors. For suitable constants a and b, these vectors can be expressed in the following form where wc and wo are the global minimum-variance and diversified portfolio vectors, respectively a) Show that any minimum-variance portfolio vector w can be expressed as 1- a -X1A Wb. b) Show that the covariance is given as follows: AC - B2 AB2 where A eTV-le, B-1TV-le, and C ,-V-1 Solution 3.31. a) Hint: express wg and wp in terms of Wa and wb, and then insert the expres- sions into b) Hint: insert the matrix expressions of wc and wD into 3.31. Let Wa and w, be any two distinct minimum-variance portfolio vectors. For suitable constants a and b, these vectors can be expressed in the following form where wc and wo are the global minimum-variance and diversified portfolio vectors, respectively a) Show that any minimum-variance portfolio vector w can be expressed as 1- a -X1A Wb. b) Show that the covariance is given as follows: AC - B2 AB2 where A eTV-le, B-1TV-le, and C ,-V-1 Solution 3.31. a) Hint: express wg and wp in terms of Wa and wb, and then insert the expres- sions into b) Hint: insert the matrix expressions of wc and wD into