Stocks x, y, and z have expected returns of 7%, 6%, and 10%, respectively, and the following

x y z
x .01 .001 .001
y .001 .04 -.04
z .001 -.04 .08
(a) determine the fraction of the portfolio to hold in each stock so as to minimize the variance of the

portfolio subject to a minimum expected return on the portfolio of 8%. (profolio variance)

(b) can the variance of the portfolio be smaller than the variance of any individual stock? explain.

(c) use the lagrange multiplier information to estimate what would happen to the variance of the

optimal portfolio if the minimum expected return were raised to 9%. compare your estimate with

the actual by resolving the model.

question 1 is 8, question 2 is 9, question 3 is 24

step-by-step explanation:

now, the numbers they give you at the top are the key. from there, you just have to plug and chug! let's try 1, 2, and 3!

key: a=3, b=5, c=6

1. a+5

remember, a=3, so we plug that in to get 3+5=8

2. 15-c

c=6, so we plug that in to get 15-6=9

3. 4b

b=6, so we plug it in to get 4*6=24

time to try the rest on your own! if you put the answers below in a comment, i'll check them for you!

54 km / hours

step-by-step explanation:

we need to convert seconds to hours

60 seconds = 1 minutes

60 minutes = 1hour

15 m         60 second   60 minutes

  * *         = 54000 meters/ hour

second     1 minute             1 hour

now we need to convert meters to km

1000 m = 1 km

54000 m       1 km

*   = 54 km / hours

hour               1000m