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April 2015 Qu 8 - Lagranigan

S

s1645544

Active Member
Hi - please could I check my understanding is correct

Below is the equations I am solving:

W = 0.0016X1^2 + 0.0144x2^2 + 0.0064x3^2 - lambda(0.02x1 + 0.04x2 + 0.03x3 - E) - mu(x1 + x2+ x3 -1)
(As I have input e.g. 0.04 in my calculations instead of '4' (meaning 4%) as the solution does)

when I solve this I get
lambda = 0.648
mu = -0.01008

however the answer is
lambda = 64.8
mu = -100.8.

As my answers which are out by different multiples compared to the solution I am not sure if they are correct? I think the reason they are out by different multiples is to do with squaring the standard deviation to get the variance, therefore the difference of '100' changes to a difference of '1000' (because I have constructed my equation as 0.04 and the solution has constructed their equation as '4' (%)?

Thanks in advance
 
Yes, this is all fine. You will get different answers depending on the units you use.

In fact, because the Lagrangian function is a mixture of units, you can get different Lagrangian multipliers (and not just obviously out by factors of 10), I believe depending on your method. But they all end up at the same efficient frontier

John
 
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