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Deriving the Mean Reverting Level Formula

Hey everyone,

i am using the Schweser notes to study for the CFA level 2 exam next June and am having a bit of trouble understanding how to derive equations algebraically by isolating variables in a ‘root’ equation.  

For example the mean reverting formula is:

b0/(1-b1)

The root formula is:

Xt+1= b0 + b1Xt

where Xt+1 = Xt

Can someone explain the algebraic process to get from the root formula to the derived formula.  Please explain as if you were communicating with a 2 year old.

Appreciate the help!

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Xt+1 = Xt

Xt+1 = b0 + b1 xt

so xt = b0+b1xt

xt - b1 xt = b0

or

xt (1-b1) = b0

so xt = b0/(1-b1)

CP

Note that we now have subscripts.

I edited the two previous posts to incorporate them; they make the formulae much easier to read.

Simplify the complicated side; don't complify the simplicated side.

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Maxwell Calgary wrote:

Hey everyone,

i am using the Schweser notes to study for the CFA level 2 exam next June and am having a bit of trouble understanding how to derive equations algebraically by isolating variables in a ‘root’ equation.  

For example the mean reverting formula is:

b0/(1-b1)

The root formula is:

Xt+1= b0 + b1Xt

where Xt+1 = Xt

Can someone explain the algebraic process to get from the root formula to the derived formula.  Please explain as if you were communicating with a 2 year old.

Appreciate the help!

Greetings Maxwell,

The mean reverting process is a long-term one, this means that a time-series will eventually revert to its “mean” in the long-term.

In that assumption, you can logically say that any pair of contiguous data points are really close to each other. So Xt = Xt-1

You can now derive for Xt as cpk123 did above.

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Hey guys. I got it!  Thx a lot for the help. Really appreciate it.