# Quant analytics: Help with 2:1 leverage formula

(Last Updated On: October 11, 2011)

Quant analytics: Help with 2:1 leverage formula

I am testing a system that calls for using 2:1 leverage when the model is > 3

The problem I am having is when the model is in the 2:1 leverage mode there is a slight tracking error over the intermediate time frame due to compounding.

Can someone recommend a better formula for calculating system equity when testing 2:1 leverage.

Here is the leveraged part of the formula IF(E2=4,((C3*2)+1)*F2

Where
A=date
B=Index
C=rate of change of index
E=The Model
F=System equity

Thanks ahead of time for any recommendations.

do you use Excel? Could you please give your formula in an analytical form, not functional? There’s something in your code that looks strange a bit, so it would be easier to consider it in analytical form and well commented.

yes it is in excel. I have copyed the full formula below. Unfortunately I can’t attach a excel spreadsheet on here. I will try and paste a small section of the spreadsheat though it does format very well. The formula will track the index 2:1 week to week perfectly, but over time it starts to have a slight tracking error. Not by a large amount though.

=IF(E2=2,(C3+1)*F2,IF(E2=0,((D3*0.01)/52+1)*F2,IF(E2=4,((C3*2)+1)*F2,”Not 0, 2, or 4″)))

B C d e g

Where
A=date
B=Index
C=rate of change of index
D=Tibll Rate
E=The Model
F=System equity

let’s put it into an analytical form â€” that’s what I asked you. You
have something like F = F[1] + C * F[1], where F is system equity on the
current bar, F[1] â€” the same on the previous bar and C â€” rate of change on
the current bar. If I got you right, what is the meaning of this formula?

This model switches from t-bills to S&P to 2:1 leverage on the S&P so,
If the model (E) = 0 then buy t-bills
If the model (E) = 2 then Long the S&P with no leverage
If the model (E) = 4 then Long the S&P with 2:1 leverage

OK, do you agree with the analytical form I provided? If yes, what does
this formula mean? If not, what is that you’re trying to implement in
Excel?

B=index
C=(b3-b2)/b2
D= T-bills
E Model Signals ranges from 0-4
f =IF(E2=2,(C3+1)*F2,IF(E2=0,((D3*0.01)/52+1)*F2,IF(E2=4,((C3*2)+1)*F2,”Not 0, 2, or 4″)))

you seem to ignore my efforts to help you. What is the meaning of
multiplying the rate of change by 2 and then adding 1? And then multiplying
it by the previous equity value?

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