I need someone to explain to me how this quadratic effect works?

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Biman C.
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Description

Experience Level: Entry
I have built a LMM (using LME4) for understanding how investment fund's structural characteristics (things like how much debt they have, their size etc) impacts upon performance.

In the analysis, I included the variable GAV (which denotes size in USD$), I have also included a quadratic term for GAV to evaluate if size beyond a certain point impacts a fund's performance.

I get the following outputs for the GAV values:

-0.067(GAV) + 0.076(GAV²)

This leads me to believe size has a positive impact upon performance and those larger funds will perform better. However, when I graph GAV's quadratic effect in R, I get the following output: GAV Quadratic Effect

I don't understand why it appears to invert at approx. $5bn. I have researched online and it seems that to have a quadratic effects graph that increases up to a point and then starts decreasing requires the squared term to be negative and the original (non-squared term in this instance just GAV) to be positive?


Also please ignore the title "European Open End Gearing Quadratic Effects" the was copied over from another graph and the title hasn't been updated.

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