# How to interpret Risk Parity Formula

Hello,

How do you interpret the formula of Risk Parity. It has a “inverted 6” in the numerator and denominator. What do they mean?

Thanks for the help.

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I’ve never seen the formula (because I’ve never looked at the CAIA curriculum), but I suspect that the “inverted 6” to which you refer is properly known as a “roundback d” and looks like this: ∂.

If so, it’s the symbol for a partial derivative: a concept from multi-variable calculus.

The short answer is that you look at the variable after the ∂ in the numerator and the variable after the ∂ in the denominator.  The expression means how fast the former changes when the latter changes, keeping all other variables fixed.

For a simple example, consider the formula:

d = rt

(Distance equals rate times time.)

The expression:

d/∂r

means “how fast distance changes when the rate changes, holding time constant”.  It’s known as the partial derivative of distance with respect to rate.

Similarly, the expression:

d/∂t

means “how fast distance changes when time changes, holding the rate constant”.  It’s known as the partial derivative of distance with respect to time.

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

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