Index under sum symbol below following equation

Question

I have a sum symbol with a quite long index underneath. This produces too much space between the following signs.

\begin{equation}
 \sum_{X\leq-VaR_\alpha(X)}{P(X)\cdot x} 
\end{equation}

I would like to see the index to reach under the P(X)x but in a very specific way: The X in the index should be left-aligned with the \sum symbol and any overlap of the index on the right of the symbol should displace the operand.

Is there any way to do this? I don't want to use a two lines index.

Answer 1

Another solution, also provided by the mathtools package, is to use its \smashoperator macro. In fact, by writing \smashoperator[r]{...}, one can arrange that the material overlaps only on the right, rather than on both sides. (Observe that the word "Note" does not overlap with the material below the summation sign.)

Note that I would also create a macro, called (say) \VaR, to typeset the string VaR with upright letters. And, do note that there's no point in encasing P(X)\cdot x in curly braces.

\documentclass{article}
\usepackage{mathtools}
\newcommand\VaR{\mathrm{VaR}}
\begin{document}
\begin{equation}
\text{Note:}\smashoperator[r]{\sum_{X\leq\VaR_\alpha(X)}} P(X)\cdot x  
\end{equation}
\end{document}

---

Addendum to address the OP's follow-up question: You may achieve your typesetting objective by (a) switching to the basic, i.e., centered version of the \smashoperator directive and inserting a suitable "kern" at the start of the subscript material. I know it's not fruitful to argue about tastes, but in my opinion the result of right-shifting the subscript material is anything but good-looking.

\documentclass{article}
\usepackage{mathtools}
\newcommand\VaR{\mathrm{VaR}}
\begin{document}
\[
\text{Note:}\smashoperator{\sum_{\mkern70mu X\leq\VaR_\alpha(X)}} P(X)\cdot x  
\]
\end{document}

Answer 2

You could use \mathclap from the mathtools package:

\documentclass{article}
\usepackage{mathtools}
\begin{document}
\begin{equation}
\sum_{\mathclap{X\leq-VaR_\alpha(X)}}{P(X)\cdot x} 
\end{equation}
\end{document}

edit2: Note, however, as Mico pointed out in the comment, that this also works on the left side. See Mico's answer for a version doing this on the right side only.

edit: A little explanation. \mathclap reduces the width of its content to zero and centers it. So, Latex does not see the true width of the box and shrinks the space to the usual space after a sum. You could use it in conjunction with another box with a specific width, if this looks too tight for you.
Note: There is also \mathrlap and \mathllap available. They don't center their content but put it ragged-right or -left.