How do I make a TextBox always align to the right, even if the text is clipped?

I have a Windows.Forms.TextBox with TextAlign = HorizontalAlignment.Right. This works when the text is short enough, however when the text is too long to fit in the box, the alignment appears to revert to left-aligned.

How can I make the TextBox always align its text to the right margin, even if the text is too long for the text box?