Python 2.7 <strike>56</strike> <strike>58</strike> <strike>56</strike> <strike>51</strike> 50
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With the stolen [Number One Dime](http://disney.wikia.com/wiki/Number_One_Dime) from [Scrooge McDuck][1], I made my fortune and now have more wealth than Scrooge.

    y=lambda s:2*abs(sum((1j)**(ord(i)%15)for i in s))

Python 2.7 - <strike>61</strike> <strike>53</strike> 52 (case insensitive)
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    y=lambda s:2*abs(sum((1j)**(ord(i)%16%9)for i in s))

**Implementation**

    >>> from random import sample
    >>> y=lambda s:2*abs(sum((-1j)**(ord(i)%15)for i in s))
    >>> path=sample('RLUD'*1000, 100)
    >>> y(path)
    20.0
    >>> path=sample('RLUD'*1000, 100)
    >>> y(path)
    34.058772731852805

  [1]: http://en.wikipedia.org/wiki/Scrooge_McDuck