Is there a long and hilly way round?

Cycling lends itself to the wandering mind. Similar to ear worms some ideas emerge that have a stickability to them. Ideas which are good for pondering on over a few miles. One of these is the question: on a route starting and ending at the same point is the elevation the same regardless of which way you might choose to ride round?  
Intuition tells me that elevation and distance should be very close to equal. Every uphill section in one direction is a downhill section in the other direction. Elevation changes must balance out. The distance remains the same in either direction as you're following the same route, just in reverse order. Seem obvious?

I was not convinced for a long time. I needed to test this out. I finally did over the past couple of days.

Clockwise

Anti Clockwise

Looks like my intuition was right albeit there is a slight difference in elevation and distance. I'm putting that down to GPS anomalies and/or minor unavoidable changes. There's two or three roundabouts and a one way section where the road one way is a little different to the one going the other way.