Does true courage always require putting something valuable to you at risk?

This is, of course, a matter of opinion.  I would argue
that true courage always does require putting something valuable to you at risk. 
However, I would emphasize that I do not think that the thing you put at risk must be
something physical.

Of course, it takes courage to put
one's body or life at risk.  However, this sort of physical courage is not the only
sort.  It also takes, for example, a great deal of courage to go against the desires of
one's friends.  In this case, you are not putting yourself at risk of physical harm. 
Instead, you are risking the loss of your status in the eyes of your friends.  This is a
major risk and it is a form of true courage.

If you are not
risking anything of much value to you, you are not showing courage because there is no
danger of any sort to you.  Courage consists of risking the loss of something valuable
in order to try to do what you think is right.