By the time ... I will have been traveling ...?

By the time I am 40 signifies the end of an action - it includes everything up to that point. It is therefore difficult to use it with the present perfect continuous unless you want to emphasise the passage of a period of time: "By the time I am 40, I will have been traveling for 30 years without a break."

For your purposes, this is correct:

"By the time I am 40, I will have traveled around the world, eaten one hundred cakes, driven a thousand miles, flown a jet fighter ..."

You're correct. The first sentence means at 40, I will have started traveling already and am still traveling at 40.

"By the time I am 40, I will have travelled around the World."

"I will have traveled around the world by the time I am 40" is correct, or else put in a modification for how much traveling you have done by then.

Technically it is incorrect, and it sounds awkward, besides. You expect it to be followed by an amount of time - ie. "traveling around the world for three months" to express that the travel is still ongoing. As an alternative, you could use:

"By my fortieth birthday, I will have traveled the world."

the later is correct i believe.

i think if you said "By the time I am 40, I will have been traveling around the world" traveling being a verb make it like your doing that at the present time.

"By the time I am 40" = Future tense

"Have been" = Past tense

So, it has to be "will have", because "will have" is future tense.

you can't say "have been", because those are conflicting tenses.