Okay, I'm going to post a cool, little conceptual example here for you guys that was relayed to me by a technical guy and close friend from one of the large funds.
You're the type of person that drives in the fast lane on the highway, speeding by everyone, and honking at people who are going slow. That's you. In this example, let's say you're driving 60 mph, while everyone else is driving 10 mph. You're very happy with the 50 mph difference and just whizzing by everyone.
Now all of a sudden, everyone else speeds up to 60 mph. Now you're all driving the exact same speed at 60 mph.
It is a mathematical reality that you are now all driving the same speed and you are not going any faster than anyone else. You cannot change the math on that. It's a stone cold fact of the universe. You're all driving the exact same speed.
Now the only question is, do you care? Well, going back to our first sentence, you're the type of person who likes to drive faster than everyone else, so yes, you care. You really liked whizzing by everyone at 50 mph faster than they were driving, so to get back to that difference, you increase your speed to 110 mph. You're now driving 110 mph, while everyone else is driving 60 mph, so you're now back to whizzing by everyone at 50 mph faster.
However, let's say you don't care. While driving 50 mph faster than everyone was nice, you're really just happy going 60 mph. You don't need to be driving faster than everyone, as long as you maintain 60 mph. In that case, you do nothing, and you're happy driving the same speed as everyone else.
In some cases -- and this is more for the crowd that listens to the whole "you don't need to calculate the yield on that thang, it's good enough!" -- everyone else may even speed up to 80 mph while you continue to drive at 60 mph. You don't care. You don't need to go 80 mph, as 60 mph is good enough, and you're happy with that.
If you understood the above example, then you now conceptually understand why certain concepts (e.g, duration and convexity) will impact your investment. If you want to know more, I'd encourage you to work through the math to see the types of impacts they have. The math is arduous, but it's not rocket science.
Having said that, your personality and investment philosophy will determine whether or not you care if things like convexity and duration impact your investments. Do they impact your investments? Yes, it is a mathematical reality. You cannot change their impact. The only thing you can do is decide if you care or not.
So going back to one of Tim's points, yes, math impacts your investment, no matter what order of derivative you're talking about. It's impactful. Now the only question is, do you care? Maybe you do, and maybe you don't.
As my friend put it, depending on how far you skew towards mom and pop versus investor will probably determine how much you care, not that either one is better than the other.