You're better off going more offensively. After ROA, Seraphs/Archangels, and Void if they are building MR, Ryze did well buyng Luden's Echo because he could proc it so often. But now, I think Deathcap would be better. I finalize the build with a defensive item, usually GA.
Final build looks like this:
other options that work: 
or: 
or if the enemy team has no CC: 
= kite city.
Basically your core items are RoA, Tear, and Void. You then get a high AP item to give you more damage, Rabadon's is looking better now that Luden's is getting nerfed in the next patch but I would usually get Luden's over Deathcap on the last few patches. 1 defensive item is basically all you need on Ryze as his shield and spell vamp will keep you alive through sustained damage and your high HP will keep you alive through burst, really just grab what you think will help you the most situationally; sometimes you can go full offense and not get punished for it. I highly recommend Merc's as they help you from getting kited or CC'd down during your passive. You can still get FH in some situations but it's no longer core for Ryze, and Randuin's will generally give you more effective HP and it does similar things. I would only get FH against a high AD comp WITH Kalista as lowering her AS is very important in catching her, and even then Randuin's can help you there as well.
A few situational items: 
for hella spell vamp, 
same here, 
for a cleanse and helps you with mana (not very recommended as Banshee's can protect you from some CC and gives better stats), 
it's pretty good as you are usually within the aura range with your spells, combines with your E shred and gives decent stats for the price; problem is you must rush RoA and AA staff so you won't be buying this til later, in which case Void is usually a better choice. Still, grab it if you have a lot of magic damage on your team and they have some meaningful magic damage on their team as well (barring your midlaner/jungler have not bought the item already). 
will still be good for it's stats and the passive proc adds to your burst but it will be a lot harder for Ryze to get multiple procs off in a fight now that it has been nerfed (5.11). 
I don't like but if you proc it while your passive is down and you are about to get destroyed it can be a lifesaver; build if you are getting focused hard. 
meh. It can help you engage, but a second RoA is better, build only if you are your team's main engage tool, and if that is the case, may God have mercy on your soul. 
can help if you are sieging as Ryze sucks at this, but the stats aren't great for him. 
DO NOT BUY THIS ITEM. It is absolute trash on Ryze. I would rather see 
on Ryze but spell blade items are pretty bad on him.
I think that covers it though. Ryze will be getting nerfed in his W soon so we'll see what happens to Ryze. He needs the nerf, but hopefully he can stay relevant. I liked where he was before the Passive change (3-->6 seconds) because right now he is kinda cheap to play. Perma root early game is a pretty big problem. Anyway. Good luck out there.
on 
. The CDR is wasted as if you get the 5% cdr in offense, you hit 35% passively. If not and you do something like a 0/17/13 build with him, you still go over by 20%. Aren't there easily better items for him?
In particular with 