I would like to craft a ring continuously giving it the effect of the level 1 spell shield. Is it possible?
How much would it cost?
Base Cost: 16,000 gp to 20,000 gp
The first step to pricing an item is to consider items with similar effects and what they cost.
Shield grants a +4 shield bonus to AC, which is roughly comparable to a +4 armor bonus to AC. Bracers of armor +4 would cost 16,000 gp, so that is a minimum of what this ring should cost. Shield also has some minor side-benefits with respect to magic missile and stacks with armor without taking up a hand, so some price premium would not be unreasonable (though probably not very much; I’d put 20,000 gp as the highest reasonable price).
Note that the item pricing guidelines suggest that a continuous 1st-level spell effect with a duration measured in minutes should cost
spell_level × caster_level × 2,000 gp × 2 = 1 × 1 × 2,000 gp × 2 = 4,000 gp
These are, however, guidelines, and explicitly stated to take backseat to simply having a decent item to compare to. Thus, the 16,000 gp is a more appropriate price than 4,000 gp.
Cost to craft: 1 feat, 1 spell, 50% in gp, 4% in XP, 0.1% in weeks
To craft this ring yourself requires that you have the Forge Ring feat, the shield spell (which you’ll have to prepare and expend each day you work on the ring), and it will require raw materials that cost half what the ring does. You’ll lose 1/25 (4%) the base cost in XP, and it will take a week for each 1,000 gp in the base cost.
This means it will take 8,000 gp to 10,000 gp, 640 to 800 XP, and 16 to 20 weeks.
There is an existing magic item that gives you a +2 shield bonus and costs 8,500 GP: the Ring of Force Shield.
This means that Wizard's price a Shield bonus magic item at 2125 times the bonus squared. So a +4 item would cost 34,000.
Apologies for blatantly stealing the last part of Dan's answer.
We also need to account for the cost of the Magic Missile immunity. A Brooch of Shielding produces a slightly weaker effect for 1500gp. The rules say that, if we add a second effect to an existing item, the cost of the second effect is multiplied by 1.5, so we should add +2250gp to the cost, for a total of 36,250gp.
However, the Shield spell behaves slightly differently to the Ring of Force Shield in that it explicitly states that it protects you against incorporeal touch attacks. This would have to be priced in seperately, but considering the Ring of Deflection and Amulet of natural armour are the same, there is precedent that this is not priced as high as it should be considering how powerful it is.
There are no rings matching that description in the Dungeon Master's Guide. You could follow the rules for creating and pricing a custom magic item, but this would require DM approval, and your DM would have the final say on the price.
The item you describe would grant a +4 shield bonus to AC, which is much better than a +4 armor bonus to AC, because it stacks with your existing armor. The rules say that an "AC bonus(other)" should cost 2500gp times the bonus squared, which is 40000gp.
We also need to account for the cost of the magic missile immunity. A brooch of shielding produces a slightly weaker effect for 1500gp. The rules say that, if we add a second effect to an existing item, the cost of the second effect is multiplied by 1.5, so we should add +2250gp to the cost, for a total of 42250gp.
In general, if you're just trying to get a mechanical combat advantage (such as better armor, more damage, etc), it's not in good taste to try to do that by asking the DM to approve custom magic items for you. It's better to use the preexisting magic items, such as the ring of protection and amulet of natural armor.