Can an Elven Wizard use a bow for an arcane focus?

Question

If an elven wizard had proficiency in a bow, could he use that as his arcane focus?

Answer 1

Going strictly by the Player's Handbook?

No.

If you're allowed to use Xanathar's Guide to Everything?

Yes, with a Ruby of the War Mage.

XGtE introduces a number of common magical items, one of which is the Ruby of the War Mage.

Ruby of the War Mage
Wondrous item, common (requires attunement by a speilcaster)

Etched with eldritch runes, this l—inch-diameter ruby allows you to use a simple or martial weapon as a spellcasting focus for your spells. For this property to work, you must attach the ruby to the weapon by pressing the ruby against it for at least 10 minutes. Thereafter, the ruby can’t be removed unless you detach it as an action or the weapon is destroyed. Not even an antimagic fieid causes it to fall off. The ruby does fall off the weapon if your attunement to the ruby ends.

By attuning to this item and attaching it to his bow, your elven wizard can use his bow as an arcane focus.

Answer 2

Not Per the RAW.

Relevant Excerpts

Spellcasting Focus
You can use an arcane focus (found in chapter 5) as a spellcasting focus for your wizard spells.

D&D Basic Rules V0.1, page 30

Arcane Focus. An arcane focus is a special item—an orb, a crystal, a rod, a specially constructed staff, a wand-like length of wood, or some similar item—designed to channel the power of arcane spells. A sorcerer, warlock, or wizard can use such an item as a spellcasting focus, as described in chapter 10.

D&D Basic Rules V0.1, page 48

Conclusion

The Adventuring Gear table on page 47 lists 5 possibilities for an Arcane Focus (which mirrors the list on page 48): Crystal, Orb, Rod, Staff, Wand. None of these are bows. None of these are even weapons.

Wait, the staff is a weapon, so there's precedent!
Just comparing the Arcane Focus Staff on page 47 to the Quarterstaff on page 45 shows that the Arcane Focus Staff is 25 times more expensive; additionally, the Arcane Focus Staff does not have weapon statistics listed anywhere. These are clearly not the same item. Presumably, the "specially constructed" Arcane Focus Staff is unsuitable for use as a weapon. I would rule that a "specially constructed" bow would have the same limitation.

I don't care about the RAW, what are my options?
You have a lot of options. Here are two:

• First, as @ESR.MourningDove pointed out in her answer, you can embed one of the "defined" Arcane Foci into the weapon you want to use. I particularly like this option (I'm imagining a wizard with an orb or crystal embedded into the end of a staff -- awesome).
• Second, you can simply rule that it's possible to pay to have any item "specially constructed" so it can be used as an Arcane Focus.

Answer 3

Note: This is my second answer on this question. It uses much of the same information as my first answer but comes to a different conclusion. I wanted to make sure that votes for my other answer did not erroneously count against this answer. Both answers feel accurate to me, based on slightly different points of view.

It's not called out, but there's precedent: go for it

Relevant Excerpts

Spellcasting Focus
You can use an arcane focus (found in chapter 5) as a spellcasting focus for your wizard spells.

D&D Basic Rules V0.2, page 30

Arcane Focus. An arcane focus is a special item—an orb, a crystal, a rod, a specially constructed staff, a wand-like length of wood, or some similar item—designed to channel the power of arcane spells. A sorcerer, warlock, or wizard can use such an item as a spellcasting focus, as described in chapter 10.

D&D Basic Rules V0.2, page 47

Analysis

The Adventuring Gear table on page 48 lists 5 possibilities for an Arcane Focus (which mirrors the list on page 47): Crystal, Orb, Rod, Staff, Wand. None of these are bows. None of these even appear to be weapons: initially, I'd rule, "No, it's not possible per RAW."

However, while researching Can the arcane/druidic focus staff double as quarterstaff?, I asked Mike Mearls: "Can the arcane/druidic focus staff double as a quarterstaff?" And received the following response: "yes"

This means that there is precedent for allowing an Arcane Focus as a weapon. Notice, however, that the Arcane Focus Staff is 25 times more expensive than a plain Quarterstaff: make sure your Arcane Focus Bow is significantly more expensive than a regular bow.

Answer 4

I think, going along with what is in the rules for 5e, that if, for example, your bow had a crystal embedded in it's wood, you could use the crystal as your focus, and it would technically be the bow, but still follow rules. Just a suggestion.

Answer 5

An Arcane Foci is an quasi magical object that has been specially tuned for spell casting. Such an item would be specifically and painstakingly attuned to the spell caster. If it is made for the character It would make sense then that any damage, or abnormality to the foci would render it inert. Much like a fighter must maintain his weapon through sharpening and oiling, a mage would have to repair damage (such as re-carving runes damaged in a battle) or purge impure or alien energy before the foci becomes useful again. While a Foci could be used for combat, it would likely be a last ditch effort as repair would take time and money.

Answer 6

The other answers do a good job of answering the possibility of using a (more expensive) bow as an arcane focus (it's a DM call). As far as balance goes, I would allow this, since there's very little benefit to it mechanically. You can hold the bow in one hand and use a component pouch on your belt, accomplishing effectively the same thing.