Randy, If you have no paperwork at all on purchases, it might be tough to convince an auditor, but you might be able to bargain to an extent. If you sell coins regularly and they aren't a huge part of your income, those sales are unlikely to trigger an audit. I sell a few coins most years and have never been questioned about declared capital gains/losses. Of course, if you get audited for some other reason, the auditor may want proof on the coins too. There can be records other than purchase invoices that can be helpful though. Photos with verifiable dates, records of sending coins for certification, including coins on a statement of assets for a loan, inventory for insurance, and records of exhibiting at a show are examples. Cal
Not if you collect modern proof and mint sets (directly from the mint) and especially of late. The prices for the recent ones have really shot up and there's very little interest for them in the after market.
The work to establish your basis is on you. For something like those mint sets you can pretty easily establish what you paid (mint prices) and a current valuation - gives you your gain (or loss). If you bought a coin in 1969, and you don't have a receipt, you can point to the Red Book for that year or an advertisement from a coin dealer. Those are reasonable ways to establish a basis. You can buy a used Red Book for $5 on fleaBay. IF it gets to an audit (and there are multiple steps before that happens), the auditor will likely accept a reasonable estimate if you can show your work.
Historical prices … Red Book, old catalogs, online sources, back issues of Coin World, etc. … are useful for establishing value on a particular date. But none of that proves when you acquired coins. A coin or set may have gone down in value 80% in the years since it was issued. But if you bought it yesterday and sold it today, your capital loss would be zip. If you don’t have purchase invoices, try to find other records that are reasonable evidence that you owned the coins on past dates. Then if an auditor questions you about basis, hope that they are reasonable too. If you get audited on a specific issue other than coins (has happened to me twice): 1. be very polite, 2. unless it’s small, do not agree to anything during first contact; just gather information, 3. do not mention other items, like coin sales, that were on your return. Consulting a tax accountant is a good idea. There are things that can change your coins’ basis. For example, if the coin collection is community property and your spouse dies, the basis switches from purchase price to the value on the day of the spouse’s death. Cal