Holding cash usually means putting it in a bank account. The banks are going to put a significant portion in their country's central bank; the European central bank and member central banks are currently charging banks to store money; at large balances, those banks will charge customers.
Now, you could put cash into a USD account at a US bank, where interest is still currently positive, but if you were storing Euros, you now have currency risk and jurisdiction risk. Negative rate German bonds have less risk than that.
Of course you could take physical cash and put it in a safe or something, but that doesn't scale well. Although maybe it does suggest a lower limit on negative interest rates, where it would actually be cheaper to store large amounts of physical cash...
You have to buy a safe, you have to have a location to store it, you need to secure the location. You need to ensure that the safe is temperature and humidity controlled, so that the currency doesn't mold, rot etc.
These costs add up. Once you've done all of those things, you're essentially a bank.
+this. As a thought experiment, assume you need three full-time guards to store 100M €. Two physical and one watching the video. (why two? Less likely your guard steals all the money).
Salaries of 30k €/year. 8760 hours/year, one FTE works 2080 hours/year, so that's 4.x times 3x redundant guards, or about 500k €/year with overhead.
That's half a percent negative return.
Presumably, the physical storage cost creates a lower bound on how negative the inflation rates can go, but I'm sure I left off a bunch of other things that would add to the bottom line costs of this proposal, such as insurance.
Instead of having a vault with just 100M euros, it probably makes more sense economically to build a huge vault that can store billions of euros, and then charge people to use the vault.
It seems absurd that the cost of storing physical notes should have an impact on workable interest rates. Surely if the government wanted to allow you to sock away vast sums of money, they should provide a secure electronic sock and avoid the destruction of wealth that is your security costs.
And conversely, if they didn't want to provide the bed for you to keep your money under because it would defeat their interest rate policies, they should (and might) make putting money under beds illegal.
It just doesn't make sense for the sizes of socks and beds and cash denominations, and the security of locks, and the wages of security guards to determine macroeconomic policy.
Now, you could put cash into a USD account at a US bank, where interest is still currently positive, but if you were storing Euros, you now have currency risk and jurisdiction risk. Negative rate German bonds have less risk than that.