Central Bank Spread - Why Cash Volume Matters to a CB?

Hi Kalin, the spread is precisely seigniorage.

Roughly speaking, the central bank puts banknotes into circulation by purchasing bonds. It keeps those bonds in its vaults. Since the central bank is not obligated to provide interest to note holders, it gets to keep the bond interest for itself, say 4%. The interest rate cost of banknotes being 0%, the spread is 4%-0% = 4%, which is pretty wide, certainly much wider than a commercial bank which is obligated to pay interest on the deposits it has put into circulation.

The more cash outstanding, the bigger the seigniorage. For instance, if a central bank has $10b in notes outstanding, it earns $0.4 b per year in interest. But if it has $100 billion in notes outstanding, it earns $4 b.