Yield-Bearing Stablecoins Can Destroy Deposits: An Illustrative Model

BPI published a recent note explaining how stablecoins, particularly yield-bearing stablecoins, do not simply move deposits around in the banking system - they drive them out of it. The misconception that stablecoins merely shift deposits around is based on analyses that trace out a chain of transactions, but fail to examine the big picture: how interest rates will adjust, how assets and liabilities will be rebalanced. To capture that bigger picture, BPI used a simple equilibrium model, presented in the following appendix. The model shows how households, banks, and stablecoin issuers simultaneously respond to one another and to shifting yields until a new equilibrium is reached. The model illustrates that stablecoin growth does not simply recycle deposits throughout the system - it reduces their total quantity. In equilibrium, deposit outflows contract bank lending and Treasury holdings, while stablecoin issuers absorb an increasing share of the fixed Treasury supply. These interconnected effects underscore why a system-based framework is necessary for evaluating the broader impact of stablecoin adoption.

The model is deliberately stylized to illustrate one of many ways a simplified financial system could reallocate as the yield on a money substitute rises relative to bank deposits. It is not calibrated to data - starting balance-sheet levels and rates and behavioral sensitivities were chosen for illustration - and it abstracts from risk, capital and liquidity regulation and monetary policy; it requires neither positive profits for its agents nor that households earn more on their assets than they pay on their loans; and its solutions are well-behaved only within a narrow range of stablecoin spreads around the baseline.

Rather than tracing individual transactions, the model shows how households, banks and stablecoin issuers simultaneously respond to one another and to shifting yields until a new equilibrium is reached. In the illustration, a higher yield on stablecoins reduces bank deposits and bank lending.

The model has three participants: a household, a bank and a stablecoin issuer. The household has wealth W and bank loans X_L as resources, and allocates those resources across deposits, stablecoins and Treasuries. The bank accepts deposits from households and holds loans and Treasuries as assets. The stablecoin issuer holds all stablecoin liabilities fully backed by Treasuries. The total supply of Treasuries is fixed at 500.

In the simple model, because only differences in returns across assets enter the model, adding a common level to all rates leaves allocations unchanged. Thus, without loss of generality, all interest rates are expressed as spreads over the deposit rate. The model solves for two endogenous spreads: the loan spread S_L and the Treasury spread S_T in response to the exogenously established stablecoin yield spread S_S. The spread of the deposit rate over the deposit rate is, of course, zero.

In what follows, each share equation below should be understood as restricted to the unit interval.

Households

Household allocation follows two stages. In the first stage, households divide total resources - wealth W plus outstanding loans X^L - between a money aggregate M and Treasuries:

Household Treasury demand is the residual after allocating to M:

The share θ_M directed toward M rises when the return on M increases relative to S_T:

The money aggregate spread is expressed as the weighted spread between stablecoin and deposits using stablecoin share θ_S defined below:

Because the spread on deposits is zero (S_D = 0), this simplifies to:

In the inner stage, households divide M between deposits and stablecoins. Stablecoins are calculated using:

Deposits absorb the remainder of M:

The stablecoin share θ_S of M increases with the stablecoin spread S_S:

where μ₁, the baseline stablecoin share of M, is set to half.

Stablecoin-deposit competition therefore operates entirely within M; the total size of M adjusts through the outer-nest term, where both S_M (rising with S_S over the simulated range) and the equilibrium Treasury spread enter, and through changes in borrowing.

Loan demand responds to the return on Treasuries, interpreted as the return on non-money investment opportunities, relative to the loan spread:

Banks

The bank's demand for deposits increases in the spread between what it earns on assets (average of S_L and S_T) and the deposit rate, which is normalized to zero:

The bank prefers an even split between loans and Treasuries but shifts the portfolio toward loans when S_L rises relative to S_T. The implicit assumption is that banks fund themselves through deposits and exhaust that funding entirely on investments in loans and Treasuries. The bank's supply for loans is thus:

And the bank's demand for Treasuries is then the residual:

Stablecoin Issuer

The stablecoin issuer holds Treasuries one-for-one against stablecoin liabilities:

Market Clearing

In equilibrium, loan supply equals loan demand:

Total Treasury holdings - by households, the bank and the stablecoin issuer - equal the fixed supply of 500. Given W = T = 500, deposit-market clearing follows residually from loan-market and Treasury-market clearing.

Experiment

At baseline, stablecoin, loan and Treasury rates are all equal to the deposit rate, and households have loan demand of 100 which, combined with their wealth of 500, gives total resources of 600 invested evenly across deposits, stablecoins and Treasuries at 200 each. The bank has 200 in deposits outstanding split evenly between loans and Treasuries at 100 each. We then vary the stablecoin rate relative to the deposit rate from -1% to +1% and solve for the equilibrium loan and Treasury spreads at each point, tracing the response of deposits, lending, Treasury holdings and stablecoin outstanding. The default parameter values used in the model are given in Table 1.

Table 1. Default Parameter Values

Results

Table 2. Simulation Results

At the baseline (S_s = 0), all spreads are zero and portfolios are balanced. As stablecoins become more attractive relative to deposits - that is, as S_s rises from a negative to positive value - households shift funds out of deposits and into stablecoins. This deposit outflow reduces bank lending and Treasury holdings, since the bank's asset portfolio shrinks with its deposit base. At the same time, the stablecoin issuer absorbs more Treasuries as reserves, crowding out household and bank Treasury holdings and pushing S_T down substantially. At positive stablecoin spreads, the loan spread falls less than the Treasury spread, leaving the loan rate above the Treasury rate. That higher loan rate relative to Treasuries leaves banks content to hold a smaller share of their portfolio as Treasuries and households to demand a smaller quantity of loans to fund investments.

It bears repeating that this model is just meant to illustrate how after the system adjusts, deposits and loans could fall; it is not meant to provide an estimate of what would actually happen. For instance, the model does not require that the profits of the stablecoin issuer or the bank be positive nor that the household earns more on its investments than it pays for its loan.

Figure 1. Balance Sheet Simulation Results

Figure 1 plots equilibrium balance sheet amounts against stablecoin outstanding. The lines illustrate how deposits, bank loans, bank Treasuries and household Treasuries all move together as stablecoin grows - each declining as households reallocate away from deposits.

Conclusion

The model illustrates that stablecoin growth does not simply recycle deposits throughout the system - it reduces their total quantity. In equilibrium, deposit outflows contract bank lending and Treasury holdings, while stablecoin issuers absorb an increasing share of the fixed Treasury supply. These interconnected effects underscore why a system-based framework is necessary for evaluating the broader impact of stablecoin adoption.